RF Blockset For Use with Simulink® Modeling Simulation Implementation User’s Guide Version 1 How to Contact The MathWorks Web Newsgroup www.mathworks.com/contact_TS.html Technical Support www.mathworks.com comp.soft-sys.matlab [email protected] [email protected] [email protected] [email protected] [email protected] Product enhancement suggestions Bug reports Documentation error reports Order status, license renewals, passcodes Sales, pricing, and general information 508-647-7000 (Phone) 508-647-7001 (Fax) The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098 For contact information about worldwide offices, see the MathWorks Web site. RF Blockset User’s Guide © COPYRIGHT 2004–2006 by The MathWorks, Inc. The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. 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Revision History June 2004 August 2004 March 2005 September 2005 March 2006 September 2006 Online Online Online Online Online Online only only only only only only New for Version 1.0 (Release 14) Revised for Version 1.0.1 (Release 14+) Revised for Version 1.1 (Release 14SP2) Revised for Version 1.2 (Release 14SP3) Revised for Version 1.3 (Release 2006a) Revised for Version 1.3.1 (Release 2006b) Contents Getting Started 1 What Is the RF Blockset? . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2 Required and Related Products . . . . . . . . . . . . . . . . . . . . . 1-3 Product Demos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-4 RF Blockset Libraries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Opening RF Blockset Libraries . . . . . . . . . . . . . . . . . . . . . . Physical Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mathematical Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6 1-6 1-7 1-9 RF Blockset Workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-10 Example — Modeling an LC Bandpass Filter . . . . . . . . . Selecting Blocks to Represent System Components . . . . . . Building the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Specifying Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . Validating Filter Components and Running the Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Analyzing the Simulation Results . . . . . . . . . . . . . . . . . . . . 1-12 1-12 1-13 1-15 1-22 1-24 Modeling an RF System 2 Modeling RF Components . . . . . . . . . . . . . . . . . . . . . . . . . . Adding RF Blocks to a Simulink Model . . . . . . . . . . . . . . . . Connecting Model Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2 2-2 2-2 Specifying or Importing Component Data . . . . . . . . . . . . 2-6 v Specifying Parameter Values . . . . . . . . . . . . . . . . . . . . . . . . Importing Data Files into RF Blocks . . . . . . . . . . . . . . . . . . Example — Importing a Touchstone Data File into an RF Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Importing Circuits from the MATLAB Workspace . . . . . . . Example — Importing a Bandstop Filter into an RF Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Modeling Thermal Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . Amplifier and Mixer Noise Specifications . . . . . . . . . . . . . . Adding Noise to Your System . . . . . . . . . . . . . . . . . . . . . . . . Plotting Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6 2-7 2-8 2-14 2-15 2-22 2-22 2-23 2-24 Plotting Model Data 3 Creating Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Validating Individual Blocks and Subsystems . . . . . . . . . . Types of Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plot Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . How to Create a Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example — Plotting Component Data on a Z Smith Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-15 Updating Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-19 ................................... 3-20 Example — Creating and Modifying Subsystem Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plotting the Network Parameters of a Subsystem . . . . . . . Adding Data to an Existing Plot . . . . . . . . . . . . . . . . . . . . . Changing Data on an Existing Plot . . . . . . . . . . . . . . . . . . . 3-22 3-22 3-24 3-26 Modifying Plots vi Contents 3-2 3-2 3-3 3-4 3-9 Blocks — By Category 4 ..................................... 4-2 Physical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ladder Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Transmission Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Black Box Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mixers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Input/Output Ports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3 4-3 4-3 4-4 4-4 4-5 4-5 Mathematical Blocks — Alphabetical List 5 RF Blockset Algorithms A Simulating an RF Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-2 Determining the Modeling Frequencies . . . . . . . . . . . . . . A-3 Mapping Network Parameters to Modeling Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-5 Modeling Noise in an RF System . . . . . . . . . . . . . . . . . . . . Calculating Noise Figure at Modeling Frequencies . . . . . . Calculating Output Noise Power . . . . . . . . . . . . . . . . . . . . . A-7 A-8 A-9 Creating a Complex Baseband-Equivalent Model . . . . . Baseband-Equivalent Modeling . . . . . . . . . . . . . . . . . . . . . . Simulation Efficiency of a Complex Baseband-Equivalent Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-10 A-10 A-13 vii Converting to and from Simulink Signals . . . . . . . . . . . . A-15 Examples B Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-2 Index viii Contents 1 Getting Started What Is the RF Blockset? (p. 1-2) Introduces the RF Blockset and describes its capabilities Required and Related Products (p. 1-3) Describes products you can use to extend the capabilities of the RF Blockset Product Demos (p. 1-4) Describes how to access the RF Blockset demos in the Help browser RF Blockset Libraries (p. 1-6) Summarizes the RF Blockset libraries RF Blockset Workflow (p. 1-10) Describes a typical workflow Example — Modeling an LC Bandpass Filter (p. 1-12) Describes how to build an RF model, modify the parameters, run the model in Simulink, and examine the results 1 Getting Started What Is the RF Blockset? The RF Blockset extends Simulink® with a library of blocks for modeling RF systems that include RF filters, transmission lines, amplifiers, and mixers. For more information about creating and running Simulink models, see “Building a Model” in the Simulink User’s Guide. You use blocks from the RF Blockset to represent the components of your RF system in a Simulink model. The blockset provides several types of component representations using network parameters (S, Y, Z, ABCD, H, and T format), mathematical descriptions, and physical properties. In the Simulink model, you cascade the components to represent your RF architecture and run the simulation. During the simulation, all blocks are modeled using a time-domain, complex-baseband representation. This way of modeling results in fast simulation and enables compatibility with other Simulink blocks. The RF Blockset lets you visualize the network parameters of the blocks using plots and Smith charts. A validated Simulink model of an RF system can provide an executable specification for RF circuit design for wireless communication systems. 1-2 Required and Related Products Required and Related Products In addition to MATLAB and Simulink, you must have the following products installed to use the RF Blockset: • RF Toolbox — Provides MATLAB functions for defining, simulating, and visualizing RF components. • Signal Processing Toolbox — Provides MATLAB functions for filtering wireless communication signals. • Signal Processing Blockset — Provides Simulink blocks for time-domain simulation of communication signals. You can build sophisticated wireless communication system models by incorporating blocks from other blocksets, such as the Signal Processing Blockset and Communications Blockset. The MathWorks provides several products that are especially relevant to the kinds of tasks you can perform with the RF Blockset. The following table summarizes the related products and describes how they complement the features of the RF Blockset. Product Description Communications Blockset Simulink blocks for time-domain simulation of modulation and demodulation of a wireless communications signal. Communications Toolbox MATLAB functions for signal modulation and demodulation. Filter Design Toolbox MATLAB functions for filtering the modulated communication signal. 1-3 1 Getting Started Product Demos You can find interactive RF Blockset demos in the MATLAB Help browser, as shown in the following figure. This example shows you how to locate and open an RF Blockset demo: 1 Type demos at the MATLAB prompt to open the Help browser to the Demos tab. 2 Select Blocksets > RF in the Demos tab to see a list of demo categories. 3 Select a model, and click Open this model in the upper-right corner of the demo window to display the Simulink model for this demo. 1-4 Product Demos 4 In the model window, select Simulation > Start to run the demo simulation. 1-5 1 Getting Started RF Blockset Libraries The RF Blockset consists of the Physical and Mathematical libraries of components for modeling RF systems within the Simulink environment. An RF model can contain blocks from both the Physical and Mathematical libraries. It can also include Simulink blocks and blocks from other MathWorks blocksets, such as those described in “Required and Related Products” on page 1-3. This section contains the following topics: • “Opening RF Blockset Libraries” on page 1-6 • “Physical Library” on page 1-7 • “Mathematical Library” on page 1-9 Opening RF Blockset Libraries To open the main library window, type the following at the MATLAB prompt: rflib The window is shown in the following figure. Each yellow icon in the window represents a library. Double-click an icon to open the corresponding library. The Physical and Mathematical libraries are discussed in the following sections. 1-6 RF Blockset Libraries Note The blue icons take you to the MATLAB Help browser. • Double-click the Demos icon to open the RF Blockset demos. • Double-click the Info icon to open the RF Blockset documentation. Physical Library Use blocks from the Physical library to model physical and electrical components by specifying physical properties or by importing measured data. The Physical library includes several sublibraries, as shown in the following figure. The following table describes the sublibraries and how they can be used. Sublibrary Description Amplifiers RF amplifiers, specified using S-, Y-, or Z-parameters, noise figure, and IP3, or a data file containing these parameters. 1-7 1 Getting Started Sublibrary Description Ladder Filters RF filters, specified using RLC parameters. The network parameters of the blocks are calculated from the topology of the filter and the RLC values. Mixers RF mixers that contain local oscillators, specified using S-, Y-, or Z-parameters and phase noise, or a data file containing these parameters. Transmission Lines RF filters, specified using physical dimensions and electrical characteristics. Black Box Passive RF components, specified using S-, Y-, or Z-parameters, or a data file containing these parameters. Input/Output Ports Blocks for specifying simulation information that pertains to all blocks in a physical subsystem, such as center frequency and sample time. Note A physical subsystem is a collection of one or more physical blocks bracketed by an Input Port block and an Output Port block that bridge the physical and mathematical parts of the model. For more information on defining components, see “Specifying or Importing Component Data” on page 2-6. 1-8 RF Blockset Libraries Mathematical Library The Mathematical library contains mathematical representations of the amplifier, mixer, and filter blocks. Use a block from the Mathematical library to model an RF component in terms of mathematical equations that describe how the block operates on an input signal. Note Mathematical blocks assume perfect impedance matching and a nominal impedance of 1 ohm. In contrast, the physical blocks do not assume perfect matching—these blocks model the reflections that occur between blocks, and you can specify the source and load impedances using the Input Port and Output Port blocks. The mathematical library is shown in the following figure. 1-9 1 Getting Started RF Blockset Workflow When you analyze an RF system using the RF Blockset, your workflow might include the following tasks: 1 Create a Simulink model of RF components. For more information , see “Modeling RF Components” on page 2-2. 2 Define component data by • Specifying network parameters, mathematical relationships, or physical properties • Importing data from an industry-standard Touchstone file, a MathWorks AMP file, or the MATLAB workspace The RF Blockset lets you access component data in Touchstone SnP, YnP, ZnP, and HnP formats. You can also import amplifier network parameters and power data from a MathWorks AMP file. For more information, see “Specifying or Importing Component Data” on page 2-6. 3 Add thermal noise to the system. For more information, see “Modeling Thermal Noise” on page 2-22. 4 Validate the behavior of individual blocks by plotting component data. Note You can plot data for individual blocks from the RF Physical library that model physical components either before or after you run a simulation. For more information, see “Creating Plots” on page 3-2. 5 Run the simulation. For more information on how the RF Blockset performs time-domain simulation of an RF system, see “Simulating an RF Model” on page A-2. 6 Generate plots to gain insight into system behavior. 1-10 RF Blockset Workflow For more information, see “Creating Plots” on page 3-2. The following plots and charts are available in the RF Blockset: • Rectangular plots • Polar plots • Smith charts • Composite plots • Budget plots 1-11 1 Getting Started Example — Modeling an LC Bandpass Filter In this example, you model the signal attenuation caused by an RF filter by comparing the signals at the input and output of the filter. The RF filter you use in this example is an LC bandpass filter with a bandwidth of 200 MHz, centered at 700 MHz. You use a three-tone input signal to stimulate a range of in-band and out-of-band frequencies of the filter. The input signal has the following tones: • 700 MHz — Center of the filter • 600 MHz — Lower edge of the filter passband • 900 MHz — Outside the filter passband You simulate the effects of the filter over a bandwidth of 500 MHz. This example illustrates how to perform the following tasks: • “Selecting Blocks to Represent System Components” on page 1-12 • “Building the Model” on page 1-13 • “Specifying Model Parameters” on page 1-15 • “Validating Filter Components and Running the Simulation” on page 1-22 • “Analyzing the Simulation Results” on page 1-24 Selecting Blocks to Represent System Components In this part of the example, you select the blocks to represent the input signal, the RF filter, and the signal displays. You model the RF filter using a physical subsystem, which is a collection of one or more physical blocks bracketed by an Input Port block and an Output Port block. The RF filter subsystem consists of an LC Bandpass Pi block, and the Input Port and Output Port blocks. The function of the Input Port and Output Port blocks is to bridge the physical and mathematical parts of the model. The following table lists the blocks that represent the RF system components and a description of the role of each block. 1-12 Example — Modeling an LC Bandpass Filter Block Description Sine Wave Generates a three-channel signal. Matrix Sum Combines the three channel signal into a single three-tone source signal. Input Port Establishes parameters that are common to all blocks in the RF filter subsystem, including the source impedance of the subsystem that is used to convert Simulink signals to the RF Blockset physical modeling environment. LC Bandpass Pi Models the signal attenuation caused by the RF filter which, in this example, is the LC Bandpass Pi filter. Output Port Establishes parameters that are common to all blocks in the RF filter subsystem. These parameters include the load impedance of the subsystem, which is used to convert RF signals to Simulink signals. Spectrum Scope Displays signals at the input to and output of the filter. Building the Model In this part of the example, you create a Simulink model, add blocks to the model, and connect the blocks. 1 Create a Simulink model. If you are new to Simulink, see the introductory Simulink example, “Building a Model”, for information on how to create a Simulink model. 2 Add to the model the blocks shown in the following table. The Library column of the table specifies the hierarchical path to each block. 1-13 1 1-14 Getting Started Block Library Path Quantity Sine Wave Signal Processing Blockset > Signal Processing Sources 1 Matrix Sum Signal Processing Blockset > Math Functions > Matrices and Linear Algebra > Matrix Operations 1 Spectrum Scope Signal Processing Blockset > Signal Processing Sinks 2 Input Port RF Blockset > Physical > Input/Output Ports 1 LC Bandpass Pi RF Blockset > Physical > Ladder Filters 1 Output Port RF Blockset > Physical > Input/Output Ports 1 Example — Modeling an LC Bandpass Filter 3 Connect the blocks as shown in the following figure. For more information on connecting physical and mathematical blocks, see “Connecting Model Blocks” on page 2-2. Now you are ready to specify block parameters. Specifying Model Parameters In this part of the example, you specify the following parameters to represent the behavior of the system components: • “Input Signal Parameters” on page 1-15 • “Filter Subsystem Parameters” on page 1-18 • “Signal Display Parameters” on page 1-21 Input Signal Parameters You generate the three-tone source signal using two blocks. You use the Sine Wave block to build a complex three-channel signal, where each channel 1-15 1 Getting Started corresponds to a different frequency. Then, you use the Matrix Sum block to combine the channels into a single three-tone source signal. The algorithm used by the RF Blockset requires you to shift the frequencies of the input signal. The RF Blockset simulates the filter subsystem using a complex-baseband modeling technique, which shifts the filter response so it is centered at zero. You must shift the frequencies of the signals outside the physical subsystem by the same amount. For more information on complex-baseband modeling, see “Creating a Complex Baseband-Equivalent Model” on page A-10. Note The RF Blockset requires that all signals in the RF model be complex to match the signals in the physical subsystem, so you create a complex input signal. The center frequency of the LC bandpass filter is 700 MHz, so you use a three-tone source signal with tones that are 700 MHz below the actual tones, at -100 MHz, 0 MHz, and 200 MHz, respectively. 1 Set the Sine Wave block parameters as follows: • Amplitude = 1e-6 • Frequency (Hz) = [-100 0 200]*1e6 • Output complexity = Complex • Sample time = 1/500e6 1-16 Example — Modeling an LC Bandpass Filter • Samples per frame = 128 1-17 1 Getting Started 2 Set the Matrix Sum block Sum along parameter to Rows. Filter Subsystem Parameters In this part of the example, you configure the blocks that model the RF filter subsystem—the Input Port, LC Bandpass Pi, and Output Port blocks. 1 Set the Input Port block parameters as follows: • Center frequency = 700e6 • Sample time(s) = 1/500e6 1-18 Example — Modeling an LC Bandpass Filter • Clear the Add noise check box so the RF Blockset will not include thermal noise in the simulation. To learn how to model thermal noise, see “Modeling Thermal Noise” on page 2-22. Note You must enter the Sample time (s) because the Input Port block does not inherit a sample time from the input signal. The specified sample time must match the sample time of the input signal. The Sample time (s) of 1/500e6 second used in this example is equivalent to a bandwidth of 500 MHz. 1-19 1 Getting Started 2 Accept default parameters for inductance and capacitance in the LC Bandpass Pi block. These parameters create a filter with the desired bandwidth of 200 MHz, centered at 700 MHz. 1-20 Example — Modeling an LC Bandpass Filter 3 Accept the default parameters for the Output Port block to use a load impedance of 50 ohms. Signal Display Parameters In this part of the example, you specify the parameters of the Spectrum Scope block to display the source signal, and the parameters of the Spectrum Scope1 block to display the filtered signal. For each scope, you set the range of the X- and Y-axes to make sure that the entire signal is visible. By default, the scope displays appear stacked on top of each other on the screen when you run the simulation, so you can only see one of them. To ensure that both scopes are visible during the simulation, you specify a different position for each scope on the screen. 1 Set the Spectrum Scope block parameters as follows: • Axis Properties pane, Frequency range = [-Fs/2...Fs/2] • Axis Properties pane, Minimum Y-limit = -160 • Axis Properties pane, Maximum Y-limit = -100 • Display Properties pane, Scope position = get(0,'defaultfigureposition').*[.15 1 1 1] 1-21 1 Getting Started 2 Set the Spectrum Scope1 block parameters as follows: • Axis Properties pane, Frequency range = [-Fs/2...Fs/2] • Axis Properties pane, Minimum Y-limit = -160 • Axis Properties pane, Maximum Y-limit = -105 • Display Properties pane, Scope position = get(0,'defaultfigureposition').*[1.85 1 1 1] Note If you do not specify the Display Properties of the scopes, you can click and drag the displays to arrange them on the screen after the simulation starts. Validating Filter Components and Running the Simulation In this part of the example, you validate the behavior of the LC Bandpass Pi filter block by plotting its network parameters and then run the simulation. Note When you plot information about a physical block, the plot displays the actual frequency response of the block at the selected passband (i.e. the response at the unshifted frequencies), and not the response at the shifted frequencies. Recall that this shift was introduced in “Input Signal Parameters” on page 1-15. 1 Double-click the LC Bandpass Pi block to open the block dialog box. 1-22 Example — Modeling an LC Bandpass Filter 2 Select the Plot the selected parameters of this block check box. Click Apply to plot the frequency response of the filter. This plots the magnitude of S21 as a function of frequency, which represents the gain of the filter. Filter Gain Note The physical blocks only model a band of frequencies around the center frequency of the physical subsystem. You must choose the sample time and center frequency such that all important frequency characteristics of your physical subsystem fall in this band of frequencies. The plot shows the frequency response of the filter for the portion of the RF spectrum that the physical blocks model. In this example, the physical blocks model a 500 MHz band that is centered at 700 MHz, defined by the Input Port block. 1-23 1 Getting Started 3 In the Simulink model window, select Simulation > Start to run the simulation. Analyzing the Simulation Results In this part of the example, you analyze the results of the simulation. This section contains the following topics: • “Comparing the Input and Output Signals of the RF Filter” on page 1-24 • “Plotting Model Parameters of the Filter Subsystem” on page 1-27 Comparing the Input and Output Signals of the RF Filter You can view the source signal and the filtered signal in the Spectrum Scope windows while the model is running. These windows appear automatically when you start the simulation. 1-24 Example — Modeling an LC Bandpass Filter The following plot shows the RF filter input signal you specified in the Sine Wave block. Display block name -101 dB Input to RF Filter 1-25 1 Getting Started The next plot shows the filtered signal. Notice that the amplitude of the peaks is attenuated as a result of the RF filter. -107 dB Attenuated Output of RF Filter Together, the Input Port and Output Port blocks introduce a 6-dB attenuation into the physical system at all frequencies. You can see this loss in the plots by comparing the input and output signals at the center frequency of the filter. The magnitude of the input signal at the center frequency approaches -101 dB in the Spectrum Scope window. The magnitude of the output signal at the center frequency approaches -107 dB in the Spectrum Scope1 window. However, as shown in the plot in the previous section, Filter Gain on page 1-23, the filter does not attenuate the signal at the center frequency. The 6 dB of loss is caused by the source and the load in the model. For more 1-26 Example — Modeling an LC Bandpass Filter information on why this loss occurs, see the note in “Converting to and from Simulink Signals” on page A-15. Plotting Model Parameters of the Filter Subsystem After you simulate an RF model, you can evaluate the behavior of the physical subsystem by plotting the network parameters of the Output Port block. Note When you plot information about a physical subsystem, the plot displays the actual frequency response of the subsystem at the selected passband (i.e. the response at the unshifted frequencies), and not the response at the shifted frequencies. To understand the frequency response of the filter, examine the S-parameters as a function of frequency for the RF filter subsystem on a composite plot. 1 Open the dialog box of the Output Port block by double-clicking the block. 2 Select the Plot the model parameters of this block check box, and click Apply. The composite plot, shown in the following figure, contains four separate plots in one figure. For the Output Port block, the composite plot shows the following as a function of frequency (counterclockwise from the upper-left plot): • An X-Y plane plot of the magnitude of the filter gain, S21, in decibels. • An X-Y plane plot of the phase of the filter gain, S21, in degrees. • A Z Smith chart showing the real and imaginary parts of the filter reflection coefficient, S11. • A Polar plane plot showing the magnitude and phase of the filter reflection coefficient, S11. 1-27 1 1-28 Getting Started X-Y Plot, Magnitude of S21 Polar Plot, S11 X-Y Plot, Phase of S21 Z Smith Chart, S11 2 Modeling an RF System Modeling RF Components (p. 2-2) Describes how to add and connect blocks in a Simulink model to represent RF components Specifying or Importing Component Data (p. 2-6) Describes how to define block behavior by entering parameter values and importing file and workspace data Modeling Thermal Noise (p. 2-22) Explains how to model thermal noise in a physical system 2 Modeling an RF System Modeling RF Components The RF Blockset lets you model an RF system using Simulink. This section describes how to build a system model that incorporates RF components and contains the following topics: • “Adding RF Blocks to a Simulink Model” on page 2-2 • “Connecting Model Blocks” on page 2-2 Adding RF Blocks to a Simulink Model You can include blocks from the RF Blockset Physical and Mathematical libraries in a Simulink model. For more information on the libraries and the available RF blocks, see “RF Blockset Libraries” on page 1-6. To add RF blocks to a Simulink model: 1 Type rflib at the MATLAB prompt to open the RF Blockset library. 2 Navigate to the desired library or sublibrary. 3 Drag instances of RF Blockset blocks into the model window using the mouse. Note You can also access RF Blockset blocks and other Simulink blocks from the Simulink Library Browser window. Open this window by typing simulink at the MATLAB prompt. Add blocks to the model by dragging them from this window and dropping them into the model window. Connecting Model Blocks You follow the same procedure for connecting RF Blockset blocks as for connecting Simulink blocks: you click a port and drag the mouse to draw a line to another port on a different block. For more information on connecting Simulink blocks, see “Connecting the Blocks” in the Simulink documentation. You can only connect blocks that use the same type of signal. RF Blockset Physical blocks use different types of signals than Mathematical blocks, and 2-2 Modeling RF Components are represented graphically by a different port style. Therefore, you can freely connect pairs of Mathematical modeling blocks. You can also freely connect pairs of Physical modeling blocks. However, you cannot directly connect Physical blocks to Mathematical blocks. Instead, you must use the Input Port and Output Port blocks to bridge them. For more information on the RF Blockset libraries, including how to open the libraries and a description of the available blocks, see “RF Blockset Libraries” on page 1-6. This section contains the following topics: • “Connecting Mathematical Blocks” on page 2-3 • “Connecting Physical Blocks” on page 2-4 • “Bridging Physical and Mathematical Blocks” on page 2-4 Connecting Mathematical Blocks The RF Blockset Mathematical blocks use the same input and output ports as standard Simulink blocks. These ports show the direction of the signal at the port, as shown in the following diagram. RF Blockset mathematical modeling ports show signal direction Similar to standard Simulink blocks, you draw lines between the ports of the Mathematical modeling blocks, called signal lines, to represent signals that are inputs to and outputs from the mathematical functions represented by the blocks. Therefore, you can connect Simulink, Signal Processing, and RF Blockset mathematical blocks by drawing signal lines between their ports. You can connect a port to multiple ports by branching the signal line, or you can leave a port unconnected. For more information on connecting Simulink blocks, see “Connecting the Blocks” in the Simulink documentation. 2-3 2 Modeling an RF System Connecting Physical Blocks The RF Blockset Physical blocks have specialized connector ports. These ports only represent physical connections; they do not imply signal direction. RF Blockset physical modeling connector ports represent only physical connections. The lines you draw between the RF Blockset physical modeling blocks, called connection lines, represent physical connections among the block components. Connection lines appear as solid black when connected and as dashed red lines when either end is unconnected. You can draw connection lines only between the connector ports of physical modeling blocks. You cannot branch these connection lines. You cannot leave connector ports unconnected. Bridging Physical and Mathematical Blocks The RF Blockset provides the Input Port and Output Port blocks to connect the physical and mathematical parts of the model. These blocks convert mathematical signals to and from the physical modeling environment. The Input Port and Output Port blocks have one of each kind of connector port: a standard Simulink style input port and a physical modeling port. These ports are shown in the following figure: Mathematical, or Simulink style, ports Physical Modeling Ports The Input Port and Output Port blocks must bound a physical subsystem to connect it to the mathematical part of a model. 2-4 Modeling RF Components For example, a simple RF model of a coaxial transmission line might resemble the following figure. The Microstrip Transmission Line block uses an Input Port block to get its white noise input from a Random Source block, and an Output Port block to pass its output to a Spectrum Scope block. The Random Source and Spectrum Scope blocks are from Signal Processing Blockset library. For information on how the RF Blockset converts mathematical signals to and from the physical modeling environment, see “Converting to and from Simulink Signals” on page A-15. 2-5 2 Modeling an RF System Specifying or Importing Component Data You can specify RF Blockset blocks by entering the RF component parameter values. The RF Blockset also lets you import • Industry-standard file formats — Touchstone S2P, Y2P, Z2P, and H2P formats specify the network parameters and noise information for measured and simulated data. For more information on Touchstone files, see http://www.vhdl.org/pub/ibis/connector/touchstone_spec11.pdf. • MathWorks amplifier (AMP) file format — Specifies amplifier network parameters, power data, noise data, and third-order intercept point For more information about .amp files, see “AMP File Format” in the RF Toolbox documentation. • MATLAB circuits — RF Toolbox circuit objects in the MATLAB workspace specify network parameters, noise data, and third-order intercept point information of circuits with different topologies. For more information about RF circuit objects, see the RF Toolbox rfckt reference page. This section contains the following topics: • “Specifying Parameter Values” on page 2-6 • “Importing Data Files into RF Blocks” on page 2-7 • “Example — Importing a Touchstone Data File into an RF Model” on page 2-8 • “Importing Circuits from the MATLAB Workspace” on page 2-14 • “Example — Importing a Bandstop Filter into an RF Model” on page 2-15 Specifying Parameter Values There are two ways to set block parameter values: • Using the GUI — Enter information in the block dialog boxes, which open when you double-click a block in the Simulink window. 2-6 Specifying or Importing Component Data • Using commands — Use the Simulink set_param and get_param commands to set and get parameter values of the blocks, respectively. For more information on these commands, see the set_param and get_param reference pages. Importing Data Files into RF Blocks The RF Blockset lets you import industry-standard data files and MathWorks AMP files into specific blocks to simulate the behavior of measured components in Simulink. This section contains the following topics: • “Blocks Used to Import Data” on page 2-7 • “How to Import Data Files” on page 2-7 Blocks Used to Import Data Three blocks in the Physical library accept data from a file. The following table lists the blocks and any corresponding data format that each supports. Block Description Supported Format(s) General Amplifier Generic amplifier Touchstone, AMP General Mixer Generic mixer Touchstone, AMP General Passive Network Generic passive component Touchstone How to Import Data Files To import a data file: 1 Choose the block that best represents your component from the list of blocks that accept file data shown in“Blocks Used to Import Data” on page 2-7. 2 Open the RF Blockset Physical library, and navigate to the sublibrary that contains the block. 3 Click and drag the block into your Simulink model. 2-7 2 Modeling an RF System 4 In the block dialog box, enter a value of read(rfdata.data, 'filename') for the RFCKT object parameter, where filename is the name of your data file. This value specifies that the RF Toolbox read function reads data from filename into an RF Toolbox data object. The RF Blockset uses this data object to simulate the data. For more information on RF Toolbox data objects, see the rfdata reference page. RFDATA object parameter value This procedure is illustrated by example in the following section. Example — Importing a Touchstone Data File into an RF Model In this example, you simulate the frequency response of a passive component using data from a Touchstone file, passive.s2p. 2-8 Specifying or Importing Component Data You use a model from one of the RF Blockset demos to perform the following tasks: • “Importing Data into a General Passive Network Block” on page 2-9 • “Validating the Passive Component” on page 2-11 • “Running the Simulation and Analyzing the Results” on page 2-13 Importing Data into a General Passive Network Block In this part of the example, you inspect the passive.s2p file and import data into the RF model using the General Passive Network block. 1 Type the following at the MATLAB prompt to open the passive.s2p file: edit passive.s2p The following figure shows a portion of the .s2p file. 2-9 2 Modeling an RF System The option line # Hz S DB R 50 specifies the following information about the contents of the data file: • Hz — Frequency units. • S — Network parameters are S-parameters. • DB — Network parameters are specified as magnitude in dB and phase in degrees. • R 50 — Reference impedance is 50 ohms. For more information about the Touchstone specification, including the option line, see http://www.vhdl.org/pub/ibis/connector/touchstone_spec11.pdf. 2 At the MATLAB prompt, type sparam_filter This opens the RF Blockset demo called “Touchstone Data File for 2-Port Passive Networks.” 2-10 Specifying or Importing Component Data 3 Double-click the General Passive Network block to display its parameters. The RFDATA object parameter specifies the data file to import. The RFDATA object parameter is set to read(rfdata.data, 'passive.s2p'). This setting reads the data from the file passive.s2p into an rfdata.data object. The block uses this data with the other block parameters during simulation. Note When the imported file contains data that is measured at frequencies other than the modeling frequencies, use the Interpolation method parameter to specify how the block determines the data values at the modeling frequencies. For more information, see“Determining the Modeling Frequencies” on page A-3 and “Mapping Network Parameters to Modeling Frequencies” on page A-5. Validating the Passive Component In this part of the example, you plot the network parameters of the General Passive Network block to validate the data you imported in “Importing Data into a General Passive Network Block” on page 2-9. 1 Open the General Passive Network block dialog box, and perform the following actions: a Select the Plot the selected parameters of this block check box. b Set the Parameter parameter to S11. c Click Apply. 2-11 2 Modeling an RF System These dialog box selections create a plot of S11 as a function of frequency. S11 versus Frequency for the Imported Data 2 Open the General Passive Network block dialog box, set the Parameter parameter to S21, and click Apply. 2-12 Specifying or Importing Component Data The block adds the S21 data to the plot. S11 and S21 versus Frequency for the Imported Data Running the Simulation and Analyzing the Results In this part of the example, you run the simulation and examine the frequency response of the passive component. Start the simulation by selecting Simulation > Start in the Simulink model window. This action opens the Vector scope plot, which displays the amplitude of the transfer function of the system in decibels as a function of frequency, as shown in the following figure: 2-13 2 Modeling an RF System Transfer Function of General Passive Network Subsystem Note The transfer function differs from S21. The differences arise from the following factors: • The 6 dB of loss introduced by the source and the load in the sparam_filter model. This loss is described in the note in “Converting to and from Simulink Signals” on page A-15. • The numerical error introduced by the calculation of the transfer function. Importing Circuits from the MATLAB Workspace You can only connect the RF Blockset Physical blocks in cascade. However, the RF Blockset works with the RF Toolbox to let you include additional circuit topologies in an RF model. To model circuit topologies that contain other types of connections, you must define a circuit in the MATLAB workspace and import it into an RF model. To import a circuit from the MATLAB workspace: 2-14 Specifying or Importing Component Data 1 Define the circuit object in the MATLAB workspace using the RF Toolbox functions. For more information about RF circuit objects, see the RF Toolbox rfckt reference page. 2 Add a General Circuit Element block to your RF model from the Black Box Elements sublibrary of the Physical library. For information on how to open this library, see “Opening RF Blockset Libraries” on page 1-6. 3 Enter the circuit object name in the RFCKT object parameter in the General Circuit Element block dialog box. This procedure is illustrated by example in the following section. Example — Importing a Bandstop Filter into an RF Model In this example, you simulate the frequency response of a filter that you model using circuit objects from the MATLAB workspace. The filter in this example is the 50-ohm bandstop filter shown in the following figure. Bandstop Filter Diagram 2-15 2 Modeling an RF System You represent the filter using four circuit objects that correspond to the four parts of the filter, ckt1, ckt2, ckt3, and ckt4 in the diagram. You use an input signal with random, complex input values that have a Gaussian distribution to stimulate the filter. The scope block displays the output signal. This example illustrates how to perform the following tasks: • “Creating Circuit Objects in the MATLAB Workspace” on page 2-16 • “Building the Model” on page 2-17 • “Specifying and Importing Component Data” on page 2-18 • “Running the Simulation and Plotting the Results” on page 2-20 Creating Circuit Objects in the MATLAB Workspace In this part of the example, you define MATLAB variables to represent the physical properties of the filter shown in the previous figure, Bandstop Filter Diagram on page 2-15, and use RF Toolbox functions to create RF circuit objects that model the filter components. 1 Type the following at the MATLAB prompt to define the filter’s resistance, capacitance, and inductance values in the MATLAB workspace: C1 C2 C3 C4 C5 C6 L1 L2 L3 L4 L5 L6 2-16 = = = = = = = = = = = = 1.734e-12; 4.394e-12; 7.079e-12; 7.532e-12; 1.734e-12; 4.394e-12; 25.70e-9; 3.760e-9; 17.97e-9; 3.775e-9; 17.63e-9; 25.70e-9; Specifying or Importing Component Data 2 Type the following at the MATLAB prompt to create RF circuit objects that model the components labeled ckt1, ckt2, ckt3, and ckt4 in the circuit diagram: ckt1 = rfckt.series('Ckts',{rfckt.shuntrlc('C',C1),rfckt.shuntrlc('L' ,L1,'C',C2)}); ckt2 = rfckt.parallel('Ckts',{rfckt.seriesrlc('L',L2),rfckt.seriesrlc ('L',L3,'C',C3)}); ckt3 = rfckt.parallel('Ckts',{rfckt.seriesrlc('L',L4),rfckt.seriesrlc ('L',L5,'C',C4)}); ckt4 = rfckt.series('Ckts',{rfckt.shuntrlc('C',C5),rfckt.shuntrlc('L' ,L6,'C',C6)}); For more information about the RF Toolbox functions used in this example, see the rfckt.series, rfckt.parallel, rfckt.shuntrlc, and rfckt.seriesrlc function reference pages in the RF Toolbox documentation. Building the Model In this portion of the example, you create a Simulink model. For more information about adding and connecting components, see “Modeling RF Components” on page 2-2. 1 Create a new Simulink model. 2 Add to the model the blocks shown in the following table. The Library column of the table specifies the hierarchical path to each block. Block Library Quantity Random Source Signal Processing Blockset > Signal Processing Sources 1 2-17 2 Modeling an RF System Block Library Quantity Input Port RF Blockset > Physical > Input/Output Ports 1 General Circuit Element RF Blockset > Physical > Black Box Elements 4 Output Port RF Blockset > Physical > Input/Output Ports 1 Spectrum Scope Signal Processing Blockset > Signal Processing Sinks 1 3 Connect the blocks as shown in the following figure. Change the names of your General Circuit Element blocks to match those in the figure by double-clicking the text below the block and typing a new name. Specifying and Importing Component Data In this portion of the example, you specify block parameters. To open the parameter dialog box for each block, double-click the block. 2-18 Specifying or Importing Component Data 1 Set the Random Source block parameters as follows: • Source type = Gaussian • Sample time = 1/(100e6) • Samples per frame = 256 • Complexity = Complex Selecting these settings creates an input signal with random, complex input values that have a Gaussian distribution. 2 Set the Input Port block parameters as follows: • Finite impulse response filter length = 256 • Center frequency (Hz) = 400e6 • Sample time = 1/(100e6) • Source impedance = 50 • Clear the Add noise check box. Selecting these settings defines the physical characteristics and modeling bandwidth of the filter. 3 Set the parameters of the General Circuit Element blocks as follows: • In the General Circuit Element1 block dialog box, set the RFCKT object parameter to ckt1. • In the General Circuit Element2 block dialog box, set the RFCKT object parameter to ckt2. • In the General Circuit Element3 block dialog box, set the RFCKT object parameter to ckt3. • In the General Circuit Element4 block dialog box, set the RFCKT object parameter to ckt4. Selecting these settings imports the circuit objects that model the filter components into the Simulink model. 4 Type 50 in the Load impedance field of the Output Port block to represent an impedance of 50 ohms. 2-19 2 Modeling an RF System 5 Set the Spectrum Scope block parameters as follows: • On the Scope Properties pane, set the Number of spectral averages parameter to 100. This parameter establishes the number of spectra that the scope averages to produce the displayed signal. You use a value of 100 because the input signal is random and you want to display the average filter response over a large number of input values. • On the Axis Properties pane, set the Frequency range parameter to [-Fs/2 ... Fs/2], the Minimum Y-limit parameter to -35, and the Maximum Y-limit parameter to 3.6. These values set the range of X- and Y-values on the display such that the entire signal is visible when you run the simulation. Running the Simulation and Plotting the Results In this part of the example, you run the simulation and examine the frequency response of the filter. Select Simulation > Start in the Simulink model window to start the simulation. 2-20 Specifying or Importing Component Data The Spectrum Scope window appears automatically and displays the following plot, which shows the frequency response of the filter. Frequency Response of Bandstop Filter References Geffe, P.R., “Novel designs for elliptic bandstop filters,” RF Design, February 1999. 2-21 2 Modeling an RF System Modeling Thermal Noise The RF Blockset lets you include the thermal noise generated by any physical block in your RF model. You only need to specify noise information for the physical amplifier and mixer blocks that generate noise other than resistor noise. For the other blocks, the RF Blockset calculates the noise automatically based on the resistor values. This section contains the following topics: • “Amplifier and Mixer Noise Specifications” on page 2-22 • “Adding Noise to Your System” on page 2-23 • “Plotting Noise” on page 2-24 Amplifier and Mixer Noise Specifications You specify noise for the physical amplifier and mixer blocks as spot noise data or as noise figure values. The following table summarizes the noise specification options for each type of physical amplifier and mixer block. 2-22 Block Noise Specification General Amplifier Spot noise data (using a Touchstone or AMP data file) or noise figure values S-Parameters Amplifier Noise figure values Y-Parameters Amplifier Noise figure values Z-Parameters Amplifier Noise figure values General Mixer Spot noise data (using a Touchstone or AMP data file) or noise figure values S-Parameters Mixer Noise figure values Y-Parameters Mixer Noise figure values Z-Parameters Mixer Noise figure values Modeling Thermal Noise Adding Noise to Your System To simulate the thermal noise of a physical subsystem, you perform the following tasks: • “Specifying or Importing Noise Data” on page 2-23 • “Adding Noise to the Simulation” on page 2-24 Specifying or Importing Noise Data The method you use to add noise data to a block depends on whether you are specifying noise figure or importing spot-noise data. The following table provides instructions for adding noise data. Noise Specification Instructions Noise figure Enter the noise figure value in the Noise figure (dB) parameter in the block dialog box. Spot noise data Import file data that includes noise information into the RFCKT object parameter of the General Amplifier or General Mixer block. Note If you import file data with no noise information into a General Amplifier or General Mixer block, the RF Blockset adds the Noise figure (dB) parameter to the block dialog box . This parameter lets you specify noise manually. 2-23 2 Modeling an RF System Adding Noise to the Simulation To include noise in the simulation, you must select the Add noise check box on the Input Port block dialog box. This check box is selected by default. Select this check box to take the noise data in the physical blocks into account. This check box is selected by default. For information on how the RF Blockset simulates thermal noise, see “Modeling Noise in an RF System” on page A-7. Plotting Noise The RF Blockset models communications systems. The noise in these systems has a very small amplitude, typically from 1e-6 to 1e-12 Watts. In contrast, the default signal power of a Communications Blockset modulator block is 1 Watt at a nominal 1 ohm. Therefore, the signal-to-noise ratio in an RF system 2-24 Modeling Thermal Noise simulation is large, making it difficult to view the noise the RF Blockset adds to your signal. To display the noise on a plot, you might need to attenuate the signal amplitude to a value within a couple orders of magnitude of the noise. For example, suppose you have the following model that contains a multitone test signal source. 2-25 2 Modeling an RF System When you simulate this model, Simulink brings up several windows showing the input and output for the physical subsystem. The Input - Frequency Domain window shown in the following figure displays the input signal in the frequency domain. Input Signal Spectrum 2-26 Modeling Thermal Noise The Real Part of Input - Time Domain window displays the real part of the complex-valued input signal in the time domain. Real Part of Input Signal 2-27 2 Modeling an RF System In the model, the physical subsystem adds noise to the input signal. The Output - Frequency Domain window shows the noisy output signal in the frequency domain. Output Signal Spectrum 2-28 Modeling Thermal Noise The amplitude of the signal is large compared to the amplitude of the noise, so the noise is not visible in the Real Part of Output - Time Domain window that shows the real part of the time-domain output signal. Therefore, you must attenuate the amplitude of the input signal to display the noise of the time-domain output signal. Real Part of Output Signal 2-29 2 Modeling an RF System Attenuate the amplitude of the input signal by setting the Gain parameter to 1e-3. This is equivalent to attenuating the input signal by 60 dB. When you run the model again, the two signal peaks are not as pronounced in the Output - Frequency Domain window. Output Signal Spectrum for Attenuated Input 2-30 Modeling Thermal Noise You can now view the noise the RF Blockset adds to your signal in the Real Part of Output - Time Domain window. Real Part of Output Signal Showing Noise 2-31 2 2-32 Modeling an RF System 3 Plotting Model Data Creating Plots (p. 3-2) Describes the available plots and explains how to plot data for components and subsystems Updating Plots (p. 3-19) Describes how to update existing plots after changing model parameters Modifying Plots (p. 3-20) Describes how to add data to a plot and how to change the plot type, format, and frequency range Example — Creating and Modifying Subsystem Plots (p. 3-22) Shows how to plot RF subsystem data, add data to the plot, and change the plot type 3 Plotting Model Data Creating Plots The RF Blockset lets you validate the behavior of individual RF components and physical subsystems in your model by plotting the following data: • S-parameters • Noise figure • Output third-order intercept point • Power data • Phase noise • Voltage standing-wave ratio The following topics describe the RF Blockset plotting options, explain the procedure for creating a plot, and illustrate this procedure with an example: • “Validating Individual Blocks and Subsystems” on page 3-2 • “Types of Plots” on page 3-3 • “Plot Formats” on page 3-4 • “How to Create a Plot” on page 3-9 • “Example — Plotting Component Data on a Z Smith Chart” on page 3-15 Validating Individual Blocks and Subsystems You can plot model data for an individual physical block or for a physical subsystem. A subsystem is a collection of one or more physical blocks bracketed by an Input Port block and an Output Port block. To gain insight into the behavior of specific subsystems, plot the data of the corresponding Output Port block after you run a simulation. To validate the behavior of individual RF components in the model, plot the data of the corresponding physical blocks. You can plot data for individual blocks from each of these components either before or after you run a simulation. You create a plot by selecting options in the block dialog box, as shown in “Example — Creating and Modifying Subsystem Plots” on page 3-22. To 3-2 Creating Plots learn about the available plots, see “Types of Plots” on page 3-3. For more information about creating plots, see “How to Create a Plot” on page 3-9. Types of Plots The RF Blockset provides a variety of plots for analyzing the behavior of RF components and subsystems. The following table summarizes the available plots and charts and describes each one. Plot Type Plot Contents X-Y Plane (Rectangular) Plot Parameters as a function of frequency, such as • S-parameters • Noise figure (NF) • Voltage standing-wave ratio (VSWR) • Output third-order intercept point (OIP3) Link Budget Plot (3-D) Parameters as a function of frequency for each component in a physical subsystem, where the curve for a given component represents the cumulative contribution of each RF component up to and including the parameter value of that component. For more information, see “Link Budget” on page 3-7. Polar Plane Plot Magnitude and phase of S-parameters as a function of frequency. Smith Chart Real and imaginary parts of S-parameters as a function of frequency, used for analyzing the reflections caused by impedance mismatch. Composite Plot Multiple plots and charts in one figure. To learn how to create these plots, see “How to Create a Plot” on page 3-9. 3-3 3 Plotting Model Data Plot Formats When you create a plot from a block dialog box, you must specify the plot Format. Plot format This plot option defines how the RF Blockset displays the data on the plot. The available formats vary with the data you select to plot. The data you can plot depends on the plot type you select. The plot format determines whether the RF Blockset converts the data to a new set of units, or performs a calculation on the data. For example, setting the format to Real tells the RF Blockset to compute and plot the real part of the selected parameter. The following topics describe the available parameters and formats for each plot type: • “Composite Data” on page 3-5 • “X-Y Plane” on page 3-7 • “Link Budget” on page 3-7 • “Polar Plane Plots and Smith Charts” on page 3-9 3-4 Creating Plots Composite Data The composite data plot automatically generates four separate plots in one figure window, showing the frequency dependence of several parameters. The following figure shows an example of such a plot. Example — Composite Data Plot Note For composite data plots, you do not need to specify the parameters or the plot format—both are set automatically. 3-5 3 Plotting Model Data The combination of plots differs based on the type of block and the specified block data. The following table describes the contents of the composite data plot for each specification. The Plot Contents column lists the types of plots as they appear on the composite plot, counterclockwise and starting in the upper-left corner. Block Specified Data Plot Contents General Amplifier or General Mixer Network parameters X-Y plot, magnitude of S12 and S21 in decibels OR X-Y plot, phase of S12 and S21 in degrees Network parameters and noise Z Smith chart, real and imaginary parts of S11 and S22 Polar plot, magnitude and phase of S11 and S22 Network parameters and power OR Other Physical block X-Y plot, output power (Pout) in dBm (decibels referenced to one milliwatt) Network parameters, noise, and power Z Smith chart, real and imaginary parts of S11 and S22 Network parameters X-Y plot, magnitude of S12 and S21 in decibels Note Only the General Amplifier and General Mixer blocks accept power and noise data. 3-6 X-Y plot, magnitude of S12 and S21 in decibels Polar plot, magnitude and phase of S11 and S22 X-Y plot, phase of S12 and S21 in degrees Z Smith chart, real and imaginary parts of S11 and S22 Polar plot, magnitude and phase of S11 and S22 Creating Plots X-Y Plane You can plot any parameters that are relevant to your block on an X-Y plane plot. The following table summarizes the parameters and formats for this type of plot. Parameter Format S11, S12, S21, S22 Magnitude (decibels) Magnitude (linear) Angle (degrees) Real Imaginary VSWRIn, VSWROut Magnitude (decibels) Magnitude (linear) OIP3 (Output Port block only) dBm W mW NF (Output Port block only) Magnitude (decibels) Magnitude (linear) Pout (General Amplifier block with dBm dBW W mW power data only) Phase (General Amplifier block with power data only) Angle (degrees) Angle (radians) AM/AM (General Amplifier block with power data only) Magnitude (decibels) Magnitude (linear) AM/PM (General Amplifier block with power data only) Angle (degrees) Angle (radians) PhaseNoise (Mixer blocks only) dBc/Hz Link Budget You use the Link budget plot to understand the individual contribution of each block to a plotted parameter value in a physical subsystem with multiple components between the Input Port and the Output Port blocks. 3-7 3 Plotting Model Data The link budget plot is a three-dimensional plot that shows one or more curves of parameter values as a function of frequency, ordered by the subsystem circuit index. The following figure shows how the circuit index is assigned to a component in a physical subsystem based on its sequential position in the subsystem. Input Port Component (Index = 1) Component (Index = 2) ... Component (Index = n) Output Port A curve on the link budget plot for each circuit index represents the contributions to the parameter value of the RF components up to that index. The following figure shows an example of a link budget plot. Contributions to S21 from components 1, 2, and 3 Contributions to S21 from components 1 and 2 Contributions to S21 from component 1 Example — Link Budget Plot The following table summarizes the parameters and formats that are available for a link budget plot. 3-8 Creating Plots Parameter Format S11, S12, S21, S22 Magnitude (decibels) Magnitude (linear) Angle (degrees) Real Imaginary VSWRIn, VSWROut Magnitude (decibels) Magnitude (linear) OIP3 dBm W mW NF Magnitude (decibels) Magnitude (linear) Polar Plane Plots and Smith Charts You can use the RF Blockset to generate Polar plots and Smith charts. When you select these plot types, you do not need to specify the plot format—it is set automatically. The following table describes the Polar plot and Smith chart options, as well as the available parameters. Plot Type Parameter Polar plane S11, S12, S21, S22 Z Smith chart S11, S22 Y Smith chart S11, S22 ZY Smith chart S11, S22 How to Create a Plot 1 Double-click the block to open the block dialog box. The following figure shows the area of the dialog box where you specify plotting options. 3-9 3 Plotting Model Data 2 Select the Plot the selected parameters of this block check box to display the plot options. Select this check box to display the plot options 3 Select the Source of frequency data. Select the source of frequencies at which to plot block data 3-10 Creating Plots This is the source of the frequency values at which to plot block data. The following table summarizes the available types of sources for the various types of blocks. Source of frequency data Description Blocks Derived from Input Port parameters Modeling frequencies derived from the Input Port block parameters. For information on how the RF Blockset computes the modeling frequencies, see “Determining the Modeling Frequencies” on page A-3. All physical blocks Vector of frequencies that you enter. All physical blocks (Available after running a simulation or clicking the Update Diagram button User-specified ) When you select User-specified in the Source of frequency data list, the Frequency range (Hz) field is displayed. Enter a vector specifying the range of frequencies you want to plot. For example, to plot block data from 0.3 MHz to 5 GHz by 0.1 MHz, enter [0.3e6:0.1e6:5e9]. 3-11 3 Plotting Model Data Source of frequency data Description Blocks Note When you select PhaseNoise in the Parameter list and User-specified in the Source of frequency data list, the Frequency range (Hz) field is not displayed. You use the Phase noise frequency offset (Hz) block parameter to specify the frequency values at which to plot block data. Same as the Frequency parameter 3-12 Frequency values specified in the Frequency block parameter. S-Parameters Passive Network, Y-Parameters Passive Network, Z-Parameters Passive Network, S-Parameters Amplifier, Y-Parameters Amplifier, Z-Parameters Amplifier, S-Parameters Mixer, Y-Parameters Mixer, Creating Plots Source of frequency data Description Blocks and Z-Parameters Mixer Extracted from RFDATA object Frequency values imported into the RFDATA object block parameter. For information about rfdata objects, see the RF Toolbox rfdata reference page. General Passive Network, General Amplifier, and General Mixer 4 Select the Plot type. Select the plot type This is the type of plot. For a description of the options, see “Types of Plots” on page 3-3. 3-13 3 Plotting Model Data 5 Select the Parameter. Select the plot parameter This is the data to be plotted. The available choices vary with the type of plot. For a description of the options for a particular plot type, see the topic on that plot type in “Plot Formats” on page 3-4. 6 Choose the Format. Select the plot format This is the format for plotting the selected parameter. The available choices vary based on the selected parameter. For a description of the options for a particular plot type, see the topic on that plot type in “Plot Formats” on page 3-4. 7 Click Apply. 3-14 Creating Plots Note By default, the RF Blockset does not add a legend to some plots. To display the plot legend, type legend show at the MATLAB prompt. Example — Plotting Component Data on a Z Smith Chart In this example, you simulate the frequency response of an amplifier using data from the default.amp AMP file. Using a model from one of the RF Blockset demos, you import the data file into a General Amplifier block and validate the amplifier by plotting the S-parameters of the block on a Z Smith Chart. 1 Type sparam_amp at the MATLAB prompt to open the RF Blockset demo called “AMP Data File for Amplifier”. 3-15 3 Plotting Model Data 2 Double-click the General Amplifier block to display its parameters. Notice that the RFDATA object parameter is set to read(rfdata.data, 'default.amp'). This value uses the RF Toolbox read function to import data from the file default.amp into an rfdata.data object. The block uses this data, along with the other block parameters, in simulation. Note The General Amplifier block models the nonlinear amplifier described by an rfdata.data object. See the RF Toolbox rfdata reference page for information about rfdata objects. See “AMP File Format” in the RF Toolbox documentation for information about .amp files. 3-16 Creating Plots 3 Set the General Amplifier block parameters as follows: • Select the Plot the selected parameters of this block check box. • In the Plot type list, select Z Smith chart. • In the Parameter list, select S22. 4 Click Apply. 3-17 3 Plotting Model Data This action creates a Z Smith® chart of the S22 parameters using the frequency data from the default.amp file. General Amplifier Frequency Response Note To display data tips for a plotted line, select Tools > Data Cursor. Click the data cursor on the plotted line to see the frequency and the parameter value at that point. See “Data Cursor — Displaying Data Values Interactively” in the MATLAB documentation for more information. 3-18 Updating Plots Updating Plots When you run a simulation, the RF Blockset continues to display any open plots, but does not update the plots to reflect new simulation results. You must update the subsystem plots after the simulation to display the behavior of the revised subsystem. Note You do not need to update the plots that represent individual RF components, because the RF Blockset redraws these plots when you make changes to the block parameters. To update an existing subsystem plot: 1 Double-click the Output Port block to open the block dialog box. 2 Clear and select the Plot the selected parameters of this block check box. 3 Click Apply. 3-19 3 Plotting Model Data Modifying Plots You can modify an existing plot by changing the plot options. The outcome depends on the parameter you change. The following table summarizes the results of changing the plot options. Block Parameter Plot Change Source of frequency data Redraws plot using the new frequency data. OR Frequency range Plot type Redraws figure in the new plot type, with the following considerations: • If the current plot options are valid for the new plot type, they retain their values. Otherwise, they revert to their default values. • If you change the Plot type to or from Composite data, the RF Blockset draws the new plot in a new figure and does not update the existing figure. 3-20 Parameter If the new parameter has the same independent variable as the one on the plot, the RF Blockset adds the new parameter to the existing plot. Otherwise, it redraws the plot for the new parameter and independent variable. Format Redraws plot using the new format. Modifying Plots To modify a plot: 1 Double-click the block to open the block dialog box. Example Block Dialog Box Showing Plot Parameters 2 Change the plot options. 3 Click Apply. 3-21 3 Plotting Model Data Example — Creating and Modifying Subsystem Plots In this example, you perform the following tasks: • “Plotting the Network Parameters of a Subsystem” on page 3-22 • “Adding Data to an Existing Plot” on page 3-24 • “Changing Data on an Existing Plot” on page 3-26 Plotting the Network Parameters of a Subsystem In this part of the example, you open and run an RF Blockset demo that uses file data to specify an amplifier in a physical subsystem. Then, you plot the network parameters of the physical subsystem, which consists of the General Amplifier, the Input Port, and the Output Port blocks. 1 Type sparam_amp at the MATLAB prompt to open the RF Blockset demo called “AMP Data File for Amplifier”. 2 In the Simulink model window, select Simulation > Start to run the simulation. 3 Double-click the Output Port block to open the block dialog box. 3-22 Example — Creating and Modifying Subsystem Plots 4 Set the Output Port block parameters as follows: • Select the Plot the selected parameters of this block check box. • In the Plot type list, select X-Y plane. • In the Parameter list, select S21. 5 Click Apply. 3-23 3 Plotting Model Data This action plots the magnitude of S21 (in decibels) as a function of frequency on an X-Y plot. S21 versus Frequency for a Physical Subsystem Adding Data to an Existing Plot In this part of the example, you add data to the plot you created in “Plotting the Network Parameters of a Subsystem” on page 3-22. 1 Double-click the Output Port block to open the block dialog box. 2 Change the value of Parameter to S22. 3-24 Example — Creating and Modifying Subsystem Plots 3 Click Apply. This action adds S22 to the plot. S21 and S22 versus Frequency for a Physical Subsystem 3-25 3 Plotting Model Data Changing Data on an Existing Plot In this part of the example, you change the data on the plot you created in the previous steps of the example by modifying the Plot type. 1 Double-click the Output Port block to open the block dialog box. 2 Change the value of Plot type to Polar plane, as shown in the following figure. Notice that the value of Parameter remains as S22, the last parameter selected for the previous plot. 3 Click Apply. 3-26 Example — Creating and Modifying Subsystem Plots This action creates a Polar plane plot of S22 as a function of frequency. S22 versus Frequency for a Physical Subsystem 3-27 3 Plotting Model Data 4 In the Output Port block dialog box, change the Plot type to Composite data to generate four plots in one figure. The parameters for the plots are defined by the block, so the Parameter field becomes invisible. 3-28 Example — Creating and Modifying Subsystem Plots The RF Blockset creates the plot in a new figure. X-Y Plot, Magnitude of S12 (blue) S21 (green) Polar Plot S11 (blue) S22 (green) X-Y Plot, Phase of S12 (blue) S21 (green) Z Smith Chart S11 (blue) S22 (green) Composite Plot for a Physical Subsystem 3-29 3 3-30 Plotting Model Data 4 Blocks — By Category Mathematical (p. 4-2) Model RF components in terms of mathematical equations. Physical (p. 4-3) Model RF components in terms of physical properties or measured data 4 Blocks — By Category Mathematical 4-2 Amplifier Complex baseband model of amplifier with noise Bandpass RF Filter Standard bandpass RF filters in baseband-equivalent complex form Bandstop RF Filter Standard bandstop RF filters in baseband-equivalent complex form Highpass RF Filter Standard highpass RF filters in baseband-equivalent complex form Lowpass RF Filter Standard lowpass RF filters in baseband-equivalent complex form Mixer Complex baseband model of mixer with phase noise Physical Physical Ladder Filters (p. 4-3) Ladder filter blocks Transmission Lines (p. 4-3) Transmission line blocks Black Box Elements (p. 4-4) Black box elements blocks Amplifiers (p. 4-4) Amplifier blocks Mixers (p. 4-5) Mixer blocks Input/Output Ports (p. 4-5) Connector blocks Ladder Filters LC Bandpass Pi Model LC bandpass pi network LC Bandpass Tee Model LC bandpass tee network LC Bandstop Pi Model LC bandstop pi network LC Bandstop Tee Model LC bandstop tee network LC Highpass Pi Model LC highpass pi network LC Highpass Tee Model LC highpass tee network LC Lowpass Pi Model LC lowpass pi network LC Lowpass Tee Model LC lowpass tee network Series RLC Model series RLC network Shunt RLC Model shunt RLC network Transmission Lines Coaxial Transmission Line Model coaxial transmission line Coplanar Waveguide Transmission Line Model coplanar waveguide transmission line Microstrip Transmission Line Model microstrip transmission line 4-3 4 Blocks — By Category Parallel-Plate Transmission Line Model parallel-plate transmission line RLCG Transmission Line Model RLCG transmission line Transmission Line Model general transmission line Two-Wire Transmission Line Model two-wire transmission line Black Box Elements General Circuit Element Model two-port network described by rfckt object General Passive Network Model two-port passive network described by rfdata object S-Parameters Passive Network Model passive network using its S-parameters Y-Parameters Passive Network Model passive network using its Y-parameters Z-Parameters Passive Network Model passive network using its Z-parameters Amplifiers 4-4 General Amplifier Model nonlinear amplifier described by rfdata object S-Parameters Amplifier Model nonlinear amplifier using its S-parameters Y-Parameters Amplifier Model nonlinear amplifier using its Y-parameters Z-Parameters Amplifier Model nonlinear amplifier using its Z-parameters Physical Mixers General Mixer Model mixer described by rfdata object S-Parameters Mixer Model mixer using its S-parameters Y-Parameters Mixer Model mixer using its Y-parameters Z-Parameters Mixer Model mixer using its Z-parameters Input/Output Ports Input Port Connection block from Simulink environment to RF physical blocks Output Port Connection block from RF physical blocks to Simulink environment 4-5 4 4-6 Blocks — By Category 5 Blocks — Alphabetical List Amplifier Purpose Complex baseband model of amplifier with noise Library Mathematical Description The Amplifier block generates a complex baseband model of an amplifier with thermal noise. It provides six methods for modeling nonlinearity and three ways to specify noise. Note This block assumes a nominal impedance of 1 ohm. Modeling Nonlinearity Specify the method of your choice using this parameter in the block dialog box. The options for the Method parameter are • Linear • Cubic polynomial • Hyperbolic tangent • Saleh model • Ghorbani model • Rapp model The linear method is implemented by a Gain block. The other nonlinear methods are implemented by subsystems underneath the block’s mask. Each subsystem has the same basic structure, as shown in the figure below. 5-2 Amplifier Application of Nonlinearity All five subsystems for the nonlinear methods apply a memoryless nonlinearity to the complex baseband input signal. Each one 1 Multiplies the signal by a gain factor. 2 Splits the complex signal into its magnitude and angle components. 3 Applies an AM/AM conversion to the magnitude of the signal, according to the selected interpolation method, to produce the magnitude of the output signal. 4 Applies an AM/PM conversion to the phase of the signal, according to the selected interpolation method, and adds the result to the angle of the signal to produce the angle of the output signal. 5 Combines the new magnitude and angle components into a complex signal and multiplies the result by a gain factor, which is controlled by the Linear gain parameter. AM/AM and AM/PM Conversions The subsystems for the nonlinear methods implement the AM/AM and AM/PM conversions differently, according to the interpolation method you specify. To see exactly how the Amplifier block implements the conversions for a specific method, you can view the AM/AM and AM/PM subsystems that implement these conversions as follows: 1 Right-click the Amplifier block. 5-3 Amplifier 2 Select Look under mask in the pop-up menu. This displays the block’s configuration underneath the mask. The block contains five subsystems corresponding to the five nonlinearity methods. 3 Double-click the subsystem for the method in which you are interested. A subsystem displays similar to the one shown in the preceding figure. 4 Double-click one of the subsystems labeled AM/AM or AM/PM to view how the block implements the conversions. The following figure shows, for the Saleh method, plots of • Output voltage against input voltage for the AM/AM conversion • Output phase against input voltage for the AM/PM conversion 5-4 Amplifier Effects of the Amplifier Block You can see the effect of the Amplifier block in the demo Intermodulation: Mathematical Amplifier. This demo uses a baseband-equivalent multitone signal as input to the Amplifier block. A Simulink Slider Gain block enables you to vary the gain from 1 to 10. The following figure shows the input signal with gain set to the default 1. 5-5 Amplifier The next figure shows the same signal after it passes through the Amplifier block, with the Method parameter set to Hyperbolic tangent. The demo uses the default Amplifier block IIP3 (dBm) value of 30. It uses no AM/PM conversion. The demo specifies thermal noise as Noise figure, for which it uses the default 3.01 dB. 5-6 Amplifier Parameters for Nonlinear Methods The following sections discuss parameters specific to the following models: • “Cubic Polynomial Model” on page 5-7 • “Hyperbolic Tangent Model” on page 5-8 • “Saleh Model” on page 5-8 • “Ghorbani Model” on page 5-9 • “Rapp Model” on page 5-10 Note The Amplifier block also enables you to model a linear amplifier. Cubic Polynomial Model The third-order input intercept point IIP3 (dBm) parameter is used to compute a scaling factor, which is then applied to the input signal. The scaling factor is equal to 3 divided by the IIP3 parameter value, converted from decibels to linear units. The scaled input is then limited to a maximum value of 1 and the amplitude gain is applied according to the following function FAM / AM (u) = u − u 3 where u is the magnitude of the scaled signal. The AM/PM conversion (degrees per dB) parameter specifies the linear phase change. This is applied within the power limits specified by the Lower input power limit for AM/PM conversion (dBm) parameter and the Upper input power limit for AM/PM conversion (dBm) parameter. Outside those limits, the phase change is constant at the values corresponding to the lower and upper input power limits, which are zero and 5-7 Amplifier (AM/PM conversion) ⋅ (upper input power limit − lower input power limit) , respectively. The Linear gain (dB) parameter scales the output signal. Hyperbolic Tangent Model The third-order input intercept point IIP3 (dBm) parameter is used to compute a scaling factor, which is then applied to the input signal. The scaling factor is equal to 3 divided by the IIP3 parameter value, converted from decibels to linear units. The amplitude gain is then applied to the scaled input according to the following function where u is the magnitude of the scaled signal. The AM/PM conversion (degrees per dB) parameter specifies the linear phase change. This is applied within the power limits specified by the Lower input power limit for AM/PM conversion (dBm) parameter and the Upper input power limit for AM/PM conversion (dBm) parameter. Outside those limits, the phase change is constant at the values corresponding to the lower and upper input power limits, which are zero and (AM/PM conversion) ⋅ (upper input power limit − lower input power limit) , respectively. The Linear gain (dB) parameter scales the output signal. Saleh Model The Input scaling (dB) parameter scales the input signal before the nonlinearity is applied. The block multiplies the input signal by the parameter value, converted from decibels to linear units. If you set the parameter to be the inverse of the input signal amplitude, the scaled signal has amplitude normalized to 1. The AM/AM parameters, alpha and beta, are used to compute the amplitude gain for an input signal using the following function 5-8 Amplifier where u is the magnitude of the scaled signal. The AM/PM parameters, alpha and beta, are used to compute the phase change for an input signal using the following function where u is the magnitude of the input signal. Note that the AM/AM and AM/PM parameters, although similarly named alpha and beta, are distinct. The Output scaling (dB) parameter scales the output signal similarly. Ghorbani Model The Input scaling (dB) parameter scales the input signal before the nonlinearity is applied. The block multiplies the input signal by the parameter value, converted from decibels to linear units. If you set the parameter to be the inverse of the input signal amplitude, the scaled signal has amplitude normalized to 1. The AM/AM parameters, [x1 x2 x3 x4], are used to compute the amplitude gain for an input signal using the following function where u is the magnitude of the scaled signal. The AM/PM parameters, [y1 y2 y3 y4], are used to compute the phase change for an input signal using the following function 5-9 Amplifier where u is the magnitude of the scaled signal. The Output scaling (dB) parameter scales the output signal similarly. Rapp Model The Smoothness factor and Output saturation level parameters are used to compute the amplitude gain for an input signal by the following function where u is the magnitude of the scaled signal, S is the Smoothness factor and Osat is the Output saturation level. The Rapp model does not apply a phase change to the input signal. The Output saturation level parameter limits the output signal level. The Smoothness factor parameter controls the transition for the amplitude gain as the input amplitude approaches saturation. The smaller the smoothness factor, the smoother the curve. Thermal Noise Simulation You can specify the amount of thermal noise in three ways, according to the Specification method parameter you select. • Noise temperature — Specifies the noise in kelvin. • Noise factor — Specifies the noise by the following equation: Noise factor = 1 + Noise temperature 290 • Noise figure — Specifies the noise in decibels relative to a noise temperature of 290 kelvin. In terms of noise factor, Noise figure = 10log(Noise factor) 5-10 Amplifier Note Some RF blocks require the sample time to perform baseband modeling calculations. To ensure the accuracy of these calculations, the Input Port block, as well as the mathematical RF blocks, compare the input sample time to the sample time you provide in the mask. If they do not match, or if the input sample time is missing because the blocks are not connected, an error message appears. Dialog Box The parameters displayed in the dialog box vary for different methods of modeling nonlinearity. Only some of these parameters are visible in the dialog box at any one time. 5-11 Amplifier You can change tunable parameters while the model is running. Method Method used to model the nonlinearity. The choices are Linear, Cubic polynomial, Hyperbolic tangent, Saleh model, Ghorbani model, Rapp model. Tunable. Linear gain (dB) Scalar specifying the linear gain for the output function. This field becomes visible if you select Linear, Cubic polynomial, Hyperbolic tangent, or Rapp model as the Method parameter. Tunable. IIP3 (dBm) Input power intercept point as a scalar value. This field becomes visible if you select Cubic polynomial or Hyperbolic tangent as the Method parameter. For both of these methods, the nominal impedance is 1 ohm. Tunable. AM/PM conversion (degrees per dB) Scalar specifying the AM/PM conversion in degrees per decibel. This field becomes visible if you select Cubic polynomial or Hyperbolic tangent as the Method parameter. Tunable. Lower input power limit for AM/PM conversion (dBm) Scalar specifying the minimum input power for which AM/PM conversion scales linearly with input power value. Below this value, the phase shift resulting from AM/PM conversion is zero. This field becomes visible if you select Cubic polynomial or Hyperbolic tangent as the Method parameter. Tunable. Upper input power limit for AM/PM conversion (dBm) Scalar specifying the maximum input power for which AM/PM conversion scales linearly with input power value. Above this value, the phase shift resulting from AM/PM conversion is constant. The value of this maximum shift is given by: (AM/PM conversion) ⋅ (upper input power limit − lower input power limit) 5-12 Amplifier This field becomes visible if you select Cubic polynomial or Hyperbolic tangent as the Method parameter. Tunable. Input scaling (dB) Number that scales the input signal level. This field becomes visible if you select Saleh model or Ghorbani model as the Method parameter. Tunable. Output scaling (dB) Number that scales the output signal level. This field becomes visible if you select Saleh model or Ghorbani model as the Method parameter. Tunable. AM/AM parameters [alpha beta] Vector specifying the AM/AM parameters. This field becomes visible if you select Saleh model as the Method parameter. Tunable. AM/PM parameters [alpha beta] Vector specifying the AM/PM parameters. This field becomes visible if you select Saleh model as the Method parameter. Tunable. AM/AM parameters [x1 x2 x3 x4] Vector specifying the AM/AM parameters. This field becomes visible if you select Ghorbani model as the Method parameter. Tunable. AM/PM parameters [y1 y2 y3 y4] Vector specifying the AM/PM parameters. This field becomes visible if you select Ghorbani model as the Method parameter. Tunable. Smoothness factor Scalar specifying the smoothness factor. This field becomes visible if you select Rapp model as the Method parameter. Tunable. Output saturation level Scalar specifying the output saturation level. This field becomes visible if you select Rapp model as the Method parameter. Tunable. 5-13 Amplifier Specification method The method by which you specify the amount of noise. The choices are Noise temperature, Noise figure, and Noise factor. Tunable. Noise temperature (K) Scalar specifying the amount of noise. This field becomes visible if you select Noise temperature as the Specification method parameter. Tunable. Noise figure (dB) Scalar specifying the amount of noise relative to a noise temperature of 290 kelvin. A Noise figure setting of 0 dB indicates a noiseless system. This field becomes visible if you select Noise figure as the Specification method parameter. Tunable. Noise factor Scalar specifying the amount of noise relative to a noise temperature of 290 kelvin. This field becomes visible if you select Noise factor as the Specification method parameter. Tunable. Initial seed Nonnegative integer specifying the initial seed for the random number generator the block uses to generate noise. References [1] Ghorbani, A. and M. Sheikhan, “The Effect of Solid State Power Amplifiers (SSPAs) Nonlinearities on MPSK and M-QAM Signal Transmission,” Sixth Int’l Conference on Digital Processing of Signals in Comm., 1991, pp. 193-197. [2] Rapp, C., “Effects of HPA-Nonlinearity on a 4-DPSK/OFDM-Signal for a Digital Sound Broadcasting System,” in Proceedings of the Second European Conference on Satellite Communications, Liege, Belgium, Oct. 22-24, 1991, pp. 179-184. 5-14 Amplifier [3] Saleh, A.A.M., “Frequency-independent and frequency-dependent nonlinear models of TWT amplifiers,” IEEE Trans. Communications, vol. COM-29, pp.1715-1720, November 1981. See Also Bandpass RF Filter, Bandstop RF Filter, Highpass RF Filter, Lowpass RF Filter, Mixer 5-15 Bandpass RF Filter Purpose Standard bandpass RF filters in baseband-equivalent complex form Library Mathematical Description The Bandpass RF Filter block lets you design standard analog bandpass filters, implemented in baseband-equivalent complex form. The following table describes the available design methods. Design Method Description Butterworth The magnitude response of a Butterworth filter is maximally flat in the passband and monotonic overall. Chebyshev I The magnitude response of a Chebyshev I filter is equiripple in the passband and monotonic in the stopband. Chebyshev II The magnitude response of a Chebyshev II filter is monotonic in the passband and equiripple in the stopband. Elliptic The magnitude response of an elliptic filter is equiripple in both the passband and the stopband. Bessel The delay of a Bessel filter is maximally flat in the passband. The block input must be a discrete-time complex signal. Note This block assumes a nominal impedance of 1 ohm. Select the design of the filter from the Design method list in the dialog box. For each design method, the block enables you to specify the filter design parameters shown in the following table. 5-16 Bandpass RF Filter Design Method Filter Design Parameters Butterworth Order, lower passband edge frequency, upper passband edge frequency Chebyshev I Order, lower passband edge frequency, upper passband edge frequency, passband ripple Chebyshev II Order, lower stopband edge frequency, upper stopband edge frequency, stopband attenuation Elliptic Order, lower passband edge frequency, upper passband edge frequency, passband ripple, stopband attenuation Bessel Order, lower passband edge frequency, upper passband edge frequency The Bandpass RF Filter block designs the filters using the Signal Processing Toolbox filter design functions buttap, cheb1ap, cheb2ap, ellipap, and besselap. Note Some RF blocks require the sample time to perform baseband modeling calculations. To ensure the accuracy of these calculations, the Input Port block, as well as the mathematical RF blocks, compare the input sample time to the sample time you provide in the mask. If they do not match, or if the input sample time is missing because the blocks are not connected, an error message appears. 5-17 Bandpass RF Filter Dialog Box The parameters displayed in the dialog box vary for different design methods. Only some of these parameters are visible in the dialog box at any one time. You can change tunable parameters while the model is running. Design method Filter design method. The design method can be Butterworth, Chebyshev I, Chebyshev II, Elliptic, or Bessel. Tunable. Filter order Order of the lowpass analog prototype filter that forms the basis for the bandpass filter design. The order of the final filter is twice this value. 5-18 Bandpass RF Filter Lower passband edge frequency (Hz) Lower passband edge frequency for Butterworth, Chebyshev I, elliptic, and Bessel designs. Tunable. Upper passband edge frequency (Hz) Upper passband edge frequency for Butterworth, Chebyshev I, elliptic, and Bessel designs. Tunable. Lower stopband edge frequency (Hz) Lower stopband edge frequency for Chebyshev II designs. Tunable. Upper stopband edge frequency (Hz) Upper stopband edge frequency for Chebyshev II designs. Tunable. Passband ripple in dB Passband ripple for Chebyshev I and elliptic designs. Tunable. Stopband attenuation in dB Stopband attenuation for Chebyshev II and elliptic designs. Tunable. Finite impulse response filter length Desired length of the baseband-equivalent impulse response for the filter. Center frequency (Hz) Center of the modeling frequencies. Sample time (s) Time interval between consecutive samples of the input signal. See Also Amplifier, Bandstop RF Filter, Highpass RF Filter, Lowpass RF Filter, Mixer buttap, cheb1ap, cheb2ap, ellipap, besselap (Signal Processing Toolbox) 5-19 Bandstop RF Filter Purpose Standard bandstop RF filters in baseband-equivalent complex form Library Mathematical Description The Bandstop RF Filter block lets you design standard analog bandstop filters, implemented in baseband-equivalent complex form. The following table describes the available design methods. Design Method Description Butterworth The magnitude response of a Butterworth filter is maximally flat in the passband and monotonic overall. Chebyshev I The magnitude response of a Chebyshev I filter is equiripple in the passband and monotonic in the stopband. Chebyshev II The magnitude response of a Chebyshev II filter is monotonic in the passband and equiripple in the stopband. Elliptic The magnitude response of an elliptic filter is equiripple in both the passband and the stopband. Bessel The delay of a Bessel filter is maximally flat in the passband. The block input must be a discrete-time complex signal. Note This block assumes a nominal impedance of 1 ohm. 5-20 Bandstop RF Filter Select the design of the filter from the Design method list in the dialog box. For each design method, the block enables you to specify the filter design parameters shown in the following table. Design Method Filter Design Parameters Butterworth Order, lower passband edge frequency, upper passband edge frequency Chebyshev I Order, lower passband edge frequency, upper passband edge frequency, passband ripple Chebyshev II Order, lower stopband edge frequency, upper stopband edge frequency, stopband attenuation Elliptic Order, lower passband edge frequency, upper passband edge frequency, passband ripple, stopband attenuation Bessel Order, lower passband edge frequency, upper passband edge frequency The Bandstop RF Filter block designs the filters using the Signal Processing Toolbox filter design functions buttap, cheb1ap, cheb2ap, ellipap, and besselap. Note Some RF blocks require the sample time to perform baseband modeling calculations. To ensure the accuracy of these calculations, the Input Port block, as well as the mathematical RF blocks, compare the input sample time to the sample time you provide in the mask. If they do not match, or if the input sample time is missing because the blocks are not connected, an error message appears. 5-21 Bandstop RF Filter Dialog Box The parameters displayed in the dialog box vary for different design methods. Only some of these parameters are visible in the dialog box at any one time. You can change tunable parameters while the model is running. Design method Filter design method. The design method can be Butterworth, Chebyshev I, Chebyshev II, Elliptic, or Bessel. Tunable. Filter order Order of the lowpass analog prototype filter that forms the basis for the bandstop filter design. The order of the final filter is twice this value. Lower passband edge frequency (Hz) Lower passband edge frequency for Butterworth, Chebyshev I, elliptic, and Bessel designs. Tunable. 5-22 Bandstop RF Filter Upper passband edge frequency (Hz) Upper passband edge frequency for Butterworth, Chebyshev I, elliptic, and Bessel designs. Tunable. Lower stopband edge frequency (Hz) Lower stopband edge frequency for Chebyshev II designs. Tunable. Upper stopband edge frequency (Hz) Upper stopband edge frequency for Chebyshev II designs. Tunable. Passband ripple in dB Passband ripple for Chebyshev I and elliptic designs. Tunable. Stopband attenuation in dB Stopband attenuation for Chebyshev II and elliptic designs. Tunable. Finite impulse response filter length Desired length of the baseband-equivalent impulse response for the filter. Center frequency (Hz) Center of the modeling frequencies. Sample time (s) Time interval between consecutive samples of the input signal. See Also Amplifier, Bandpass RF Filter, Highpass RF Filter, Lowpass RF Filter, Mixer buttap, cheb1ap, cheb2ap, ellipap, besselap (Signal Processing Toolbox) 5-23 Coaxial Transmission Line Purpose Model coaxial transmission line Library Transmission Lines sublibrary of the Physical library Description The Coaxial Transmission Line block models the coaxial transmission line described in the block dialog box in terms of its frequency-dependent S-parameters. A coplanar waveguide transmission line is shown here in cross-section. Its physical characteristics include the radius of the inner conductor a and the radius of the outer conductor b. The block lets you model the transmission line as a stub or as a stubless line. Stubless Transmission Line If you model a coaxial transmission line as a stubless line, the Coaxial Transmission Line block calculates the frequency-dependent S-parameters using the physical length of the transmission line, D, and the complex propagation constant, k. 5-24 Coaxial Transmission Line k is a vector whose elements correspond to the elements of f, a vector of modeling frequencies. It can be expressed in terms of the resistance (R), inductance (L), conductance (G), and capacitance (C) per unit length (meters) as where In these equations, is the conductivity in the conductor and is the conductivity in the dielectric. is the permeability of the dielectric, is its permittivity, and skin depth is calculated as . f is a vector of modeling frequencies determined by the Output Port block. The Coaxial Transmission Line block normalizes the resulting S-parameters to a reference impedance of 50 ohms. Shunt and Series Stubs If you model the transmission line as a shunt or series stub, the Coaxial Transmission Line block first calculates the ABCD-parameters at each frequency contained in the modeling frequencies vector. It then uses the abcd2s function to convert the ABCD-parameters to S-parameters. Shunt ABCD-Parameters When you set the Stub mode parameter in the mask dialog box to Shunt, the two-port network consists of a stub transmission line that you can terminate with either a short circuit or an open circuit as shown here. 5-25 Coaxial Transmission Line Zin is the input impedance of the shunt circuit. The ABCD-parameters for the shunt stub are calculated as Series ABCD-Parameters When you set the Stub mode parameter in the mask dialog box to Series, the two-port network consists of a series transmission line that you can terminate with either a short circuit or an open circuit as shown here. Zin is the input impedance of the series circuit. The ABCD-parameters for the series stub are calculated as 5-26 Coaxial Transmission Line Dialog Box Outer radius (m) Radius of the outer conductor of the coaxial transmission line. 5-27 Coaxial Transmission Line Inner radius (m) Radius of the inner conductor of the coaxial transmission line. Relative permeability constant Relative permeability of the dielectric expressed as the ratio of the permeability of the dielectric to permeability in free space . Relative permittivity constant Relative permittivity of the dielectric expressed as the ratio of the permittivity of the dielectric to permittivity in free space . Conductivity in conductor (S/m) Conductivity of the conductor in siemens per meter. Conductivity in dielectric (S/m) Conductivity of the dielectric in siemens per meter. Transmission line length (m) Physical length of the transmission line. Stub mode Type of stub. Choices are Not a stub, Shunt, or Series. Termination of stub Stub termination for stub modes Shunt and Series. Choices are Open or Short. This parameter becomes visible only when Stub mode is set to Shunt or Series. Note For information about plotting, see Chapter 3, “Plotting Model Data”. 5-28 References [1] Ludwig, Reinhold and Pavel Bretchko, RF Circuit Design: Theory and Applications, Prentice-Hall, 2000. See Also Coplanar Waveguide Transmission Line, General Passive Network, Transmission Line, Microstrip Transmission Line, Parallel-Plate Transmission Line, Two-Wire Transmission Line Coplanar Waveguide Transmission Line Purpose Model coplanar waveguide transmission line Library Transmission Lines sublibrary of the Physical library Description The Coplanar Waveguide Transmission Line block models the coplanar waveguide transmission line described in the block dialog box in terms of its frequency-dependent S-parameters. A coplanar waveguide transmission line is shown here in cross-section. Its physical characteristics include the conductor width (w), the conductor thickness (t), the slot width (s), the substrate height (d), and the relative permittivity constant ( ). The block lets you model the transmission line as a stub or as a stubless line. Stubless Transmission Line If you model a coplanar waveguide transmission line as a stubless line, the Coplanar Waveguide Transmission Line block calculates the frequency-dependent S-parameters using the physical length of the transmission line, D, and the complex propagation constant, k. , where is the attenuation coefficient and is the wave number. The attenuation coefficient is related to the loss, , by 5-29 Coplanar Waveguide Transmission Line where is the reduction in signal strength, in dB, per unit length. combines both conductor loss and dielectric loss and is derived from the physical parameters specified in the Coplanar Waveguide Transmission Line block dialog box. The wave number is related to the phase velocity, VP, by , where is the frequency-dependent effective dielectric constant. f is a vector of modeling frequencies determined by the Output Port block. The phase velocity VP is also known as the wave propagation velocity. The Coplanar Waveguide Transmission Line block normalizes the resulting S-parameters to a reference impedance of 50 ohms. Shunt and Series Stubs If you model the transmission line as a shunt or series stub, the Coplanar Waveguide Transmission Line block first calculates the ABCD-parameters at each frequency contained in the vector of modeling frequencies. It then uses the abcd2s function to convert the ABCD-parameters to S-parameters. Shunt ABCD-Parameters When you set the Stub mode parameter in the mask dialog box to Shunt, the two-port network consists of a stub transmission line that you can terminate with either a short circuit or an open circuit as shown here. 5-30 Coplanar Waveguide Transmission Line Zin is the input impedance of the shunt circuit. The ABCD-parameters for the shunt stub are calculated as Series ABCD-Parameters When you set the Stub mode parameter in the mask dialog box to Series, the two-port network consists of a series transmission line that you can terminate with either a short circuit or an open circuit as shown here. Zin is the input impedance of the series circuit. The ABCD-parameters for the series stub are calculated as 5-31 Coplanar Waveguide Transmission Line Dialog Box 5-32 Coplanar Waveguide Transmission Line Conductor width (m) Physical width of the conductor. Slot width (m) Physical width of the slot. Substrate height (m) Thickness of the dielectric on which the conductor resides. Strip thickness (m) Physical thickness of the conductor. Relative permittivity constant Relative permittivity of the dielectric expressed as the ratio of the permittivity of the dielectric to permittivity in free space . Conductivity in conductor (S/m) Conductivity of the conductor in siemens per meter. Loss tangent in dielectric Loss angle tangent of the dielectric. Transmission line length (m) Physical length of the transmission line. Stub mode Type of stub. Choices are Not a stub, Shunt, or Series. Termination of stub Stub termination for stub modes Shunt and Series. Choices are Open or Short. This parameter becomes visible only when Stub mode is set to Shunt or Series. Note For information about plotting, see Chapter 3, “Plotting Model Data”. References [1] Gupta, K. C., Ramesh Garg, Inder Bahl, and Prakash Bhartia, Microstrip Lines and Slotlines, 2nd Edition, Artech House, Inc., Norwood, MA, 1996. 5-33 Coplanar Waveguide Transmission Line See Also 5-34 Coaxial Transmission Line, General Passive Network, Transmission Line, Microstrip Transmission Line, Parallel-Plate Transmission Line, Two-Wire Transmission Line General Amplifier Purpose Model nonlinear amplifier described by rfdata object Library Amplifiers sublibrary of the Physical library Description The General Amplifier block models the nonlinear amplifier described by an RF Toolbox data (rfdata.data) object. Network Parameters If network parameter data and their corresponding frequencies exist as S-parameters in the rfdata.data object, the General Amplifier block interpolates the S-parameters to determine their values at the modeling frequencies. If the block contains network Y- or Z-parameters, the block first converts them to S-parameters. See Appendix A, “RF Blockset Algorithms” for more details. Nonlinearity If power data exists in the rfdata.data object, the block extracts the AMAM/AMPM nonlinearities from the power data. If the rfdata.data object contains no power data, then you can enter either the OIP3 or IIP3 as a scalar value for nonlinearity in the General Amplifier block dialog box. Active Noise If active spot noise data exists in the rfdata.data object, the block uses the data to calculate the noise figure. The block first interpolates the noise data for the modeling frequencies, using the specified Interpolation method. It then calculates the noise figure using the resulting values. If the rfdata.data object contains no noise data, then you can enter a value for the noise figure in the General Amplifier block dialog box. Data Consistency If you create the rfdata.data object by reading data from a MathWorks AMP file that contains both network parameter data and power data, the RF Blockset checks the data for consistency and reconciles it as necessary. 5-35 General Amplifier The RF Blockset compares the small-signal amplifier gain defined by the network parameters, S21, and by the power data, Pout-Pin. The discrepancy between the two is computed in dBm using the following equation: ΔP = S21 ( f P ) − Pout ( f P ) + Pin ( f P ) (dBm) where fP is the lowest frequency for which power data is specified. P is more than 0.4 dB, a warning appears and the RF Blockset adds P to the output power values at each specified input power value to resolve the discrepancy for simulation. This discrepancy is shown in the following graph. If Small Signal Network Data *** Specified Power Data xxx Reconciled Power Data x x x * * * x Pout (dBm) x * DP * * fP 5-36 x Pin (dBm) General Amplifier Dialog Box RFDATA object An RF Toolbox data (rfdata.data) object. You can specify the object as (1) the handle of a data object previously created using the RF Toolbox, (2) an RF Toolbox command such as rfdata.data, which creates a default data object, or (3) a MATLAB expression that generates such an object. See the RF Toolbox documentation for more information about data objects. Interpolation method For network data, the method used to interpolate the parameters contained in the rfdata.data object. Interpolation can be Cubic, Linear (default), or Spline. IP3 type Type of third-order intercept point. The value can be IIP3 (input intercept point) or OIP3 (output intercept point). This parameter becomes visible only if the rfdata.data object contains no power data. 5-37 General Amplifier IIP3 (dBm) Input power intercept point as a scalar value. This field becomes visible if you select IIP3 as the IP3 type. This parameter becomes visible only if the rfdata.data object contains no power data. OIP3 (dBm) Output power intercept point as a scalar value. This field becomes visible if you select OIP3 as the IP3 type. This parameter becomes visible only if the rfdata.data object contains no power data. Noise figure (dB) Scalar ratio of the available signal-to-noise power ratio at the input to the available signal-to-noise power ratio at the output, (Si/Ni)/(So/No). This parameter becomes visible only if the rfdata.data object contains no noise data. Note For information about plotting the amplifier parameters, see Chapter 3, “Plotting Model Data”. Use rftool or the RF Toolbox plotting functions to plot other data. Examples Creating a General Amplifier Block from File Data This example uses the RF Toolbox read function to create an rfdata.data object that describes the nonlinear amplifier in the file default.amp. The file, which is read into an RF Toolbox data (rfdata.data) object, contains S-parameters for frequencies from 1.0 to 2.9 GHz at intervals of 0.01 GHz, power data at frequency 2.1 GHz, and active noise parameters. The General Amplifier block uses linear interpolation to model the network described in the object. Note See “AMP File Format” in the RF Toolbox documentation for information about .amp files. 5-38 General Amplifier The plot parameters in the dialog box request a Z Smith chart of the S22 parameters using the frequencies taken from the RFDATA object parameter. 5-39 General Amplifier See Also Output Port, S-Parameters Amplifier, Y-Parameters Amplifier, Z-Parameters Amplifier rfdata, rfdata.data (RF Toolbox) interp1 (MATLAB) 5-40 General Circuit Element Purpose Model two-port network described by rfckt object Library Black Box Elements sublibrary of the Physical library Description The General Circuit Element block models the two-port network described by an RF Toolbox circuit (rfckt) object. The block uses the rfckt/analyze method to calculate the network parameters at the modeling frequencies. Dialog Box RFCKT object An RF Toolbox circuit (rfckt) object. You can specify the object as (1) the handle of a circuit object previously created using the RF Toolbox, (2) an RF Toolbox command such as rfckt.txline, rfckt.coaxial, or rfckt.cascade that creates a default circuit object of the specified type, or (3) a MATLAB expression that generates such an object. See the RF Toolbox documentation for more information about circuit objects. 5-41 General Circuit Element Note For information about plotting, see Chapter 3, “Plotting Model Data”. Examples Creating a General Circuit Element from an RF Toolbox Object This example uses the rfckt.txline object, which describes a transmission line. The plot parameters in the dialog box request an X-Y plane plot of the S12 parameters in the frequency range 1.9 to 2.2 GHz. 5-42 General Circuit Element See Also General Passive Network, S-Parameters Passive Network, Y-Parameters Passive Network, Z-Parameters Passive Network rfckt (RF Toolbox) interp1 (MATLAB) 5-43 General Mixer Purpose Model mixer described by rfdata object Library Mixer sublibrary of the Physical library Description The General Mixer block models the mixer described by an RF Toolbox data (rfdata.data) object. Network Parameters The network parameter values all refer to the mixer input frequency. If network parameter data and their corresponding frequencies exist as S-parameters in the rfdata.data object, the General Mixer block interpolates the S-parameters to determine their values at the modeling frequencies. If the block contains network Y- or Z-parameters, the block first converts them to S-parameters. See “Mapping Network Parameters to Modeling Frequencies” on page A-5 for more details. The RF Blockset computes the normalized reflected amplitude at the mixer input ( Er1 ) and at the mixer output ( Er2 ) from the interpolated S-parameters as Er1 ( fin ) = S11 ( fin ) Ei1 ( fin ) + S12 ( fin ) Ei2 ( fout ) Er 2 ( fout ) = S21 ( fin ) Ei1 ( fin ) + S22 ( fin ) Ei2 ( fout ) where • fin and f out are the mixer input and output frequencies, respectively. • Ei1 and Ei2 are the normalized incident amplitudes at the mixer input and output, respectively. The interpolated S21 parameter values describe the conversion gain as a function of frequency, referred to the mixer input frequency. Active Noise If active spot noise data exists in the rfdata.data object, the block uses the data to calculate the noise figure. It first interpolates the noise 5-44 General Mixer data for the modeling frequencies, using the specified Interpolation method. It then calculates the noise figure using the resulting values. If the rfdata.data object contains no noise data, the General Mixer block dialog lets you enter a value for the noise figure. Phase Noise The General Mixer block applies phase noise to a complex baseband signal. The block first applies generates additive white Gaussian noise (AWGN) and filters it with a digital filter. It then adds the resulting noise to the angle component of the input signal. 5-45 General Mixer Dialog Box RFDATA object An RF Toolbox data object (rfdata.data) that describes a mixer. You can specify the object as (1) the handle of a data object previously created using the RF Toolbox, (2) an RF Toolbox command such as rfdata.data that creates a default data object, or (3) a MATLAB expression that generates such an object. See the RF Toolbox documentation for more information about data objects. 5-46 General Mixer Interpolation method For network data, the method used to interpolate the parameters contained in the rfdata.data object. Interpolation can be Cubic, Linear (default), or Spline. Type Type of mixer. Choices are Downconverter (default) and Upconverter. LO frequency (Hz) Local oscillator frequency. If you choose Downconverter, the RF Blockset computes the mixer output frequency, f out , from the mixer input frequency, f in , and the local oscillator frequency, f lo , . . If you choose Upconverter, as Note The mixer output frequency must be positive. This means that if you choose a downconverting mixer, than fin must be greater flo . Otherwise, an error appears. IP3 type Type of third-order intercept point. The value can be IIP3 (input intercept point) or OIP3 (output intercept point). This parameter becomes visible only if the rfdata.data object contains no power data. IIP3 (dBm) Input power intercept point as a scalar value. This field becomes visible if you select IIP3 as the IP3 type. This parameter becomes visible if the rfdata.data object contains no power data and you select IIP3 as the IP3 type. OIP3 (dBm) Output power intercept point as a scalar value. This field becomes visible if you select OIP3 as the IP3 type. This parameter becomes 5-47 General Mixer visible if the rfdata.data object contains no power data and you select OIP3 as the IP3 type. Noise figure (dB) Scalar ratio of the available signal-to-noise power ratio at the input to the available signal-to-noise power ratio at the output, (Si/Ni)/(So/No). This parameter becomes visible only if the rfdata.data object contains no noise data. Phase noise frequency offset (Hz) Vector specifying the frequency offset. Phase noise level (dBc/Hz) Vector specifying the phase noise level. Note For information about plotting the mixer parameters, see Chapter 3, “Plotting Model Data”. Use RF Tool or the RF Toolbox plotting functions to plot other data. See Also Output Port, S-Parameters Mixer, Y-Parameters Mixer, Z-Parameters Mixer rfdata, rfdata.data (RF Toolbox) 5-48 General Passive Network Purpose Model two-port passive network described by rfdata object Library Black Box Elements sublibrary of the Physical library Description The General Passive Network block models the two-port passive network described by an RF Toolbox data (rfdata.data) object. If network parameter data and their corresponding frequencies exist as S-parameters in the rfdata.data object, the General Passive Network block interpolates the S-parameters to determine their values at the modeling frequencies. If the block contains network Y- or Z-parameters, the block first converts them to S-parameters. See “Mapping Network Parameters to Modeling Frequencies” on page A-5 for more details. Dialog Box RFDATA object An RF Toolbox data (rfdata.data) object. You can specify the object as (1) the handle of a data object previously created using the RF Toolbox, (2) an RF Toolbox command such as rfdata.data that creates a default data object, or (3) a MATLAB expression 5-49 General Passive Network that generates such an object. See the RF Toolbox documentation for more information about data objects. Interpolation method Method used to interpolate the parameters contained in the rfdata object. Interpolation can be Linear (default), Spline, or Cubic. Note For information about plotting, see Chapter 3, “Plotting Model Data”. Examples Creating a General Passive Network Block from File Data This example uses the RF Toolbox read function to create an rfdata.data object that describes the two-port passive network in the file passive.s2p. The file contains S-parameters for frequencies from about 0.315 MHz to 6.0 GHz. The General Passive Network block uses linear interpolation to model the network described in the object. 5-50 General Passive Network The plot parameters in the dialog box request a Z Smith chart of the S11 parameters using the frequencies taken from the RFDATA object parameter. See Also General Circuit Element, Output Port, S-Parameters Passive Network, Y-Parameters Passive Network, Z-Parameters Passive Network rfdata, rfdata.data (RF Toolbox) interp1 (MATLAB) 5-51 Highpass RF Filter Purpose Standard highpass RF filters in baseband-equivalent complex form Library Mathematical Description The Highpass RF Filter block lets you design standard analog highpass filters, implemented in baseband-equivalent complex form. The following table describes the available design methods. Design Method Description Butterworth The magnitude response of a Butterworth filter is maximally flat in the passband and monotonic overall. Chebyshev I The magnitude response of a Chebyshev I filter is equiripple in the passband and monotonic in the stopband. Chebyshev II The magnitude response of a Chebyshev II filter is monotonic in the passband and equiripple in the stopband. Elliptic The magnitude response of an elliptic filter is equiripple in both the passband and the stopband. Bessel The delay of a Bessel filter is maximally flat in the passband. The block input must be a discrete-time complex signal. Note This block assumes a nominal impedance of 1 ohm. Select the design of the filter from the Design method list in the dialog box. For each design method, the block lets you specify the filter design parameters shown in the following table. 5-52 Highpass RF Filter Design Method Filter Design Parameters Butterworth Order, passband edge frequency Chebyshev I Order, passband edge frequency, passband ripple Chebyshev II Order, stopband edge frequency, stopband attenuation Elliptic Order, passband edge frequency, passband ripple, stopband attenuation Bessel Order, passband edge frequency The Highpass RF Filter block designs the filters using the Signal Processing Toolbox filter design functions buttap, cheb1ap, cheb2ap, ellipap, and besselap. Note Some RF blocks require the sample time to perform baseband modeling calculations. To ensure the accuracy of these calculations, the Input Port block, as well as the mathematical RF blocks, compare the input sample time to the sample time you provide in the mask. If they do not match, or if the input sample time is missing because the blocks are not connected, an error message appears. 5-53 Highpass RF Filter Dialog Box The parameters displayed in the dialog box vary for different design methods. Only some of these parameters are visible in the dialog box at any one time. You can change tunable parameters while the model is running. Design method Filter design method. The design method can be Butterworth, Chebyshev I, Chebyshev II, Elliptic, or Bessel. Tunable. Filter order Order of the filter. Passband edge frequency (Hz) Passband edge frequency for Butterworth, Chebyshev I, elliptic, and Bessel designs. Tunable. Stopband edge frequency (Hz) Stopband edge frequency for Chebyshev II designs. Tunable. 5-54 Highpass RF Filter Passband ripple in dB Passband ripple for Chebyshev I and elliptic designs. Tunable. Stopband attenuation in dB Stopband attenuation for Chebyshev II and elliptic designs. Tunable. Finite impulse response filter length Desired length of the baseband-equivalent impulse response for the filter. Center frequency (Hz) Center of the modeling frequencies. Sample time Time interval between consecutive samples of the input signal. See Also Amplifier, Bandpass RF Filter, Bandstop RF Filter, Lowpass RF Filter, Mixer buttap, cheb1ap, cheb2ap, ellipap, besselap (Signal Processing Toolbox) 5-55 Input Port Purpose Connection block from Simulink environment to RF physical blocks Library Input/Output Ports sublibrary of the Physical library Description The Input Port block serves as a connecting port from the Simulink, or mathematical, part of the model to an RF physical part of the model. The Input Port block lets you provide the parameter data needed to calculate the modeling frequencies and the baseband-equivalent impulse response for the physical subsystem. For more information about how the Input Port block converts the mathematical Simulink signals to RF Blockset physical modeling environment signals, see “Converting to and from Simulink Signals” on page A-15. For more information about connecting mathematical and physical parts of a model, see Chapter 2, “Modeling an RF System”. Note Some RF blocks require the sample time to perform baseband modeling calculations. To ensure the accuracy of these calculations, the Input Port block, as well as the mathematical RF blocks, compare the input sample time to the sample time you provide in the Input Port mask. If they do not match, or if the input sample time is missing because the blocks are not connected, an error message appears. 5-56 Input Port Dialog Box Finite impulse response filter length Desired length of the baseband-equivalent impulse response for the physical model. The longer the FIR filter in the time-domain, the finer the frequency resolution in the frequency domain. The frequency resolution is approximately equal to 1/ (finite impulse response filter length*sample time). For a graphical representation of this parameter, see “Baseband-Equivalent Modeling” on page A-10. Center frequency (Hz) Center of the modeling frequencies. See the Output Port block reference page for information about calculating the modeling frequencies. 5-57 Input Port Sample time (s) Time interval between consecutive samples of the input signal. Source impedance Source impedance of the RF network described in the physical model to which it connects. Add noise If you select this parameter, noise data in the RF physical blocks that are bracketed by the Input Port block and Output Port block is taken into consideration. If you do not select this block, noise data is ignored. Initial seed Nonnegative integer specifying the initial seed for the random number generator the block uses to generate noise. This parameter becomes visible if you select the Add noise parameter. See Also 5-58 Output Port LC Bandpass Pi Purpose Model LC bandpass pi network Library Ladder Filters sublibrary of the Physical library Description The LC Bandpass Pi block models the LC bandpass pi network described in the block dialog box, in terms of its frequency-dependent S-parameters. For each inductor and capacitor pair in the network, the block first calculates the ABCD-parameters at each frequency contained in the vector of modeling frequencies. For each series pair, A = 1, B = Z, C = 0, and D = 1, where Z is the impedance of the series pair. For each shunt pair, A = 1, B = 0, C = Y, and D = 1, where Y is the admittance of the shunt pair. The LC Bandpass Pi block then cascades the ABCD-parameters for each series and shunt pair at each of the modeling frequencies, and converts the cascaded parameters to S-parameters using the RF Toolbox abcd2s function. See the Output Port block for information about determining the modeling frequencies. The LC bandpass pi network object is a two-port network as shown in the circuit diagram below. C2 L2 L1 C1 C4 L4 L3 C3 [L1, L2, L3, L4, ...] is the value of the 'L' property, and [C1, C2, C3, C4, ...] is the value of the 'C' property. 5-59 LC Bandpass Pi Dialog Box Inductance (H) Vector containing the inductances, in order from source to load, of all inductors in the network. The inductance vector must contain at least three elements. All values must be strictly positive. Capacitance (F) Vector containing the capacitances, in order from source to load, of all capacitors in the network. Its length must be equal to the length of the vector you provide in the Inductance parameter. All values must be strictly positive. Note For information about plotting, see Chapter 3, “Plotting Model Data”. 5-60 LC Bandpass Pi Examples Using a Ladder Filter Block to Filter Gaussian Noise This example provides complex random noise in Gaussian form as input to an LC Bandpass Pi block. A Spectrum Scope block (Signal Processing Blockset) plots the filtered output. The Random Source block (Signal Processing Blockset) produces frame-based output at 512 samples per frame. Its Sample time parameter is set to 1.0e-9. This sample time must match the sample time for the physical part of the model, which you provide in the Input Port block diagram. 5-61 LC Bandpass Pi The Input Port block specifies Finite impulse response filter length as 256, Center frequency as 700.0e6 Hz, Sample time as 1.0e-9, and Source impedance as 50 ohms. The LC Bandpass Pi block provides the inductances for three inductors, in order from source to load, [1.4446e-9, 4.3949e-8, 1.4446e-9]. Similarly, it provides the capacitances for three capacitors [3.5785e-11, 1.1762e-12, 3.5785e-11]. 5-62 LC Bandpass Pi The following plot shows a sample of the baseband-equivalent RF signal generated by this LC Bandpass Pi block. Zero (0) on the frequency axis corresponds to the center frequency specified in the Input Port block. The bandwidth of the frequency spectrum is 1/sample time. You specify the Sample time parameter in the Input Port block. 5-63 LC Bandpass Pi The Axis Properties of the Spectrum Scope block have been adjusted to show the frequencies above and below the carrier. The Minimum Y-limit parameter is -90, and Maximum Y-limit is 0. References [1] Ludwig, Reinhold and Pavel Bretchko, RF Circuit Design: Theory and Applications, Prentice-Hall, 2000. [2] Zverev, Anatol I., Handbook of Filter Synthesis, John Wiley & Sons, 1967. See Also 5-64 General Passive Network, LC Bandpass Tee, LC Bandstop Pi, LC Bandstop Tee, LC Highpass Pi, LC Highpass Tee, LC Lowpass Pi, LC Lowpass Tee, Series RLC, Shunt RLC LC Bandpass Tee Purpose Model LC bandpass tee network Library Ladder Filters sublibrary of the Physical library Description The LC Bandpass Tee block models the LC bandpass tee network described in the block dialog box, in terms of its frequency-dependent S-parameters. For each inductor and capacitor pair in the network, the block first calculates the ABCD-parameters at each frequency contained in the vector of modeling frequencies. For each series pair, A = 1, B = Z, C = 0, and D = 1, where Z is the impedance of the series pair. For each shunt pair, A = 1, B = 0, C = Y, and D = 1, where Y is the admittance of the shunt pair. The LC Bandpass Tee block then cascades the ABCD-parameters for each series and shunt pair at each of the modeling frequencies, and converts the cascaded parameters to S-parameters using the RF Toolbox abcd2s function. See the Output Port block reference page for information about determining the modeling frequencies. The LC bandpass tee network object is a two-port network as shown in the circuit diagram below. L1 C1 L3 L2 C3 C2 L4 C4 [L1, L2, L3, L4, ...] is the value of the 'L' property, and [C1, C2, C3, C4, ...] is the value of the 'C' property. 5-65 LC Bandpass Tee Dialog Box Inductance (H) Vector containing the inductances, in order from source to load, of all inductors in the network. The inductance vector must contain at least three elements. All values must be strictly positive. Capacitance (F) Vector containing the capacitances, in order from source to load, of all capacitors in the network. Its length must be equal to the length of the vector you provide in the Inductance parameter. All values must be strictly positive. Note For information about plotting, see Chapter 3, “Plotting Model Data”. Examples 5-66 See the LC Bandpass Pi block for an example of an LC filter. LC Bandpass Tee References [1] Ludwig, Reinhold and Pavel Bretchko, RF Circuit Design: Theory and Applications, Prentice-Hall, 2000. [2] Zverev, Anatol I., Handbook of Filter Synthesis, John Wiley & Sons, 1967. See Also General Passive Network, LC Bandpass Pi, LC Bandstop Pi, LC Bandstop Tee, LC Highpass Pi, LC Highpass Tee, LC Lowpass Pi, LC Lowpass Tee, Series RLC, Shunt RLC 5-67 LC Bandstop Pi Purpose Model LC bandstop pi network Library Ladder Filters sublibrary of the Physical library Description The LC Bandstop Pi block models the LC bandstop pi network described in the block dialog box, in terms of its frequency-dependent S-parameters. For each inductor and capacitor pair in the network, the block first calculates the ABCD-parameters at each frequency contained in the vector of modeling frequencies. For each series pair, A = 1, B = Z, C = 0, and D = 1, where Z is the impedance of the series pair. For each shunt pair, A = 1, B = 0, C = Y, and D = 1, where Y is the admittance of the shunt pair. The LC Bandstop Pi block then cascades the ABCD-parameters for each series and shunt pair at each of the modeling frequencies, and converts the cascaded parameters to S-parameters using the RF Toolbox abcd2s function. See the Output Port block for information about determining the modeling frequencies. The LC bandstop pi network object is a two-port network as shown in the circuit diagram below. L2 L4 C2 C4 L1 L3 C1 C3 [L1, L2, L3, L4, ...] is the value of the 'L' property, and [C1, C2, C3, C4, ...] is the value of the 'C' property. 5-68 LC Bandstop Pi Dialog Box Inductance (H) Vector containing the inductances, in order from source to load, of all inductors in the network. The inductance vector must contain at least three elements. All values must be strictly positive. Capacitance (F) Vector containing the capacitances, in order from source to load, of all capacitors in the network. Its length must be equal to the length of the vector you provide in the Inductance parameter. All values must be strictly positive. Note For information about plotting, see Chapter 3, “Plotting Model Data”. Examples See the LC Bandpass Pi block for an example of an LC filter. 5-69 LC Bandstop Pi References [1] Ludwig, Reinhold and Pavel Bretchko, RF Circuit Design: Theory and Applications, Prentice-Hall, 2000. [2] Zverev, Anatol I., Handbook of Filter Synthesis, John Wiley & Sons, 1967. See Also 5-70 General Passive Network, LC Bandpass Pi, LC Bandpass Tee, LC Bandstop Tee, LC Highpass Pi, LC Highpass Tee, LC Lowpass Pi, LC Lowpass Tee, Series RLC, Shunt RLC LC Bandstop Tee Purpose Model LC bandstop tee network Library Ladder Filters sublibrary of the Physical library Description The LC Bandstop Tee block models the LC bandstop tee network described in the block dialog box, in terms of its frequency-dependent S-parameters. For each inductor and capacitor pair in the network, the block first calculates the ABCD-parameters at each frequency contained in the vector of modeling frequencies. For each series pair, A = 1, B = Z, C = 0, and D = 1, where Z is the impedance of the series pair. For each shunt pair, A = 1, B = 0, C = Y, and D = 1, where Y is the admittance of the shunt pair. The LC Bandstop Tee block then cascades the ABCD-parameters for each series and shunt pair at each of the modeling frequencies, and converts the cascaded parameters to S-parameters using the RF Toolbox abcd2s function. See the Output Port block for information about determining the modeling frequencies. The LC bandstop tee network object is a two-port network as shown in the circuit diagram below. L1 L3 C1 C3 L2 L4 C2 C4 [L1, L2, L3, L4, ...] is the value of the 'L' property, and [C1, C2, C3, C4, ...] is the value of the 'C' property. 5-71 LC Bandstop Tee Dialog Box Inductance (H) Vector containing the inductances, in order from source to load, of all inductors in the network. The inductance vector must contain at least three elements. All values must be strictly positive. Capacitance (F) Vector containing the capacitances, in order from source to load, of all capacitors in the network. Its length must be equal to the length of the vector you provide in the Inductance parameter. All values must be strictly positive. Note For information about plotting, see Chapter 3, “Plotting Model Data”. Examples 5-72 See the LC Bandpass Pi block for an example of an LC filter. LC Bandstop Tee References [1] Ludwig, Reinhold and Pavel Bretchko, RF Circuit Design: Theory and Applications, Prentice-Hall, 2000. [2] Zverev, Anatol I., Handbook of Filter Synthesis, John Wiley & Sons, 1967. See Also General Passive Network, LC Bandpass Pi, LC Bandpass Tee, LC Bandstop Pi, LC Highpass Pi, LC Highpass Tee, LC Lowpass Pi, LC Lowpass Tee, Series RLC, Shunt RLC 5-73 LC Highpass Pi Purpose Model LC highpass pi network Library Ladder Filters sublibrary of the Physical library Description The LC Highpass Pi block models the LC highpass pi network described in the block dialog box, in terms of its frequency-dependent S-parameters. For each inductor and capacitor in the network, the block first calculates the ABCD-parameters at each frequency contained in the vector of modeling frequencies. For each series circuit, A = 1, B = Z, C = 0, and D = 1, where Z is the impedance of the series circuit. For each shunt, A = 1, B = 0, C = Y, and D = 1, where Y is the admittance of the shunt circuit. The LC Highpass Pi block then cascades the ABCD-parameters for each circuit element at each of the modeling frequencies, and converts the cascaded parameters to S-parameters using the RF Toolbox abcd2s function. See the Output Port block reference page for information about determining the modeling frequencies. The LC highpass pi network object is a two-port network as shown in the circuit diagram below. C2 C1 L1 L2 L3 [L1, L2, L3, ...] is the value of the 'L' property, and [C1, C2, ...] is the value of the 'C' property. 5-74 LC Highpass Pi Dialog Box Inductance (H) Vector containing the inductances, in order from source to load, of all inductors in the network. The inductance vector must contain at least two elements. All values must be strictly positive. Capacitance (F) Vector containing the capacitances, in order from source to load, of all capacitors in the network. Its length must be equal to or one less than the length of the vector you provide in the Inductance parameter. All values must be strictly positive. Note For information about plotting, see Chapter 3, “Plotting Model Data”. Examples See the LC Bandpass Pi block for an example of an LC filter. 5-75 LC Highpass Pi References [1] Ludwig, Reinhold and Pavel Bretchko, RF Circuit Design: Theory and Applications, Prentice-Hall, 2000. [2] Zverev, Anatol I., Handbook of Filter Synthesis, John Wiley & Sons, 1967. See Also 5-76 General Passive Network, LC Bandpass Pi, LC Bandpass Tee, LC Bandstop Pi, LC Bandstop Tee, LC Highpass Tee, LC Lowpass Pi, LC Lowpass Tee, Series RLC, Shunt RLC LC Highpass Tee Purpose Model LC highpass tee network Library Ladder Filters sublibrary of the Physical library Description The LC Highpass Tee block models the LC highpass tee network described in the block dialog box, in terms of its frequency-dependent S-parameters. For each inductor and capacitor in the network, the block first calculates the ABCD-parameters at each frequency contained in the vector of modeling frequencies. For each series circuit, A = 1, B = Z, C = 0, and D = 1, where Z is the impedance of the series circuit. For each shunt, A = 1, B = 0, C = Y, and D = 1, where Y is the admittance of the shunt circuit. The LC Highpass Tee block then cascades the ABCD-parameters for each circuit element at each of the modeling frequencies, and converts the cascaded parameters to S-parameters using the RF Toolbox abcd2s function. See the Output Port block reference page for information about determining the modeling frequencies. The LC highpass tee network object is a two-port network as shown in the circuit diagram below. C3 C2 C1 L1 L2 L3 [L1, L2, L3, ...] is the value of the 'L' property, and [C1, C2, C3, ...] is the value of the 'C' property. 5-77 LC Highpass Tee Dialog Box Inductance (H) Vector containing the inductances, in order from source to load, of all inductors in the network. All values must be strictly positive. The vector cannot be empty. Capacitance (F) Vector containing the capacitances, in order from source to load, of all capacitors in the network. The capacitance vector must contain at least two elements. Its length must be equal to or one greater than the length of the vector you provide in the Inductance parameter. All values must be strictly positive. Note For information about plotting, see Chapter 3, “Plotting Model Data”. Examples 5-78 See the LC Bandpass Pi block for an example of an LC filter. LC Highpass Tee References [1] Ludwig, Reinhold and Pavel Bretchko, RF Circuit Design: Theory and Applications, Prentice-Hall, 2000. [2] Zverev, Anatol I., Handbook of Filter Synthesis, John Wiley & Sons, 1967. See Also General Passive Network, LC Bandpass Pi, LC Bandpass Tee, LC Bandstop Pi, LC Bandstop Tee, LC Highpass Pi, LC Lowpass Pi, LC Lowpass Tee, Series RLC, Shunt RLC 5-79 LC Lowpass Pi Purpose Model LC lowpass pi network Library Ladder Filters sublibrary of the Physical library Description The LC Lowpass Pi block models the LC lowpass pi network described in the block dialog box, in terms of its frequency-dependent S-parameters. For each inductor and capacitor in the network, the block first calculates the ABCD-parameters at each frequency contained in the vector of modeling frequencies. For each series circuit, A = 1, B = Z, C = 0, and D = 1, where Z is the impedance of the series circuit. For each shunt, A = 1, B = 0, C = Y, and D = 1, where Y is the admittance of the shunt circuit. The LC Lowpass Pi block then cascades the ABCD-parameters for each circuit element at each of the modeling frequencies, and converts the cascaded parameters to S-parameters using the RF Toolbox abcd2s function. See the Output Port block reference page for information about determining the modeling frequencies. The LC lowpass pi network object is a two-port network as shown in the circuit diagram below. L1 C1 L2 C2 C3 [L1, L2, ...] is the value of the 'L' property, and [C1, C2, C3, ...] is the value of the 'C' property. 5-80 LC Lowpass Pi Dialog Box Inductance (H) Vector containing the inductances, in order from source to load, of all inductors in the network. All values must be strictly positive. The vector cannot be empty. Capacitance (F) Vector containing the capacitances, in order from source to load, of all capacitors in the network. The capacitance vector must contain at least two elements. Its length must be equal to or one greater than the length of the vector you provide in the Inductance parameter. All values must be strictly positive. Note For information about plotting, see Chapter 3, “Plotting Model Data”. Examples See the LC Bandpass Pi block for an example of an LC filter. 5-81 LC Lowpass Pi References [1] Ludwig, Reinhold and Pavel Bretchko, RF Circuit Design: Theory and Applications, Prentice-Hall, 2000. [2] Zverev, Anatol I., Handbook of Filter Synthesis, John Wiley & Sons, 1967. See Also 5-82 General Passive Network, LC Bandpass Pi, LC Bandpass Tee, LC Bandstop Pi, LC Bandstop Tee, LC Highpass Pi, LC Highpass Tee, LC Lowpass Tee, Series RLC, Shunt RLC LC Lowpass Tee Purpose Model LC lowpass tee network Library Ladders Filters sublibrary of the Physical library Description The LC Lowpass Tee block models the LC lowpass tee network described in the block dialog box in terms of its frequency-dependent S-parameters. For each inductor and capacitor in the network, the block first calculates the ABCD-parameters at each frequency contained in the vector of modeling frequencies. For each series circuit, A = 1, B = Z, C = 0, and D = 1, where Z is the impedance of the series circuit. For each shunt, A = 1, B = 0, C = Y, and D = 1, where Y is the admittance of the shunt circuit. The LC Lowpass Tee block then cascades the ABCD-parameters for each circuit element at each of the modeling frequencies, and converts the cascaded parameters to S-parameters using the RF Toolbox abcd2s function. See the Output Port block reference page for information about determining the modeling frequencies. The LC lowpass tee network object is a two-port network as shown in the circuit diagram below. L2 L1 C1 L3 C2 C3 [L1, L2, L3, ...] is the value of the 'L' property, and [C1, C2, C3, ...] is the value of the 'C' property. 5-83 LC Lowpass Tee Dialog Box Inductance (H) Vector containing the inductances, in order from source to load, of all inductors in the network. The inductance vector must contain at least two elements. All values must be strictly positive. Capacitance (F) Vector containing the capacitances, in order from source to load, of all capacitors in the network. Its length must be equal to or one less than the length of the vector you provide in the Inductance parameter. All values must be strictly positive. Note For information about plotting, see Chapter 3, “Plotting Model Data”. Examples 5-84 See the LC Bandpass Pi block for an example of an LC filter. LC Lowpass Tee References [1] Ludwig, Reinhold and Pavel Bretchko, RF Circuit Design: Theory and Applications, Prentice-Hall, 2000. [2] Zverev, Anatol I., Handbook of Filter Synthesis, John Wiley & Sons, 1967. See Also General Passive Network, LC Bandpass Pi, LC Bandpass Tee, LC Bandstop Pi, LC Bandstop Tee, LC Highpass Pi, LC Highpass Tee, LC Lowpass Pi, Series RLC, Shunt RLC 5-85 Lowpass RF Filter Purpose Standard lowpass RF filters in baseband-equivalent complex form Library Mathematical Description The Lowpass RF Filter block lets you design standard analog lowpass filters, implemented in baseband-equivalent complex form. The following table describes the available design methods. Design Method Description Butterworth The magnitude response of a Butterworth filter is maximally flat in the passband and monotonic overall. Chebyshev I The magnitude response of a Chebyshev I filter is equiripple in the passband and monotonic in the stopband. Chebyshev II The magnitude response of a Chebyshev II filter is monotonic in the passband and equiripple in the stopband. Elliptic The magnitude response of an elliptic filter is equiripple in both the passband and the stopband. Bessel The delay of a Bessel filter is maximally flat in the passband. The block input must be a discrete-time complex signal. Note This block assumes a nominal impedance of 1 ohm. 5-86 Lowpass RF Filter Select the design of the filter from the Design method list in the dialog box. For each design method, the block enables you to specify the filter design parameters shown in the following table. Design Method Filter Design Parameters Butterworth Order, passband edge frequency Chebyshev I Order, passband edge frequency, passband ripple Chebyshev II Order, stopband edge frequency, stopband attenuation Elliptic Order, passband edge frequency, passband ripple, stopband attenuation Bessel Order, passband edge frequency The Lowpass RF Filter block designs the filters using the Signal Processing Toolbox filter design functions buttap, cheb1ap, cheb2ap, ellipap, and besselap. Note Some RF blocks require the sample time to perform baseband modeling calculations. To ensure the accuracy of these calculations, the Input Port block, as well as the mathematical RF blocks, compare the input sample time to the sample time you provide in the mask. If they do not match, or if the input sample time is missing because the blocks are not connected, an error message appears. 5-87 Lowpass RF Filter Dialog Box The parameters displayed in the dialog box vary for different design methods. Only some of these parameters are visible in the dialog box at any one time. Parameters that are tunable can be changed while the model is running. Design method Filter design method. The design method can be Butterworth, Chebyshev I, Chebyshev II, Elliptic, or Bessel. Tunable. Filter order Order of the filter. Passband edge frequency (Hz) Passband edge frequency for Butterworth, Chebyshev I, elliptic, and Bessel designs. Tunable. Stopband edge frequency (Hz) Stopband edge frequency for Chebyshev II designs. Tunable. 5-88 Lowpass RF Filter Passband ripple in dB Passband ripple for Chebyshev I and elliptic designs. Tunable. Stopband attenuation in dB Stopband attenuation for Chebyshev II and elliptic designs. Tunable. Finite impulse response filter length Desired length of the baseband-equivalent impulse response for the filter. Center frequency (Hz) Center of the modeling frequencies. Sample time (s) Time interval between consecutive samples of the input signal. See Also Amplifier, Bandpass RF Filter, Bandstop RF Filter, Highpass RF Filter, Mixer buttap, cheb1ap, cheb2ap, ellipap, besselap (Signal Processing Toolbox) 5-89 Microstrip Transmission Line Purpose Model microstrip transmission line Library Transmission Lines sublibrary of the Physical library Description The Microstrip Transmission Line block models the microstrip transmission line described in the block dialog in terms of its frequency-dependent S-parameters. A microstrip transmission line is shown here in cross-section. Its physical characteristics include the microstrip width (w), the microstrip thickness (t), the substrate height (d), and the relative permittivity constant ( ). The block lets you model the transmission line as a stub or as a stubless line. Stubless Transmission Line If you model a microstrip transmission line as a stubless line, the Microstrip Transmission Line block calculates the frequency-dependent S-parameters using the physical length of the transmission line, D, and the complex propagation constant, k. , where is the attenuation coefficient and is the wave number. The attenuation coefficient is related to the loss, , by 5-90 Microstrip Transmission Line where is the reduction in signal strength, in dB, per unit length. combines both conductor loss and dielectric loss and is derived from the physical parameters specified in the Microstrip Transmission Line block dialog box. The wave number is related to the phase velocity, VP, by where , and is the frequency dependent effective dielectric constant. f is the vector of modeling frequencies determined by the Output Port block. The phase velocity VP is also known as the wave propagation velocity. The Microstrip Transmission Line block normalizes the resulting S-parameters to a reference impedance of 50 ohms. Shunt and Series Stubs If you model the transmission line as a shunt or series stub, the Microstrip Transmission Line block first calculates the ABCD-parameters at each frequency contained in the vector of modeling frequencies. It then uses the abcd2s function to convert the ABCD-parameters to S-parameters. Shunt ABCD-Parameters When you set the Stub mode parameter in the mask dialog box to Shunt, the two-port network consists of a stub transmission line that you can terminate with either a short circuit or an open circuit as shown here. 5-91 Microstrip Transmission Line Zin is the input impedance of the shunt circuit. The ABCD-parameters for the shunt stub are calculated as Series ABCD-Parameters When you set the Stub mode parameter in the mask dialog box to Series, the two-port network consists of a series transmission line that you can terminate with either a short circuit or an open circuit as shown here. Zin is the input impedance of the series circuit. The ABCD-parameters for the series stub are calculated as 5-92 Microstrip Transmission Line Dialog Box Strip width (m) Width of the microstrip transmission line. 5-93 Microstrip Transmission Line Substrate height (m) Thickness of the dielectric on which the microstrip resides. Strip thickness (m) Physical thickness of the microstrip. Relative permittivity constant Relative permittivity of the dielectric expressed as the ratio of the permittivity of the dielectric to permittivity in free space . Conductivity in conductor (S/m) Conductivity of the conductor in siemens per meter. Loss tangent in dielectric Loss angle tangent of the dielectric. Transmission line length (m) Physical length of the transmission line. Stub mode Type of stub. Choices are Not a stub, Shunt, or Series. Termination of stub Stub termination for stub modes Shunt and Series. Choices are Open or Short. This parameter becomes visible only when Stub mode is set to Shunt or Series. Note For information about plotting, see Chapter 3, “Plotting Model Data”. 5-94 References [1] Gupta, K.C., G. Ramesh, I. Bahl, and P. Bhartia, Microstrip Lines and Slotlines, Second Edition, Artech House, 1996. pp. 102-109. See Also Coaxial Transmission Line, Coplanar Waveguide Transmission Line, General Passive Network, Transmission Line, Parallel-Plate Transmission Line, Two-Wire Transmission Line Mixer Purpose Complex baseband model of mixer with phase noise Library Mathematical Description The Mixer block generates a complex baseband model of a mixer, with phase noise whose spectrum is characterized by a 1/f slope. The level of the spectrum is specified by the noise power contained in one hertz bandwidth offset from the carrier by a certain frequency. Note This block assumes a nominal impedance of 1 ohm. The block applies the phase noise to the signal as follows: 1 Generates additive white Gaussian noise (AWGN) and filters it with a digital filter. 2 Adds the resulting noise to the angle component of the input signal. You can view the block’s implementation of phase noise by right-clicking the block and selecting Look under mask from the pop-up menu. This displays the following figure. You can view the construction of the Noise Source subsystem by double-clicking it. 5-95 Mixer Note Some RF blocks require the sample time to perform baseband modeling calculations. To ensure the accuracy of these calculations, the Input Port block, as well as the mathematical RF blocks, compare the input sample time to the sample time you provide in the mask. If they do not match, or if the input sample time is missing because the blocks are not connected, an error message appears. Dialog Box You can change parameters that are marked as tunable while the model is running. Conversion loss (dB) Scalar specifying the conversion loss for the mixer. Tunable. Phase noise level (dBc/Hz) Scalar specifying the phase noise level in decibels relative to the carrier, per hertz. Tunable. Frequency offset (Hz) Scalar specifying the frequency offset. Tunable. 5-96 Mixer Initial seed Nonnegative integer specifying the initial seed for the random number generator the block uses to generate noise. References [1] Kasdin, N.J., “Discrete Simulation of Colored Noise and Stochastic Processes and 1/(f^alpha); Power Law Noise Generation,” The Proceedings of the IEEE, May, 1995, Vol. 83, No. 5. See Also Amplifier, Bandpass RF Filter, Bandstop RF Filter, Highpass RF Filter, Lowpass RF Filter 5-97 Output Port Purpose Connection block from RF physical blocks to Simulink environment Library Input/Output Ports sublibrary of the Physical library Description The Output Port block produces the baseband-equivalent time-domain response of an input signal traveling through a series of RF physical components. The Output Port block 1 Partitions the RF physical components into linear and nonlinear subsystems. 2 Extracts the complex impulse response of the linear subsystem for baseband-equivalent modeling of the RF linear system. 3 Extracts the nonlinear AMAM/AMPM modeling for RF nonlinearity. The Output Port block also serves as a connecting port from an RF physical part of the model to the Simulink, or mathematical, part of the model. For more information about how the Output Port block converts the RF Blockset physical modeling environment signals to mathematical Simulink signals, see “Converting to and from Simulink Signals” on page A-15. For more information about connecting mathematical and physical parts of a model, see Chapter 2, “Modeling an RF System”. Note Some RF blocks require the sample time to perform baseband modeling calculations. To ensure the accuracy of these calculations, the Input Port block, as well as the mathematical RF blocks, compare the input sample time to the sample time you provide in the mask. If they do not match, or if the input sample time is missing because the blocks are not connected, an error message appears. Linear Subsystem For the linear subsystem, the Output Port block uses the Input Port block parameters and the interpolated S-parameters calculated by each 5-98 Output Port of the cascaded physical blocks to calculate the baseband-equivalent impulse response. Specifically, it 1 Determines the modeling frequencies f as an N-element vector. The modeling frequencies are a function of the center frequency fc, the sample time ts, and the finite impulse response filter length N, all of which you specify in the Input Port block dialog box. The nth element of f, fn, is given by fn = fmin + n −1 n = 1,..., N ts N where fmin = fc − 1 2ts 2 Calculates the passband transfer function for the frequency range as H( f ) = VL ( f ) VS ( f ) where VS and VL are the source and load voltages, and f represents the modeling frequencies. More specifically, H( f ) = S21 * (1 + Γ l ) * (1 − Γ s ) 2 * (1 − S22 * Γ l ) (1 − Γin * Γ s ) 5-99 Output Port where Γl = Zl − Zo Zl + Zo Γs = Zs − Zo Zs + Zo ⎛ ⎞ Γl Γin = S11 + ⎜⎜ S12 * S21 * ⎟ (1 − S22 * Γ l ) ⎟⎠ ⎝ and • ZS is the source impedance. • ZL is the load impedance. • Sij are the S-parameters of a two-port network. 5-100 Output Port The passband transfer function is shown in the following figure. Specify these parameters in the Input Port dialog box: Passband Spectrum of a Modulated RF Carrier Finite impulse response filter length = N Center frequency = fc Sample time = ts Magnitude 1/(ts*N) Index = n Frequency fmin Index = 1 fc 1/ts fn fmax Index = N 3 Translates the passband transfer function to baseband as , where fc is the specified center frequency. 5-101 Output Port The baseband transfer function is shown in the following figure. Baseband-Equivalent Spectrum Magnitude Centered at zero 1/2ts -1/2ts Frequency 1/ts 4 Obtains the baseband-equivalent impulse response by calculating the inverse FFT of the baseband transfer function. For faster simulation, the block calculates the IFFT using the next power of 2 greater than the specified finite impulse response filter length. Then, it truncates the impulse response to a length equal to the filter length specified. For the linear subsystem, the Output Port block uses the calculated impulse response as input to the Signal Processing Blockset Digital Filter block to determine the output. Nonlinear Subsystem The nonlinear subsystem is implemented by AM/AM and AM/PM nonlinear models, as shown in the figure below. 5-102 Output Port The nonlinearities of AM/AM and AM/PM conversions are extracted from the power data of an amplifier or mixer by the equations where AMin is the AM of the input voltage, AMout and PMout are the AM and PM of the output voltage, Rs, is the source resistance (50 ohms), Rl is the load resistance (50 ohms), Pin is the input power, Pout is the output power, and Phase is the phase shift between the input and output voltage. Note You can provide power data via a .amp file. See “AMP File Format” in the RF Toolbox documentation for information about this format. 5-103 Output Port The following figure shows the original power data of an amplifier. 5-104 Output Port This figure shows the extracted AM/AM nonlinear conversion. Dialog Box Load impedance Load impedance of the RF network described in the physical model to which it connects. 5-105 Output Port Plot the selected parameters of the RF system This parameter and the associated plotting parameters shown below become visible if you display the Output Port mask after you run the model. For more information about plotting, see Chapter 3, “Plotting Model Data”. See Also Input Port s2y (RF Toolbox) 5-106 Parallel-Plate Transmission Line Purpose Model parallel-plate transmission line Library Transmission Lines sublibrary of the Physical library Description The Parallel-Plate Transmission Line block models the parallel-plate transmission line described in the block dialog box in terms of its frequency-dependent S-parameters. A parallel-plate transmission line is shown here in cross-section. Its physical characteristics include the plate width and the plate separation . The block lets you model the transmission line as a stub or as a stubless line. Stubless Transmission Line If you model a parallel-plate transmission line as a stubless line, the Parallel-Plate Transmission Line block calculates the frequency-dependent S-parameters using the physical length of the transmission line, D, and the complex propagation constant, k. k can be expressed in terms of the resistance (R), inductance (L), conductance (G), and capacitance (C) per unit length (meters) as 5-107 Parallel-Plate Transmission Line where In these equations, is the conductivity in the conductor and is the conductivity in the dielectric. is the permeability of the dielectric, is its permittivity, and skin depth is calculated as . f is the vector of modeling frequencies for the specified parameters. See the Output Port block reference page for information about determining the modeling frequencies. The Parallel-Plate Transmission Line block normalizes the resulting S-parameters to a reference impedance of 50 ohms. Shunt and Series Stubs If you model the transmission line as a shunt or series stub, the Parallel-Plate Transmission Line block first calculates the ABCD-parameters at each frequency contained in the vector of modeling frequencies. It then uses the abcd2s function to convert the ABCD-parameters to S-parameters. Shunt ABCD-Parameters When you set the Stub mode parameter in the mask dialog box to Shunt, the two-port network consists of a stub transmission line that you can terminate with either a short circuit or an open circuit as shown here. 5-108 Parallel-Plate Transmission Line Zin is the input impedance of the shunt circuit. The ABCD-parameters for the shunt stub are calculated as Series ABCD-Parameters When you set the Stub mode parameter in the mask dialog box to Series, the two-port network consists of a series transmission line that you can terminate with either a short circuit or an open circuit as shown here. Zin is the input impedance of the series circuit. The ABCD-parameters for the series stub are calculated as 5-109 Parallel-Plate Transmission Line Dialog Box Plate width (m) Physical width of the parallel-plate transmission line. 5-110 Parallel-Plate Transmission Line Plate separation (m) Thickness of the dielectric separating the plates. Relative permeability constant Relative permeability of the dielectric expressed as the ratio of the permeability of the dielectric to permeability in free space . Relative permittivity constant Relative permittivity of the dielectric expressed as the ratio of the permittivity of the dielectric to permittivity in free space . Conductivity in conductor (S/m) Conductivity of the conductor in siemens per meter. Conductivity in dielectric (S/m) Conductivity of the dielectric in siemens per meter. Transmission line length (m) Physical length of the transmission line. Stub mode Type of stub. Choices are Not a stub, Shunt, or Series. Termination of stub Stub termination for stub modes Shunt and Series. Choices are Open or Short. This parameter becomes visible only when Stub mode is set to Shunt or Series. Note For information about plotting, see Chapter 3, “Plotting Model Data”. References [1] Ludwig, Reinhold and Pavel Bretchko, RF Circuit Design: Theory and Applications, Prentice-Hall, 2000. See Also Coaxial Transmission Line, Coplanar Waveguide Transmission Line, General Passive Network, Transmission Line, Microstrip Transmission Line, Two-Wire Transmission Line 5-111 RLCG Transmission Line Purpose Model RLCG transmission line Library Transmission Lines sublibrary of the Physical library Description The RLCG Transmission Line block models the RLCG transmission line described in the block dialog box in terms of its frequency-dependent resistance, inductance, capacitance, and conductance. The transmission line, which can be lossy or lossless, is treated as a two-port linear network. I(z) I(z) L R V(z) G V(z) z z where C . The block lets you model the transmission line as a stub or as a stubless line. Stubless Transmission Line If you model a RLCG transmission line as a stubless line, the RLCG Transmission Line block calculates the frequency-dependent S-parameters using the physical length of the transmission line, D, and the complex propagation constant, k. 5-112 RLCG Transmission Line k can be expressed in terms of the resistance (R), inductance (L), conductance (G), and capacitance (C) per unit length (meters) as The RLCG Transmission Line block normalizes the resulting S-parameters to a reference impedance of 50 ohms. Shunt and Series Stubs If you model the transmission line as a shunt or series stub, the RLCG Transmission Line block first calculates the ABCD-parameters at each frequency contained in the vector of modeling frequencies. It then uses the abcd2s function to convert the ABCD-parameters to S-parameters. Shunt ABCD-Parameters When you set the Stub mode parameter in the mask dialog box to Shunt, the two-port network consists of a stub transmission line that you can terminate with either a short circuit or an open circuit as shown here. Zin is the input impedance of the shunt circuit. The ABCD-parameters for the shunt stub are calculated as 5-113 RLCG Transmission Line Series ABCD-Parameters When you set the Stub mode parameter in the mask dialog box to Series, the two-port network consists of a series transmission line that you can terminate with either a short circuit or an open circuit as shown here. Zin is the input impedance of the series circuit. The ABCD-parameters for the series stub are calculated as 5-114 RLCG Transmission Line Dialog Box Resistance per length (ohms/m) Vector of resistance values in ohms per meter. Inductance per length (H/m) Vector of inductance values in henries per meter. Capacitance per length (F/m) Vector of capacitance values in farads per meter. Conductance per length (S/m) Vector of conductance values in siemens per meter. 5-115 RLCG Transmission Line Frequency (Hz) Vector of frequency values at which the resistance, inductance, capacitance, and conductance values are known. Interpolation method Specify the interpolation method the block uses to calculate the parameter values at the modeling frequencies. Your choices are Linear, Spline, or Cubic. Transmission line length (m) Physical length of the transmission line. Stub mode Type of stub. Your choices are Not a stub, Shunt, or Series. Termination of stub Stub termination for stub modes Shunt and Series. Choices are Open or Short. This parameter becomes visible only when Stub mode is set to Shunt or Series. Note For information about plotting, see Chapter 3, “Plotting Model Data”. References [1] Ludwig, Reinhold and Pavel Bretchko, RF Circuit Design: Theory and Applications, Prentice-Hall, 2000. See Also Coaxial Transmission Line, Coplanar Waveguide Transmission Line, General Passive Network, Parallel-Plate Transmission Line, Transmission Line, Microstrip Transmission Line, Two-Wire Transmission Line 5-116 S-Parameters Amplifier Purpose Model nonlinear amplifier using its S-parameters Library Amplifiers sublibrary of the Physical library Description The S-Parameters Amplifier block models the nonlinear amplifier described in the block dialog box, in terms of its frequency-dependent S-parameters, their frequencies, and the reference impedance of the S-parameters. The block also takes into account the IP3 value and the noise figure. In the S-parameters field of the block dialog box, provide the S-parameters for each of M frequencies as a 2-by-2-by-M array. In the Frequency field, specify the frequencies for the S-parameters as an M-element vector. The elements of the frequencies vector must be in the same order as the S-parameters. All frequencies must be positive. For example, the following figure shows the correspondence between the S-parameters array and the vector of frequencies. The S-Parameters Amplifier block interpolates the given S-parameters to determine their values at the modeling frequencies. The modeling frequencies are determined by the Output Port block. See Appendix A, “RF Blockset Algorithms” for more details. 5-117 S-Parameters Amplifier Dialog Box S-Parameters S-parameters for a nonlinear amplifier in a 2-by-2-by-M array. M is the number of S-parameters. Frequency (Hz) Frequencies of the S-parameters as an M-element vector. The order of the frequencies must correspond to the order of the S-parameters in S-Parameters. All frequencies must be positive. 5-118 S-Parameters Amplifier Reference impedance Reference impedance of the S-parameters as a scalar or a vector of length M. The value of this parameter can be real or complex. If you provide a scalar, that value is applied to all frequencies. Interpolation method Method used to interpolate the given S-parameters over the range of frequencies. Interpolation can be Cubic, Linear (default), or Spline. IP3 type Type of third-order intercept point. The value can be IIP3 (input intercept point) or OIP3 (output intercept point). IIP3 (dBm) Input power intercept point as a scalar value. This field becomes visible if you select IIP3 as the IP3 type. OIP3 (dBm) Output power intercept point as a scalar value. This field becomes visible if you select OIP3 as the IP3 type. Noise figure (dB) Scalar ratio of the available signal-to-noise power ratio at the input to the available signal-to-noise power ratio at the output, ((Si/Ni)/(So/No)). Note For information about plotting, see Chapter 3, “Plotting Model Data”. Examples Plotting Parameters with the S-Parameters Amplifier Block The following example specifies S-parameters [-.33+.71i, -.03i; 8.12-.02i, -.37-.37i] and [0.16+.20i, -.03-.04i; 7.71-8.04i, -.70-.12i] at frequencies 2.0 GHz and 2.1 GHz respectively, with a reference impedance of 50 ohms. It uses the MATLAB cat function to create the 2-by-2-by-2 S-parameters array. 5-119 S-Parameters Amplifier cat(3,[-.33+0.71i, -.03i; 8.12-.02i, -.37-.37i],... [ .16+0.20i, -.03-.04i; 7.71-8.04i, -.70-.12i]) The plot parameters in the dialog box request an X-Y Plane plot of the S11 parameters in the frequency range 1.8 to 2.3 GHz. 5-120 S-Parameters Amplifier See Also General Amplifier, Output Port, Y-Parameters Amplifier, Z-Parameters Amplifier interp1 (MATLAB) 5-121 S-Parameters Mixer Purpose Model mixer using its S-parameters Library Mixer sublibrary of the Physical library Description The S-Parameters Mixer block models the nonlinear mixer described in the block dialog box, in terms of its frequency-dependent S-parameters, their frequencies, and the reference impedance of the S-parameters. The block also takes phase noise into account. The S21 parameter values describe the conversion gain as a function of frequency, referred to the mixer input frequency. The other S-parameters also refer to the mixer input frequency. The S-Parameters Mixer block interpolates the given S-parameters to determine their values at the modeling frequencies. The modeling frequencies are determined by the Output Port block. See Appendix A, “RF Blockset Algorithms” for more details. The RF Blockset computes the normalized reflected amplitude at the mixer input ( Er1 ) and at the mixer output ( Er2 ) from the interpolated S-parameters as Er1 ( fin ) = S11 ( fin ) Ei1 ( fin ) + S12 ( fin ) Ei2 ( fout ) Er 2 ( fout ) = S21 ( fin ) Ei1 ( fin ) + S22 ( fin ) Ei2 ( fout ) where • fin and f out are the mixer input and output frequencies, respectively. • Ei1 and Ei2 are the normalized incident amplitudes at the mixer input and output, respectively. The interpolated S21 parameter values describe the conversion gain as a function of frequency, referred to the mixer input frequency. 5-122 S-Parameters Mixer Dialog Box S-Parameters S-parameters for a nonlinear mixer in a 2-by-2-by-M array. M is the number of S-parameters. 5-123 S-Parameters Mixer Frequency (Hz) Frequencies of the S-parameters as an M-element vector. The order of the frequencies must correspond to the order of the S-parameters in S-Parameters. All frequencies must be positive. The following figure shows the correspondence between the S-parameters array and the vector of frequencies. Reference impedance Reference impedance of the S-parameters as a scalar or a vector of length M. The value of this parameter can be real or complex. If you provide a scalar, that value is applied to all frequencies. Interpolation method Method used to interpolate the given S-parameters over the range of frequencies. Interpolation can be Linear (default), Spline, or Cubic. Type Type of mixer. Choices are Downconverter (default) and Upconverter. LO frequency (Hz) Local oscillator frequency. If you choose Downconverter, the RF Blockset computes the mixer output frequency, f out , from the mixer input frequency, f in , and the local oscillator frequency, f lo , . If you choose Upconverter, . as 5-124 S-Parameters Mixer Note The mixer output frequency must be positive. This means that if you choose a downconverting mixer, than fin must be greater flo . Otherwise, an error appears. IP3 type Type of third-order intercept point. The value can be IIP3 (input intercept point) or OIP3 (output intercept point). IIP3 (dBm) Input power intercept point as a scalar value. This field becomes visible if you select IIP3 as the IP3 type. OIP3 (dBm) Output power intercept point as a scalar value. This field becomes visible if you select OIP3 as the IP3 type. Noise figure (dB) Scalar ratio of the available signal-to-noise power ratio at the input to the available signal-to-noise power ratio at the output (Si/Ni)/(So/No). Phase noise frequency offset (Hz) Vector specifying the frequency offset. Phase noise level (dBc/Hz) Vector specifying the phase noise level. Note For information about plotting the mixer parameters, see Chapter 3, “Plotting Model Data”. See Also General Mixer, Output Port, Y-Parameters Mixer, Z-Parameters Mixer 5-125 S-Parameters Passive Network Purpose Model passive network using its S-parameters Library Black Box Elements sublibrary of the Physical library Description The S-Parameters Passive Network block models the two-port passive network described in the block dialog box, in terms of its S-parameters, their frequencies, and the reference impedance of the S-parameters. In the S-Parameters field of the block dialog box, provide the S-parameters for each of M frequencies as a 2-by-2-by-M array. In the Frequency field, specify the frequencies for the S-parameters as an M-element vector. The elements of the vector must be in the same order as the S-parameters. All frequencies must be positive. For example, the following figure shows the correspondence between the S-parameters array and the vector of frequencies. The S-Parameters Passive Network block interpolates the given S-parameters to determine their values at the modeling frequencies. The modeling frequencies are determined by the Output Port block. See Appendix A, “RF Blockset Algorithms” for more details. 5-126 S-Parameters Passive Network Dialog Box S-Parameters S-parameters for a two-port passive network in a 2-by-2-by-M array. M is the number of S-parameters. Frequency (Hz) Frequencies of the S-parameters as an M-element vector. The order of the frequencies must correspond to the order of the S-parameters in S-Parameters. All frequencies must be positive. Reference impedance Reference impedance of the network as a scalar or a vector of length M. The value of this parameter can be real or complex. If you provide a scalar, that value is applied to all frequencies. 5-127 S-Parameters Passive Network Interpolation method Method used to interpolate the given S-parameters over the range of frequencies. Interpolation can be Cubic, Linear (default), or Spline. Note For information about plotting, see Chapter 3, “Plotting Model Data”. Examples Plotting Parameters with the S-Parameters Passive Network Block The following example specifies S-parameters [-.96-.23i, .03-.12i; .03-.12i, -.96-.23i] and [-.96-.11i, .02-.21i; .02-.21i, -.96-.11i] at frequencies 2.0 GHz and 2.1 GHz respectively. It uses the MATLAB cat function to create the 2-by-2-by-2 S-parameters array. cat(3,[-.96-.23i, .03-.12i; .03-.12i, -.96-.23i],... [-.96-.11i, .02-.21i; .02-.21i, -.96-.11i]) You could also use the MATLAB reshape function. The following statement produces the same result as the one shown above. reshape([-.96-.23i;.03-.12i;.03-.12i;-.96-.23i;... -.96-.11i;.02-.21i;.02-.21i;-.96-.11i],2,2,2) 5-128 S-Parameters Passive Network The plot parameters in the dialog box request an X-Y Plane plot of the S21 S-parameter magnitudes, in decibels, in the frequency range 1.9 to 2.2 GHz. 5-129 S-Parameters Passive Network See Also General Circuit Element, General Passive Network, Output Port, Y-Parameters Passive Network, Z-Parameters Passive Network interp1 (MATLAB) 5-130 Series RLC Purpose Model series RLC network Library Ladders Filters sublibrary of the Physical library Description The Series RLC block models the series RLC network described in the block dialog box, in terms of its frequency-dependent S-parameters. For the given resistance, inductance, and capacitance, the block first calculates the ABCD-parameters at each frequency contained in the vector of modeling frequencies, and then converts the ABCD-parameters to S-parameters using the RF Toolbox abcd2s function. See the Output Port block reference page for information about determining the modeling frequencies. For this circuit, A = 1, B = Z, C = 0, and D = 1, where and . The series RLC object is a two-port network as shown in the circuit diagram below. R L C 5-131 Series RLC Dialog Box Resistance (ohms) Scalar value for the resistance. The value must be nonnegative. Inductance (H) Scalar value for the inductance. The value must be nonnegative. Capacitance (F) Scalar value for the capacitance. The value must be nonnegative. 5-132 Series RLC Note For information about plotting, see Chapter 3, “Plotting Model Data”. See Also General Passive Network, LC Bandpass Pi, LC Bandpass Tee, LC Bandstop Pi, LC Bandstop Tee, LC Highpass Pi, LC Highpass Tee, LC Lowpass Pi, LC Lowpass Tee, Shunt RLC 5-133 Shunt RLC Purpose Model shunt RLC network Library Ladders Filters sublibrary of the Physical library Description The Shunt RLC block models the shunt RLC network described in the block dialog box, in terms of its frequency-dependent S-parameters. For the given resistance, inductance, and capacitance, the block first calculates the ABCD-parameters at each frequency contained in the vector of modeling frequencies, and then converts the ABCD-parameters to S-parameters using the RF Toolbox abcd2s function. See the Output Port block reference page for information about determining the modeling frequencies. For this circuit, A = 1, B = 0, C = Y, and D = 1, where and . The shunt RLC object is a two-port network as shown in the circuit diagram below. R 5-134 L C Shunt RLC Dialog Box Resistance (ohms) Scalar value for the resistance. The value must be nonnegative. Inductance (H) Scalar value for the inductance. The value must be nonnegative. Capacitance (F) Scalar value for the capacitance. The value must be nonnegative. 5-135 Shunt RLC Note For information about plotting, see Chapter 3, “Plotting Model Data”. See Also 5-136 General Passive Network, LC Bandpass Pi, LC Bandpass Tee, LC Bandstop Pi, LC Bandstop Tee, LC Highpass Pi, LC Highpass Tee, LC Lowpass Pi, LC Lowpass Tee, Series RLC Transmission Line Purpose Model general transmission line Library Transmission Lines sublibrary of the Physical library Description The Transmission Line block models the transmission line described in the block dialog box in terms of its physical parameters. The transmission line, which can be lossy or lossless, is treated as a two-port linear network. The block enables you to model the transmission line as a stub or as a stubless line. Stubless Transmission Line If you model the transmission line as a stubless line, the Transmission Line block calculates the frequency-dependent S-parameters using the physical length of the transmission line, D, and the complex propagation constant, k. , where is the attenuation coefficient and is the wave number. The attenuation coefficient is related to the loss, , by and the wave number is related to the phase velocity, VP, by 5-137 Transmission Line where is the vector of modeling frequencies determined by the Output Port block. The phase velocity VP is also known as the wave propagation velocity. The Transmission Line block normalizes the resulting S-parameters to a reference impedance of 50 ohms. Shunt and Series Stubs If you model the transmission line as a shunt or series stub, the Transmission Line block first calculates the ABCD-parameters at each frequency contained in the vector of modeling frequencies. It then uses the abcd2s function to convert the ABCD-parameters to S-parameters. Shunt ABCD-Parameters When you set the Stub mode parameter in the mask dialog box to Shunt, the two-port network consists of a stub transmission line that you can terminate with either a short circuit or an open circuit as shown here. Zin is the input impedance of the shunt circuit. The ABCD-parameters for the shunt stub are calculated as 5-138 Transmission Line Series ABCD-Parameters When you set the Stub mode parameter in the mask dialog box to Series, the two-port network consists of a series transmission line that you can terminate with either a short circuit or an open circuit as shown here. Zin is the input impedance of the series circuit. The ABCD-parameters for the series stub are calculated as 5-139 Transmission Line Dialog Box Characteristic impedance Characteristic impedance of the transmission line. The value can be complex. Phase velocity (m/s) Propagation velocity of a uniform plane wave on the transmission line. Loss (dB/m) Reduction in strength of the signal as it travels over the transmission line. Must be positive. 5-140 Transmission Line Transmission line length (m) Physical length of the transmission line. Stub mode Type of stub. Choices are Not a stub, Shunt, or Series. Termination of stub Stub termination for stub modes Shunt and Series. Choices are Open or Short. This parameter becomes visible only when Stub mode is set to Shunt or Series. Note For information about plotting, see Chapter 3, “Plotting Model Data”. References [1] Ludwig, Reinhold and Pavel Bretchko, RF Circuit Design: Theory and Applications, Prentice-Hall, 2000. See Also Coaxial Transmission Line, Coplanar Waveguide Transmission Line, General Passive Network, Microstrip Transmission Line, Parallel-Plate Transmission Line, Two-Wire Transmission Line 5-141 Two-Wire Transmission Line Purpose Model two-wire transmission line Library Transmission Lines sublibrary of the Physical library Description The Two-Wire Transmission Line block models the two-wire transmission line described in the block dialog box in terms of its frequency-dependent S-parameters. A parallel-plate transmission line is shown here in cross-section. Its physical characteristics include the radius of the wires a, and the distance between the wire centers D. The block enables you to model the transmission line as a stub or as a stubless line. Stubless Transmission Line If you model a parallel-plate transmission line as a stubless line, the Two-Wire Transmission Line block calculates the frequency-dependent S-parameters using the physical length of the transmission line, D, and the complex propagation constant, k. k can be expressed in terms of the resistance (R), inductance (L), conductance (G), and capacitance (C) per unit length (meters) as 5-142 Two-Wire Transmission Line where In these equations, is the conductivity in the conductor and is the conductivity in the dielectric. is the permeability of the dielectric, is its permittivity, and skin depth is calculated as . f is the vector of modeling frequencies for the specified parameters. See the Output Port block reference page for information about determining the modeling frequencies. The Two-Wire Transmission Line block normalizes the resulting S-parameters to a reference impedance of 50 ohms. Shunt and Series Stubs If you model the transmission line as a shunt or series stub, the Two-Wire Transmission Line block first calculates the ABCD-parameters at each frequency contained in the vector of modeling frequencies. It then uses the abcd2s function to convert the ABCD-parameters to S-parameters. Shunt ABCD-Parameters When you set the Stub mode parameter in the mask dialog box to Shunt, the two-port network consists of a stub transmission line that you can terminate with either a short circuit or an open circuit as shown here. 5-143 Two-Wire Transmission Line Zin is the input impedance of the shunt circuit. The ABCD-parameters for the shunt stub are calculated as Series ABCD-Parameters When you set the Stub mode parameter in the mask dialog box to Series, the two-port network consists of a series transmission line that you can terminate with either a short circuit or an open circuit as shown here. Zin is the input impedance of the series circuit. The ABCD-parameters for the series stub are calculated as 5-144 Two-Wire Transmission Line Dialog Box Wire radius (m) Radius of the conducting wires of the two-wire transmission line. 5-145 Two-Wire Transmission Line Wire separation (m) Physical distance between the wires. Relative permeability constant Relative permeability of the dielectric expressed as the ratio of the permeability of the dielectric to permeability in free space . Relative permittivity constant Relative permittivity of the dielectric expressed as the ratio of the permittivity of the dielectric to permittivity in free space . Conductivity in conductor (S/m) Conductivity of the conductor in siemens per meter. Conductivity in dielectric (S/m) Conductivity of the dielectric in siemens per meter. Transmission line length (m) Physical length of the transmission line. Stub mode Type of stub. Choices are Not a stub, Shunt, or Series. Termination of stub Stub termination for stub modes Shunt and Series. Choices are Open or Short. This parameter becomes visible only when Stub mode is set to Shunt or Series. Note For information about plotting, see Chapter 3, “Plotting Model Data”. References [1] Ludwig, Reinhold and Pavel Bretchko, RF Circuit Design: Theory and Applications, Prentice-Hall, 2000. See Also Coaxial Transmission Line, Coplanar Waveguide Transmission Line, General Passive Network, Transmission Line, Microstrip Transmission Line, Parallel-Plate Transmission Line 5-146 Y-Parameters Amplifier Purpose Model nonlinear amplifier using its Y-parameters Library Amplifiers sublibrary of the Physical library Description The Y-Parameters Amplifier block models the nonlinear amplifier described in the block dialog box, in terms of its frequency-dependent Y-parameters and their frequencies. The block also takes into account the IP3 value and the noise figure. In the Y-Parameters field of the block dialog box, provide the Y-parameters for each of M frequencies as a 2-by-2-by-M array. In the Frequency field, specify the frequencies for the Y-parameters as an M-element vector. The elements of the frequencies vector must be in the same order as the Y-parameters. All frequencies must be positive. For example, the following figure shows the correspondence between the Y-parameters array and the vector of frequencies. The Y-Parameters Amplifier block uses the RF Toolbox y2s function to convert the Y-parameters to S-parameters, and then interpolates the resulting S-parameters to determine their values at the modeling frequencies. The modeling frequencies are determined by the Output Port block. See Appendix A, “RF Blockset Algorithms” for more details. 5-147 Y-Parameters Amplifier Dialog Box Y-Parameters Y-parameters for a nonlinear amplifier in a 2-by-2-by-M array. M is the number of Y-parameters. Frequency (Hz) Frequencies of the Y-parameters as an M-element vector. The order of the frequencies must correspond to the order of the Y-parameters in Y-Parameters. All frequencies must be positive. Interpolation method Method used to interpolate the S-parameters, as derived from the Y-parameters, over the range of frequencies. Interpolation can be Cubic, Linear (default), or Spline. 5-148 Y-Parameters Amplifier IP3 type Type of third-order intercept point. The value can be IIP3 (input intercept point) or OIP3 (output intercept point). IIP3 (dBm) Input power intercept point as a scalar value. This field becomes visible if you select IIP3 as the IP3 type. OIP3 (dBm) Output power intercept point as a scalar value. This field becomes visible if you select OIP3 as the IP3 type. Noise figure (dB) Scalar ratio of the available signal-to-noise power ratio at the input to the available signal-to-noise power ratio at the output, (Si/Ni)/(So/No). Note For information about plotting, see Chapter 3, “Plotting Model Data”. Examples Plotting Parameters with the Y-Parameters Amplifier Block The following example specifies Y-parameters [-.06+.58i, -.08i; 1.14-1.82i, -.07+.28i] and [.02-.21i, 0.03i; -.21+.72i, .03-.11i] at frequencies 2.0 GHz and 2.1 GHz respectively. It uses the MATLAB cat function to create the 2-by-2-by-2 Y-parameters array cat(3,[-.06+.58i, -.08i; 1.14-1.82i, -.07+.28i],... [ .02-.21i, 0.03i; -.21+.72i, .03-.11i]) 5-149 Y-Parameters Amplifier The plot parameters in the dialog box request an X-Y plane plot of the S11 parameters in the frequency range 1.8 to 2.3 GHz. 5-150 Y-Parameters Amplifier See Also General Amplifier, Output Port, S-Parameters Amplifier, Z-Parameters Amplifier y2s (RF Toolbox) interp1 (MATLAB) 5-151 Y-Parameters Mixer Purpose Model mixer using its Y-parameters Library Mixer sublibrary of the Physical library Description The Y-Parameters Mixer block models the nonlinear mixer described in the block dialog box in terms of its frequency-dependent Y-parameters, their frequencies, and the reference impedance of the Y-parameters. The block also takes phase noise into account. The Y-parameter values all refer to the mixer input frequency. The Y-Parameters Mixer block uses the RF Toolbox y2s function to convert the Y-parameters to S-parameters and then interpolates the resulting S-parameters to determine their values at the modeling frequencies. The modeling frequencies are determined by the Output Port block. See Appendix A, “RF Blockset Algorithms” for more details. The RF Blockset computes the normalized reflected amplitude at the mixer input ( Er1 ) and at the mixer output ( Er2 ) from the interpolated S-parameters as Er1 ( fin ) = S11 ( fin ) Ei1 ( fin ) + S12 ( fin ) Ei2 ( fout ) Er 2 ( fout ) = S21 ( fin ) Ei1 ( fin ) + S22 ( fin ) Ei2 ( fout ) where • fin and f out are the mixer input and output frequencies, respectively. • Ei1 and Ei2 are the normalized incident amplitudes at the mixer input and output, respectively. The interpolated S21 parameter values describe the conversion gain as a function of frequency, referred to the mixer input frequency. 5-152 Y-Parameters Mixer Dialog Box Y-Parameters Y-parameters for a nonlinear mixer in a 2-by-2-by-M array. M is the number of Y-parameters. 5-153 Y-Parameters Mixer Frequency (Hz) Frequencies of the Y-parameters as an M-element vector. The order of the frequencies must correspond to the order of the Y-parameters in Y-Parameters. All frequencies must be positive. The following figure shows the correspondence between the Y-parameters array and the vector of frequencies. Interpolation method Method used to interpolate the S-parameters, as derived from the Y-parameters, over the range of frequencies. Interpolation can be Linear (default), Spline, or Cubic. Type Type of mixer. Choices are Downconverter (default) and Upconverter. LO frequency (Hz) Local oscillator frequency. If you choose Downconverter, the RF Blockset computes the mixer output frequency, f out , from the mixer input frequency, f in , and the local oscillator frequency, f lo , . If you choose Upconverter, . as 5-154 Y-Parameters Mixer Note The mixer output frequency must be positive. This means that if you choose a downconverting mixer, than fin must be greater flo . Otherwise, an error appears. IP3 type Type of third-order intercept point. The value can be IIP3 (input intercept point) or OIP3 (output intercept point). IIP3 (dBm) Input power intercept point as a scalar value. This field becomes visible if you select IIP3 as the IP3 type. OIP3 (dBm) Output power intercept point as a scalar value. This field becomes visible if you select OIP3 as the IP3 type. Noise figure (dB) Scalar ratio of the available signal-to-noise power ratio at the input to the available signal-to-noise power ratio at the output, (Si/Ni)/(So/No). Phase noise frequency offset (Hz) Vector specifying the frequency offset. Phase noise level (dBc/Hz) Vector specifying the phase noise level. Note For information about plotting the mixer parameters, see Chapter 3, “Plotting Model Data”. See Also General Mixer, Output Port, S-Parameters Mixer, Z-Parameters Mixer 5-155 Y-Parameters Passive Network Purpose Model passive network using its Y-parameters Library Black Box Elements sublibrary of the Physical library Description The Y-Parameters Passive Network block models the two-port passive network described in the block dialog box, in terms of its Y-parameters and their associated frequencies. In the Y-Parameters field of the block dialog box, provide the Y-parameters for each of M frequencies as a 2-by-2-by-M array. In the Frequency field, specify the frequencies for the Y-parameters as an M-element vector. The elements of the vector must be in the same order as the Y-parameters. All frequencies must be positive. For example, the following figure shows the correspondence between the Y-parameters array and the vector of frequencies. The Y-Parameters Passive Network block uses the RF Toolbox y2s function to convert the Y-parameters to S-parameters, and then interpolates the resulting S-parameters to determine their values at the modeling frequencies. The modeling frequencies are determined by the Output Port block. See Appendix A, “RF Blockset Algorithms” for more details. 5-156 Y-Parameters Passive Network Dialog Box Y-Parameters Y-parameters for a two-port passive network in a 2-by-2-by-M array. M is the number of Y-parameters. Frequency (Hz) Frequencies of the Y-parameters as an M-element vector. The order of the frequencies must correspond to the order of the Y-parameters in Y-Parameters. All frequencies must be positive. Interpolation method Method used to interpolate the S-parameters, as derived from the Y-parameters, over the range of frequencies. Interpolation can be Cubic, Linear (default), or Spline. Note For information about plotting, see Chapter 3, “Plotting Model Data”. 5-157 Y-Parameters Passive Network Examples Plotting Parameters with the Y-Parameters Passive Network Block The following example specifies Y-parameters [.23i, -.12i; -.12i, .23i] and [.02-.13i, -.02+.25i; -.02+.25i, .02-.13i] at frequencies 2.0 GHz and 2.1 GHz respectively. It uses the MATLAB cat function to create the 2-by-2-by-2 Y-parameters array. cat(3,[.23i,-.12i;-.12i,.23i],... [.02-.13i,-.02+.25i;-.02+.25i, .02-.13i]) The plot parameters in the dialog box request a polar plane plot of the S11 parameters in the frequency range 1.9 to 2.2 GHz. 5-158 Y-Parameters Passive Network See Also General Circuit Element, General Passive Network, Output Port, S-Parameters Passive Network, Z-Parameters Passive Network y2s (RF Toolbox) interp1 (MATLAB) 5-159 Z-Parameters Amplifier Purpose Model nonlinear amplifier using its Z-parameters Library Amplifiers sublibrary of the Physical library Description The Z-Parameters Amplifier block models the nonlinear amplifier described in the block dialog box, in terms of its frequency-dependent Z-parameters and their frequencies. The block also takes into account the IP3 value and the noise figure. In the Z-Parameters field of the block dialog box, provide the Z-parameters for each of M frequencies as a 2-by-2-by-M array. In the Frequency field, specify the frequencies for the Z-parameters as an M-element vector. The elements of the frequencies vector must be in the same order as the Z-parameters. All frequencies must be positive. For example, the following figure shows the correspondence between the Z-parameters array and the vector of frequencies. The Z-Parameters Amplifier block uses the RF Toolbox y2s function to convert the Z-parameters to S-parameters, and then interpolates the resulting S-parameters to determine their values at the modeling frequencies. The modeling frequencies are determined by the Output Port block. See Appendix A, “RF Blockset Algorithms” for more details. 5-160 Z-Parameters Amplifier Dialog Box Z-Parameters Z-parameters for a nonlinear amplifier in a 2-by-2-by-M array. M is the number of Z-parameters. Frequency (Hz) Frequencies of the Z-parameters as an M-element vector. The order of the frequencies must correspond to the order of the Z-parameters in Z-Parameters. All frequencies must be positive. Interpolation method Method used to interpolate the S-parameters, as derived from the Z-parameters, over the range of frequencies. Interpolation can be Cubic, Linear (default), or Spline. 5-161 Z-Parameters Amplifier IP3 type Type of third-order intercept point. The value can be IIP3 (input intercept point) or OIP3 (output intercept point). IIP3 (dBm) Input power intercept point as a scalar value. This field becomes visible if you select IIP3 as the IP3 type. OIP3 (dBm) Output power intercept point as a scalar value. This field becomes visible if you select OIP3 as the IP3 type. Noise figure (dB) Scalar ratio of the available signal-to-noise power ratio at the input to the available signal-to-noise power ratio at the output, (Si/Ni)/(So/No). Note For information about plotting, see Chapter 3, “Plotting Model Data”. Examples Plotting Parameters with the Z-Parameters Amplifier Block The following example specifies Z-parameters [12.60+3.80i, 3.77-0.17i; 80.02+54.68i, 26.02+3.84i] and [15.12+3.55i, 4.14-0.92i; 92.10+23.67i, 27.59+2.71i] at frequencies 2.0 GHz and 2.1 GHz respectively. It uses the MATLAB cat function to create the 2-by-2-by-2 Z-parameters array. cat(3,[12.60+3.80i, 3.77-0.17i; 80.02+54.68i, 26.02+3.84i],... [15.12+3.55i, 4.14-0.92i; 92.10+23.67i, 27.59+2.71i]) 5-162 Z-Parameters Amplifier The plot parameters in the dialog box request an X-Y plane plot of the S11 parameters in the frequency range 1.9 to 2.2 GHz. 5-163 Z-Parameters Amplifier See Also General Amplifier, Output Port, S-Parameters Amplifier, Y-Parameters Amplifier z2s (RF Toolbox) interp1 (MATLAB) 5-164 Z-Parameters Mixer Purpose Model mixer using its Z-parameters Library Mixer sublibrary of the Physical library Description The Z-Parameters Mixer block models the nonlinear mixer described in the block dialog box in terms of its frequency-dependent Z-parameters, their frequencies, and the reference impedance of the Z-parameters. The block also takes phase noise into account. The Z-parameter values all refer to the mixer input frequency. The Z-Parameters Mixer block uses the RF Toolbox y2s function to convert the Z-parameters to S-parameters and then interpolates the resulting S-parameters to determine their values at the modeling frequencies. The modeling frequencies are determined by the Output Port block. See Appendix A, “RF Blockset Algorithms” for more details. The RF Blockset computes the normalized reflected amplitude at the mixer input ( Er1 ) and at the mixer output ( Er2 ) from the interpolated S-parameters as Er1 ( fin ) = S11 ( fin ) Ei1 ( fin ) + S12 ( fin ) Ei2 ( fout ) Er 2 ( fout ) = S21 ( fin ) Ei1 ( fin ) + S22 ( fin ) Ei2 ( fout ) where • fin and f out are the mixer input and output frequencies, respectively. • Ei1 and Ei2 are the normalized incident amplitudes at the mixer input and output, respectively. The interpolated S21 parameter values describe the conversion gain as a function of frequency, referred to the mixer input frequency. 5-165 Z-Parameters Mixer Dialog Box Z-Parameters Z-parameters for a nonlinear mixer in a 2-by-2-by-M array. M is the number of Z-parameters. 5-166 Z-Parameters Mixer Frequency (Hz) Frequencies of the Z-parameters as an M-element vector. The order of the frequencies must correspond to the order of the Z-parameters in Z-Parameters. All frequencies must be positive. The following figure shows the correspondence between the Z-parameters array and the vector of frequencies. Interpolation method Method used to interpolate the S-parameters, as derived from the Z-parameters, over the range of frequencies. Interpolation can be Linear (default), Spline, or Cubic. Type Type of mixer. Choices are Downconverter (default) and Upconverter. LO frequency (Hz) Local oscillator frequency. If you choose Downconverter, the RF Blockset computes the mixer output frequency, f out , from the mixer input frequency, f in , and the local oscillator frequency, f lo , . If you choose Upconverter, . as 5-167 Z-Parameters Mixer Note The mixer output frequency must be positive. This means that if you choose a downconverting mixer, than fin must be greater flo . Otherwise, an error appears. IP3 type Type of third-order intercept point. The value can be IIP3 (input intercept point) or OIP3 (output intercept point). IIP3 (dBm) Input power intercept point as a scalar value. This field becomes visible if you select IIP3 as the IP3 type. OIP3 (dBm) Output power intercept point as a scalar value. This field becomes visible if you select OIP3 as the IP3 type. Noise figure (dB) Scalar ratio of the available signal-to-noise power ratio at the input to the available signal-to-noise power ratio at the output, (Si/Ni)/(So/No). Phase noise frequency offset (Hz) Vector specifying the frequency offset. Phase noise level (dBc/Hz) Vector specifying the phase noise level. Note For information about plotting the mixer parameters, see Chapter 3, “Plotting Model Data”. See Also 5-168 General Mixer, Output Port, S-Parameters Mixer, Y-Parameters Mixer Z-Parameters Passive Network Purpose Model passive network using its Z-parameters Library Black Box Elements sublibrary of the Physical library Description The Z-Parameters Passive Network block models the two-port passive network described in the block dialog box, in terms of its Z-parameters and their associated frequencies. In the Z-Parameters field of the block dialog box, provide the Z-parameters for each of M frequencies as a 2-by-2-by-M array. In the Frequency field, specify the frequencies for the Z-parameters as an M-element vector. The elements of the vector must be in the same order as the Z-parameters. All frequencies must be positive. For example, the following figure shows the correspondence between the Z-parameters array and the vector of frequencies. The Z-Parameters Passive Network block uses the RF Toolbox y2s function to convert the Z-parameters to S-parameters, and then interpolates the resulting S-parameters to determine their values at the modeling frequencies. The modeling frequencies are determined by the Output Port block. See Appendix A, “RF Blockset Algorithms” for more details. 5-169 Z-Parameters Passive Network Dialog Box Z-Parameters Z-parameters for a two-port passive network in a 2-by-2-by-M array. M is the number of Z-parameters. Frequency (Hz) Frequencies of the Z-parameters as an M-element vector. The order of the frequencies must correspond to the order of the Z-parameters in Z-Parameters. All frequencies must be positive. Interpolation method Method used to interpolate the S-parameters, as derived from the Z-parameters, over the range of frequencies. Interpolation can be Cubic, Linear (default), or Spline. Note For information about plotting, see Chapter 3, “Plotting Model Data”. 5-170 Z-Parameters Passive Network Examples Plotting Parameters with the Z-Parameters Passive Network Block The following example specifies Z-parameters [0.13 - 5.93i, .03-3.16i; 0.03-3.16i, .13-5.93i] and [0.27-2.86i, -.09-5.41i; -.09-5.41i, .27-2.86i] at frequencies 2.0 GHz and 2.1 GHz respectively. It uses the MATLAB cat function to create the 2-by-2-by-2 Z-parameters array. cat(3,[0.13-5.93i, .03-3.16i; 0.03-3.16i, .13-5.93i],... [0.27-2.86i,-.09-5.41i; -.09-5.41i, .27-2.86i]) The plot parameters in the dialog box request an X-Y plane plot of the S12 parameters in the frequency range 1.9 to 2.2 GHz. 5-171 Z-Parameters Passive Network See Also General Circuit Element, General Passive Network, Output Port, S-Parameters Passive Network, Y-Parameters Passive Network z2s (RF Toolbox) interp1 (MATLAB) 5-172 A RF Blockset Algorithms Simulating an RF Model (p. A-2) Gives an overview of how the RF Blockset simulates an RF model. Determining the Modeling Frequencies (p. A-3) Describes how the RF Blockset computes the modeling frequencies of a physical system. Mapping Network Parameters to Modeling Frequencies (p. A-5) Describes how the RF Blockset determines the values of the S-parameters of the physical blocks at the modeling frequencies. Modeling Noise in an RF System (p. A-7) Describes how the RF Blockset models thermal noise in an RF system. Creating a Complex Baseband-Equivalent Model (p. A-10) Describes how the RF Blockset uses the frequency-domain parameters of the RF blocks to create a baseband-equivalent model for time-domain simulation. Converting to and from Simulink Signals (p. A-15) Explains how the Input Port and Output Port convert Simulink signals to and from the RF Blockset physical modeling environment during a simulation. A RF Blockset Algorithms Simulating an RF Model When you simulate a model that contains physical blocks, the RF Blockset determines the modeling frequencies of the physical system using the Input Port block parameters. The modeling frequencies are the frequencies at which the blockset takes information from the blocks to construct the baseband-equivalent model. Then, the RF Blockset determines the block parameter values at those frequencies and uses the information to create a baseband-equivalent model for time-domain simulation in Simulink. A-2 Determining the Modeling Frequencies Determining the Modeling Frequencies When you simulate an RF model, the Output Port block uses Input Port block parameters to determine the modeling frequencies f for the physical system that is bracketed between the Input Port block and the Output Port block. f is an N-element vector, where N is the finite impulse response filter length. The modeling frequencies are a function of the center frequency fc and the sample time ts. The following figure shows the Input Port block parameters that determine the modeling frequencies. N fc ts A-3 A RF Blockset Algorithms fn is the nth element of the vector of modeling frequencies, f, and is given by fn = fmin + n −1 n = 1,..., N ts N where fmin = fc − A-4 1 2ts Mapping Network Parameters to Modeling Frequencies Mapping Network Parameters to Modeling Frequencies In a physical system, each block provides network parameters at different frequencies. These frequencies are not necessarily the modeling frequencies for the physical system in which the block resides. To create a baseband-equivalent model, the RF Blockset must calculate the values of the S-parameters at the modeling frequencies. Individual physical blocks calculate the S-parameters at the modeling frequencies determined by the Input Port block parameters. Each block interpolates its S-parameters to determine the S-parameters at the modeling frequencies. If the block contains network Y- or Z-parameters, it first converts them to S-parameters. Specifically, the block orders the S-parameters in the ascending order of their frequencies, fn. Then, it interpolates the S-parameters using the MATLAB interp1 function. For example, the curve in the following diagram illustrates the result of interpolating the S11 parameters at original frequencies f1 through f5. Interpolated S11 parameter values Original S11 parameter values f1 (fmin) f2 f4 f5 f3 (fmax) Frequencies in ascending order of magnitude The Interpolation field in the individual block dialog boxes enables you to specify the interpolation method as Cubic, Linear (default), or Spline. For more information about these methods, see “One-Dimensional Interpolation” and the interp1 reference page in the MATLAB documentation. As shown in the previous diagram, each block uses the parameter values at fmin for all modeling frequencies smaller than fmin. The block uses the A-5 A RF Blockset Algorithms parameter values at fmax for all modeling frequencies greater than fmax. In both cases, the results may not be accurate, so you need to specify network parameter values over a range of frequencies that is wide enough to account for the block behavior. A-6 Modeling Noise in an RF System Modeling Noise in an RF System The RF Blockset physical blocks model thermal noise. The Input Port block parameters specify whether to include noise in a simulation. When you include noise information in your model, the RF Blockset simulates the thermal noise of the physical system. This section explains how the RF Blockset simulates noise from user-specified information. For information on how to add noise to an RF model, see “Modeling Thermal Noise” on page 2-22. In general, you can specify output-referred noise in one of three ways: • Noise temperature — Specifies the noise in kelvin. • Noise factor — Specifies the noise by the following equation Noise factor = 1 + Noise temperature 290 • Noise figure — Specifies the noise in decibels relative to the standard reference noise temperature of 290 K. In terms of noise factor, Noise figure = 10log(Noise factor) These three specifications are equivalent, since you can compute each one from any of the others. For RF Blockset physical amplifier and mixer blocks, you can specify noise using frequency-independent noise figure values. The General Amplifier and General Mixer blocks also provide the option to specify noise as frequency-dependent noise figure or as spot noise data. For other RF blocks, such as transmission lines and filters, noise is only generated by the resistors in the network. The RF Blockset calculates this noise from basic resistor equations, so there are no noise parameters on the block dialog boxes. When you run the simulation, the RF Blockset first computes the noise figure values at the modeling frequencies and then uses the noise figure information to calculate the output noise power. A-7 A RF Blockset Algorithms This section contains the following topics: • “Calculating Noise Figure at Modeling Frequencies” on page A-8 • “Calculating Output Noise Power” on page A-9 Calculating Noise Figure at Modeling Frequencies To include noise information in a simulation, the RF Blockset must compute the noise figure values at the modeling frequencies. If you specify the noise figure value directly, or if the blockset computes the noise figure value from the block resistance, the RF Blockset uses this value for the noise figure value at each of the modeling frequencies. If you specify spot noise data using a Touchstone or AMP data file, the RF Blockset computes frequency-dependent noise figure information from the data in the file. It takes the minimum noise figure, NFmin, equivalent noise resistance, Rn, and optimal source admittance, Yopt, values in the file and interpolates to find the values at the modeling frequencies. Then, it uses the following equation to calculate the noise correlation matrix, CA. CA ⎡ Rn ⎢ = 2kT ⎢ ⎢ NFmin − 1 − R Y n opt ⎢⎣ 2 NFmin − 1 ⎤ − Rn Yopt∗ ⎥ 2 ⎥ 2 ⎥ Rn Yopt ⎥⎦ In the above equation, k is Boltzmann’s constant and T is the noise temperature in kelvin. The RF Blockset then calculates the noise factor, F, from the noise correlation matrix as follows: F =1+ z+ C A z 2kT Re {ZS } ⎡ 1 ⎤ z = ⎢ *⎥ ⎢⎣ ZS ⎥⎦ In the two preceding equations, ZS is the nominal impedance, which is 50 ohms, and z+ is the Hermitian conjugation of z. A-8 Modeling Noise in an RF System The RF Blockset obtains the noise figure, NF, from the noise factor: NF = 10 log( F ) For more information about these calculation techniques, see the following article: Hillbrand, H. and P.H. Russer, “An Efficient Method for Computer Aided Noise Analysis of Linear Amplifier Networks,” IEEE Transactions on Circuits and Systems, Vol. CAS-23, Number 4, pp. 235-238, 1976. Calculating Output Noise Power The RF Blockset uses noise power to determine the amplitude of the noise that it adds to the system using a Gaussian distributed pseudorandom number generator. It uses both the noise temperature and the modeling bandwidth to calculate the noise power: Noise power = kTB Here, k is Boltzmann’s constant, which is 1.38e-23 J/K, T is the noise temperature in kelvin and B is the bandwidth in hertz. The RF Blockset computes noise temperature from the specified or calculated noise figure values, and it computes the modeling bandwidth from the model’s sample time and center frequency. For more information, see the rfdata.noise and rfdata.nf reference pages. A-9 A RF Blockset Algorithms Creating a Complex Baseband-Equivalent Model The RF Blockset simulates the physical system in the time domain using a baseband-equivalent model that it creates from the frequency-domain parameters of the physical blocks. This section contains the following topics: • “Baseband-Equivalent Modeling” on page A-10 • “Simulation Efficiency of a Complex Baseband-Equivalent Model” on page A-13 Baseband-Equivalent Modeling To create a complex baseband-equivalent model in the time domain based on the network parameters of the physical system, the RF Blockset performs a mathematical transformation that consists of the following three steps: 1 “Calculating the Passband Transfer Function” on page A-10 2 “Calculating the Baseband Transfer Function” on page A-12 3 “Calculating the Baseband-Equivalent Impulse Response” on page A-13 Calculating the Passband Transfer Function The RF Blockset calculates the passband transfer function from the physical block parameters at the modeling frequencies. Note To learn how the RF Blockset uses the specified network parameters to compute the network parameters at the modeling frequencies, see “Mapping Network Parameters to Modeling Frequencies” on page A-5. The transfer function is defined as H( f ) = A-10 VL ( f ) VS ( f ) Creating a Complex Baseband-Equivalent Model where VS and VL are the source and load voltages shown in the following figure, and f represents the modeling frequencies. Zs + Vs - + Vin - + Physical Subsystem Z L VL - More specifically, H( f ) = S21 * (1 + Γ l ) * (1 − Γ s ) 2 * (1 − S22 * Γ l ) (1 − Γin * Γ s ) where Γl = Zl − Zo Zl + Zo Γs = Zs − Zo Zs + Zo ⎛ ⎞ Γl Γin = S11 + ⎜⎜ S12 * S21 * ⎟ (1 − S22 * Γ l ) ⎟⎠ ⎝ and • ZS is the source impedance. • ZL is the load impedance. • Sij are the S-parameters of a two-port network. A-11 A RF Blockset Algorithms The passband transfer function is shown in the following figure: Specify these parameters in the Input Port dialog box: Passband Spectrum of a Modulated RF Carrier Finite impulse response filter length = N Center frequency = fc Sample time = ts Magnitude 1/(ts*N) Index = n Frequency fmin Index = 1 fc fn 1/ts fmax Index = N Calculating the Baseband Transfer Function The RF Blockset calculates the baseband transfer function, Hbaseband ( f ) , by translating the passband transfer function to its equivalent baseband transfer function: Hbaseband ( f ) = H passband ( f + fc ) where fc is the specified center frequency. The resulting baseband-equivalent spectrum is centered at zero, so the RF Blockset can simulate the system using a much larger time step than Simulink can use for the same system. For information on why this translation allows for a larger time step, see “Simulation Efficiency of a Complex Baseband-Equivalent Model” on page A-13. A-12 Creating a Complex Baseband-Equivalent Model The baseband transfer function is shown in the following figure: Baseband-Equivalent Spectrum Magnitude Centered at zero 1/2ts -1/2ts Frequency 1/ts Calculating the Baseband-Equivalent Impulse Response The RF Blockset calculates the baseband-equivalent impulse response by calculating the inverse FFT of the baseband transfer function. For faster simulation, the block calculates the IFFT using the next power of 2 greater than the specified finite impulse response filter length. Then, it truncates the impulse response to a length equal to the filter length specified. Simulation Efficiency of a Complex Baseband-Equivalent Model The baseband-equivalent modeling technique improves simulation speed by allowing the simulator to take larger time steps. To simulate a system in the time domain, Simulink would require a step size of: tstep = 1 2 fmax A-13 A RF Blockset Algorithms Using the baseband-equivalent model of the same system, whose spectrum has been shifted down by fc, allows for a much larger time step of: tstep = A-14 1 2( fmax − fc ) = 1 fmax − fmin Converting to and from Simulink Signals Converting to and from Simulink Signals When you simulate an RF model, the RF Blockset must convert the mathematical Simulink signals to and from the RF Blockset physical modeling environment. To perform this conversion, the RF Blockset interprets the Simulink signal that enters the Input Port block, Sin, as the voltage VS across the source impedance ZS. This process is shown in the following figure. Simulink signal Vs Zs + Vin - Sin=Vs Input Port Block Zin RF System Parameters Z L + VL - Simulink signal Sout = V L Output Port Block The RF Blockset interprets the output Simulink signal as the voltage VL over the load impedance ZL. You specify the source and load impedances in the Input Port and Output Port dialog boxes, respectively. The RF Blockset interpretation of the input Simulink signal as the source voltage, VS, produces different results than the interpretation that the input Simulink signal is the input voltage, Vin. When the source and load A-15 A RF Blockset Algorithms impedances are the same, the former interpretation produces 6 dB of loss compared to the latter. You can see how this loss arises by analyzing the equivalent circuit model for each interpretation when there are no blocks between the Input Port and Output Port blocks. The following figure shows the equivalent circuit model when the input Simulink signal, Sin, is taken to be the input voltage shown in the previous diagram. + + Sin VL R - - The load power is PL = 2 VL2 Sin = R R In decibels, the load power is ⎛ S2 ⎞ 10 log ( PL ) = 10 log ⎜ in ⎟ ⎜ R ⎟ ⎝ ⎠ (A-1) The following figure shows the equivalent circuit model when the input Simulink signal, Sin, is taken to be the source voltage shown in the previous diagram. R + Sin + R - The load power is A-16 VL - Converting to and from Simulink Signals PL = VL2 R = ( Sin 2 ) 2 R In decibels, the load power is ⎛ S2 ⎞ ⎛ S2 ⎞ 10 log ( PL ) = 10 log ⎜ in ⎟ = 10 log ⎜ in ⎟ − 6.02 ⎜ 4R ⎟ ⎜ R ⎟ ⎝ ⎠ ⎝ ⎠ (A-2) This load power is 6 dB less than the load power computed in Equation A-1. A-17 A A-18 RF Blockset Algorithms B Examples Use this list to find examples in the documentation. B Examples Examples “Example — Modeling an LC Bandpass Filter” on page 1-12 “Example — Importing a Touchstone Data File into an RF Model” on page 2-8 “Example — Importing a Bandstop Filter into an RF Model” on page 2-15 “Example — Plotting Component Data on a Z Smith Chart” on page 3-15 “Example — Creating and Modifying Subsystem Plots” on page 3-22 B-2 Index A Index active noise General Amplifier block 5-35 General Mixer block 5-44 adding noise 2-23 adding physical and mathematical blocks 2-2 algorithm simulation A-2 amplifier modeling from file data 5-38 modeling from rfdata object 5-35 Amplifier block 5-2 effects 5-5 modeling nonlinearity 5-2 methods 5-7 sample time comparison 5-11 thermal noise simulation 5-10 See also General Amplifier block amplifier blocks mathematical 4-2 physical 4-4 B Bandpass RF Filter block 5-16 sample time comparison 5-17 Bandstop RF Filter block 5-20 sample time comparison 5-21 baseband-equivalent model creating A-10 simulation efficiency A-13 baseband-equivalent time domain modeling 5-98 linear subsystem 5-98 nonlinear subsystem 5-102 Bessel filter design Bandpass RF Filter block 5-16 Bandstop RF Filter block 5-20 Highpass RF Filter block 5-52 Lowpass RF Filter block 5-86 black box elements blocks 4-4 block parameters setting 2-6 blocks connecting 2-2 mathematical 4-2 physical 4-3 Butterworth filter design Bandpass RF Filter block 5-16 Bandstop RF Filter block 5-20 Highpass RF Filter block 5-52 Lowpass RF Filter block 5-86 C Chebyshev I filter design Bandpass RF Filter block 5-16 Bandstop RF Filter block 5-20 Highpass RF Filter block 5-52 Lowpass RF Filter block 5-86 Chebyshev II filter design Bandpass RF Filter block 5-16 Bandstop RF Filter block 5-20 Highpass RF Filter block 5-52 Lowpass RF Filter block 5-86 circuit element modeling from rfckt object 5-42 circuit objects importing 2-14 Coaxial Transmission Line block 5-24 shunt and series stubs 5-25 stubless 5-24 composite data plots 3-5 connecting blocks RF Physical blocks to Simulink 2-2 Simulink to RF Physical blocks 2-2 connector blocks 4-5 Input Port 5-56 Output Port 5-98 Index-1 Index conversion Simulink signal to RF signal A-15 Coplanar Waveguide Transmission Line block 5-29 shunt and series stubs 5-30 stubless 5-29 D data consistency General Amplifier block 5-35 data files importing 2-7 demos in Help browser 1-4 E Elliptic filter design Bandpass RF Filter block 5-16 Bandstop RF Filter block 5-20 Highpass RF Filter block 5-52 Lowpass RF Filter block 5-86 example creating and modifying plots 3-22 importing circuit objects 2-15 importing Touchstone file 2-8 F filter blocks mathematical 4-2 physical 4-3 filter design physical blocks LC Lowpass Tee block 5-83 filter design mathematical blocks Bandpass RF Filter block 5-16 Bandstop RF Filter block 5-20 Highpass RF Filter block 5-52 Lowpass RF Filter block 5-86 Index-2 filter design physical blocks LC Bandpass Pi block 5-59 LC Bandpass Tee block 5-65 LC Bandstop Pi block 5-68 LC Bandstop Tee block 5-71 LC Highpass Pi block 5-74 LC Highpass Tee block 5-77 LC Lowpass Pi block 5-80 format changing in plot 3-20 frequency range changing in plot 3-20 G General Amplifier block 5-35 active noise 5-35 generating from file data 5-38 nonlinearity 5-35 See also Amplifier block General Circuit Element block 5-41 generating from rfckt object 5-42 General Mixer block 5-44 active noise 5-44 phase noise 5-45 See also Mixer block General Passive Network block 5-49 generating from file data 5-50 Ghorbani model 5-9 H Help browser demos 1-4 Highpass RF Filter block 5-52 sample time comparison 5-53 I importing circuit objects 2-14 Index data files 2-7 Input Port block 5-56 parameter input for physical subsystem 5-56 sample time comparison 5-56 See also Output Port block interpolation network parameters A-5 L ladder filter blocks 4-3 ladder filters example to filter Gaussian noise 5-61 LC Bandpass Pi block 5-59 example to filter Gaussian noise 5-61 LC Bandpass Tee block 5-65 LC Bandstop Pi block 5-68 LC Bandstop Tee block 5-71 LC Highpass Pi block 5-74 LC Highpass Tee block 5-77 LC Lowpass Pi block 5-80 LC Lowpass Tee block 5-83 libraries RF physical and mathematical 1-6 library RF mathematical 1-9 RF physical 1-7 link budget plots 3-7 Lowpass RF Filter block 5-86 sample time comparison 5-87 M mathematical and physical models connecting 2-2 mathematical modeling blocks 1-9 Microstrip Transmission Line block 5-90 shunt and series stubs 5-91 stubless 5-90 Mixer block 5-95 sample time comparison 5-96 See also General Mixer block mixer blocks mathematical 4-2 physical 4-5 model adding RF components to 2-2 modeling amplifier from file data 5-38 amplifier from rfdata object 5-35 baseband-equivalent time domain 5-98 circuit element from rfckt object 5-42 passive network from file data 5-50 modeling frequencies calculating A-3 calculating noise A-8 S-parameter interpolation A-5 models physical and mathematical blocks 1-6 N network parameters adding to a plot 3-20 interpolation at modeling frequencies A-5 noise active General Amplifier block 5-35 General Mixer block 5-44 adding 2-23 calculating at modeling frequencies A-8 phase General Mixer block 5-45 plotting 2-24 specifying mixer and amplifier 2-22 noise output power calculating A-9 noise simulation A-7 nonlinearity Index-3 Index Amplifier block 5-2 General Amplifier block 5-35 O opening block libraries 1-6 Output Port block 5-98 baseband-equivalent time domain modeling 5-98 plotting RF subsystem parameters 5-106 See also Input Port block output power calculating noise A-9 P Parallel-Plate Transmission Line block 5-107 shunt and series stubs 5-108 stubless 5-107 parameter input to physical subsystem 5-56 parameters adding to a plot 3-20 passive network modeling from file data 5-50 phase noise General Mixer block 5-45 physical and mathematical models connecting blocks 2-2 physical modeling blocks 1-7 physical subsystem parameter input for 5-56 plot types modifying 3-20 plots budget 3-7 changing format of 3-20 changing frequency range of 3-20 composite 3-5 Index-4 creating 3-9 displaying legend 3-15 example of creating and modifying 3-22 format 3-4 modifying 3-20 noise 2-24 RF subsystem parameters 5-106 Smith chart example 3-15 types of 3-3 updating 3-19 using block parameters to specify 3-9 X-Y plane 3-7 product demos 1-4 R Rapp model 5-10 RF block libraries Mathematical 4-2 Physical 4-3 RF Blockset required and related products 1-3 RF Blockset libraries 1-6 how to open 1-6 RF models connecting blocks 2-2 rfckt object modeling general circuit element 5-41 rfdata object modeling nonlinear amplifier 5-35 RLCG Transmission Line block 5-112 shunt and series stubs 5-113 stubless 5-112 S S-Parameters Amplifier block 5-117 S-Parameters Mixer block 5-122 S-Parameters Passive Network block 5-126 Saleh model 5-8 Index Series RLC block 5-131 setting block parameters 2-6 Shunt RLC block 5-134 simulation noise A-7 simulation algorithm overview A-2 Simulink signal converting to and from A-15 Smith chart example 3-15 specifying mixer and amplifier thermal noise 2-22 stubless transmission lines Coaxial Transmission Line block 5-24 Coplanar Waveguide Transmission Line block 5-29 Microstrip Transmission Line block 5-90 Parallel-Plate Transmission Line block 5-107 RLCG Transmission Line block 5-112 Transmission Line block 5-137 Two-Wire Transmission Line block 5-142 stubs (shunt and series) Coaxial Transmission Line block 5-25 Coplanar Waveguide Transmission Line block 5-30 Microstrip Transmission Line block 5-91 Parallel-Plate Transmission Line block 5-108 RLCG Transmission Line block 5-113 Transmission Line block 5-138 Two-Wire Transmission Line block 5-143 specifying mixer and amplifier 2-22 time-domain modeling baseband-equivalent 5-98 Touchstone file importing 2-8 Transmission Line block 5-137 shunt and series stubs 5-138 stubless 5-137 transmission line blocks 4-3 Two-Wire Transmission Line block 5-142 shunt and series stubs 5-143 stubless 5-142 V viewing demos 1-4 W workflow RF Blockset 1-10 workflow example RF Blockset 1-12 Y Y-Parameters Amplifier block 5-147 Y-Parameters Mixer block 5-152 Y-Parameters Passive Network block 5-156 Z Z-Parameters Amplifier block 5-160 Z-Parameters Mixer block 5-165 Z-Parameters Passive Network block 5-169 T thermal noise Index-5

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