Application Report SNOA375B – April 1996 – Revised April 2013 OA-12 Noise Analysis for Comlinear Amplifiers ..................................................................................................................................................... ABSTRACT This application report covers the noise model for all current-feedback op amps, simple design techniques and useful approximations. This is a frequency-domain model to simplify circuit analysis and design. This information simplifies the selection of a low-noise current-feedback op amp. This revision obsoletes the previous revision of this document, and covers additional material. Contents 1 Contents ...................................................................................................................... 2 Scope of Noise Analysis ................................................................................................... 3 Noise Model ................................................................................................................. 4 Integrated Noise ............................................................................................................. 5 Dynamic Range ............................................................................................................. 6 Improving Output Noise .................................................................................................... 7 1/f Noise ...................................................................................................................... 8 SPICE Models ............................................................................................................... 9 Design Example ............................................................................................................. 10 Conclusions .................................................................................................................. 11 References ................................................................................................................... Appendix A Derivation of Noise Power Bandwidth Formula ................................................................ 2 2 2 3 4 4 5 5 6 8 8 9 List of Figures 1 2 ................................................................................................................................ .............................................................................................. Non-Inverting Gain Amplifier 3 6 List of Tables All trademarks are the property of their respective owners. SNOA375B – April 1996 – Revised April 2013 Submit Documentation Feedback OA-12 Noise Analysis for Comlinear Amplifiers Copyright © 1996–2013, Texas Instruments Incorporated 1 Contents 1 www.ti.com Contents The subjects covered are: • The noise model for current-feedback op amps • Converting noise densities to integrated noise • Interpreting integrated noise as SNR • Output noise improvement • 1/f noise calculations • SPICE models • A design example • A derivation of the noise power bandwidth (NPBW) approximation (see Appendix A) • A reference section 2 Scope of Noise Analysis The noise analysis in this application report deals with random noise generated by the devices and components in a circuit. Noise analysis gives the greatest benefit when: • The signal level is low • The signal to noise ratio (SNR) is high • The signal sees a substantial gain Noise analysis will not help: • Identify and eliminate oscillation or instability problems • Reduce EMI (Electro-Magnetic Interference) • Reduce cross talk 3 Noise Model Three input-referred noise density (spot noise) sources model the noise generated by current-feedback (CFB) op amps. Noise power density (en2 or in2 ) is the power measured in a narrow bandwidth, normalized to the load resistance, in units of V2/Hz or A2/Hz. Voltage noise density (en) and current noise density (in) are the square-root of noise power density in units of V/√Hz or A/√Hz. Notice that these noise densities are functions of frequency. Figure 1 shows the three input noise density sources, eni2 , ibn2 and ibi2 , in a standard amplifier circuit. The specifications give densities that are constant over frequency (white noise). Ground RT for inverting gain circuits, and ground Rg for non-inverting gain circuits 2 OA-12 Noise Analysis for Comlinear Amplifiers Copyright © 1996–2013, Texas Instruments Incorporated SNOA375B – April 1996 – Revised April 2013 Submit Documentation Feedback Integrated Noise www.ti.com Figure 1. The equation for the output voltage noise density is: (1) The load resistor (RL ) has a negligible contribution to the noise because the output resistance of the op amp is very small. The system transfer function will shape the output noise. See References [1] and [2] for information on how to generate noise transfer functions. The 1/f Noise section covers excess noise (noise that exceeds the white noise specifications). 4 Integrated Noise Convert the output voltage noise density to the integrated output voltage noise by integrating over frequency: SNOA375B – April 1996 – Revised April 2013 Submit Documentation Feedback OA-12 Noise Analysis for Comlinear Amplifiers Copyright © 1996–2013, Texas Instruments Incorporated 3 Dynamic Range www.ti.com (2) where: • Heno (jf) is the noise transfer function for eno • f1 is the lower -3dB corner frequency for AC-coupled systems, or the lowest frequency that affects your system’s performance • f2 is the upper -3dB corner frequency • The NPBW approximation holds when: – There is ≤ 3dB of gain peaking – f1 << f2 – If the NPBW approximation does not hold, use numerical integration instead The integrated output noise, Eno , is the standard deviation of the output noise in units of Vrms . It is also a measure of the lower end of the useful dynamic range. Because integrated output noise depends on the circuit architecture, component values and the op amp, it is best to compare op amps based on the input noise densities To see how each noise source contributes to Eno , integrate each term separately: (3) This information is useful for improving the amplifier’s SNR. 5 Dynamic Range Signal to noise ratio (SNR) describes how much dynamic range a signal has. It compares the lower end of the useful dynamic range (Eno) to the signal magnitude (in units of Vrms). The input and output signal to noise ratios are: (4) where: • Vin(rms is the signal voltage at the input (VS1 or VS2), Vrms • Enin is the integrated voltage noise at the input (at VS1 or VS2 ), Vrms • Vo(rms) is the signal voltage at the output, Vrms • Eno is the integrated voltage noise at the output, Vrms 6 Improving Output Noise To • • • • • 4 reduce output noise, do the following: Band-limit the signal after the op amp to limit the final output noise AC couple when possible Use a low-pass filter, or a band-pass filter Reduce gain peaking to lower the NPBW Reduce resistor values to lower thermal noise, but keep in mind that: – Rf values smaller than that recommended in the device-specific data sheet causes gain peaking and increased bandwidth; the NPBW may increase faster than the intended noise reduction OA-12 Noise Analysis for Comlinear Amplifiers Copyright © 1996–2013, Texas Instruments Incorporated SNOA375B – April 1996 – Revised April 2013 Submit Documentation Feedback 1/f Noise www.ti.com – Smaller loads at the op amp’s output increase distortion and power consumption – Resistors connected to the input of current-sensing amplifiers act as current noise sources; increase these resistor values to reduce thermal noise For those op amps with an adjustable supply current, the input noise sources change with supply current. As the supply current increases, the input voltage noise decreases, the input current noises increase, the distortion improves and the bandwidth increases. For the best voltage noise performance, use the highest supply current. For the best current noise performance, use the lowest supply current. 7 1/f Noise At low frequencies, the three input noise density terms are larger than predicted by the specifications. The dominant source of this excess noise is 1/f (or flicker) noise. Burst noise also contributes to excess noise, but is not covered in this application report. The input noise sources, with both the 1/f noise and white noise terms included, are: (5) where: • • • eni2(f) is the sum of the white noise term, eni2, and the 1/f noise term, fc(eni) is the corner frequency of the 1/f noise for eni2(f); this is the point where eni2(f) doubles its white noise value the other input noise terms are defined similarly Notice that flicker noise power density is proportional to 1/f; flicker voltage noise density and flicker current noise densities are proportional to 1/√f. To integrate both white noise and 1/f noise, evaluate individual noise terms separately. For each term obtain: (6) The 1/f noise contribution is negligible when f2 >> fc . f1 is the largest frequency that does not affect your system’s performance when the amplifier is DC-coupled. Use metal-film resistors to minimize 1/f noise. 8 SPICE Models SPICE models are available for most of Comlinear’s amplifiers. These models support AC noise simulations at room temperature. We recommend simulating with Comlinear’s SPICE models to: • Predict a better value for NPBW • Support quicker design cycles To verify your simulations, we recommend breadboarding your circuit. Evaluation boards are available for building and testing Comlinear’s amplifiers. SNOA375B – April 1996 – Revised April 2013 Submit Documentation Feedback OA-12 Noise Analysis for Comlinear Amplifiers Copyright © 1996–2013, Texas Instruments Incorporated 5 Design Example 9 www.ti.com Design Example This design example demonstrates the noise design of a simple circuit. The CFB op amp in this example is not an actual product; the parameter values shown are arbitrary and are for illustration purposes only. This example uses the non-inverting gain amplifier in Figure 2. The components shown are: • VS1 is the input voltage source (with very low output impedance). The signal at VS1 is 100mVrms , and the voltage noise ens1 (at VS1) is 3.0nV/√Hz. • A 50Ω coax cable is placed between the source and the amplifier • RT1 = 50Ω to match the coax cable’s impedance and prevent reflections • RT2 prevents gain peaking, and filters the input signal with CT • CT filters the input signal (this reduces the signal’s slew rate) • Rf and Rg set the gain; the recommended Rf is 250Ω for a gain of 10 • RL is 100Ω • The op amp noise terms are: • eni = 3.0nV/√Hz and fc(eni) = 1.0kHz • ibn = 2.0pA/√Hz and fc(ibn) = 5.0kHz • ibi = 12pA/√Hz and fc(ibi) = 10kHz • Ambient temperature (T) is 25°C • Power dissipation of the op amp causes a 15°C junction temperature rise Figure 2. Non-Inverting Gain Amplifier The design goals are: • Provide a gain of 10 (= Gn for non-inverting gains) • DC-couple the signal; the lowest frequency that affects system performance is 10Hz (f1) • Set an upper 3dB corner frequency of 10MHz (f2) • Achieve an output SNR of 74dB The initial design choices that are made are: • 20MHz pole at the input set by CT and RT2 (this will cause reflections in the coax cable for any signal above this pole) • 10MHz filter after this amplifier (not shown); this will set f 2 (NPBW) 6 OA-12 Noise Analysis for Comlinear Amplifiers Copyright © 1996–2013, Texas Instruments Incorporated SNOA375B – April 1996 – Revised April 2013 Submit Documentation Feedback Design Example www.ti.com • • • • RT2 = 1.0kΩ CT = 8pF Rf = 250Ω, its recommended value, to avoid gain peaking Rg = 27.8Ω to set the gain to Gn = 10 The resulting junction temperature of the op amp, input integrated noise and input SNR are: (7) RT1 does not contribute to the output noise; VS1is a nearly ideal voltage source. The input source produces an output noise of: The individual white noise contributions of the op amp to the output noise are: (8) The individual white noise contributes of the op amp to output noise are: (9) The individual 1/f noise contributions of the op amp to the output noise are: (10) The contributions of the other components to the output noise are: (11) The resulting output integrated noise, output signal and output SNR are: Eno ≈ 227μVrms Vo(rms) = GnVin(rms) ≈ 1.00Vrms SNRo ≈ 72.9dB (12) (13) (14) Reduce RT2 to improve SNR; this has little impact on other performance parameters. Changing RT2 to 200Ω gives: CT = 40pF Eno ≈ 169μVrms SNRo ≈ 75.4dB (15) (16) (17) In an actual design, the next step would be SPICE simulations, then breadboarding the circuit. SNOA375B – April 1996 – Revised April 2013 Submit Documentation Feedback OA-12 Noise Analysis for Comlinear Amplifiers Copyright © 1996–2013, Texas Instruments Incorporated 7 Conclusions 10 www.ti.com Conclusions The important points to remember when designing low noise circuits are: • Employ noise analysis where small signals are present • Select correct resistor values to reduce thermal noise • Select op amps based on their input noise densities (integrated noise is circuit-dependent) • Reduce NPBW and gain peaking to minimize integrated output noise • Estimate your signal’s dynamic range using SNR • Simulate with Comlinear’s SPICE models to estimate noise performance • Build and measure your circuit to verify the design • Refer to Section 11 for additional background information 11 References 1. C. D. Motchenbacher and J. A. Connelly, Low-Noise Electronic System Design, New York, John Wiley & Sons, 1993. 2. P. R. Gray and R. G. Meyer, Analysis and Design of Analog Integrated Circuits, 2nd Ed. New York: John Wiley & Sons, 1984. 3. J. D. Gibson, Principles of Digital and Analog Communications, New York: Macmillan, 1989. 4. A. B. Carlson, Communication Systems: An Introduction to Signals and Noise in Electrical Communication, 3rd Ed. New York: McGraw-Hill, 1986. 5. P. Antognetti and G. Massobrio (Editors), Semiconductor Device Modeling with SPICE, New York: McGraw-Hill, 1988. 6. CLC to LMH Conversion Table (SNOA428) • NOTE: The circuits included in this application report have been tested with Texas Instruments parts that may have been obsoleted and/or replaced with newer products. To find the appropriate replacement part for the obsolete device, see the CLC to LMH Conversion Table (SNOA428). 8 OA-12 Noise Analysis for Comlinear Amplifiers Copyright © 1996–2013, Texas Instruments Incorporated SNOA375B – April 1996 – Revised April 2013 Submit Documentation Feedback www.ti.com Appendix A Derivation of Noise Power Bandwidth Formula The goal is to estimate NPBW using common, easy to measure parameters: the -3dB bandwidth and gain peaking. Assume a second-order transfer function for the op amp circuit’s high-frequency behavior: (18) where, ωo = 2πfo is the natural frequency of this transfer function. Integrating the magnitude squared of the transfer function gives: (19) Solving for the upper -3dB corner frequency (f2), and substituting the result in Equation 19, gives: (20) Gain peaking is easy to measure, and is a strong function of Q for large Q. It is easy to show that: (21) where, Hmax is the peak gain magnitude. These results support the following approximations: (22) with a 20% maximum error. This translates to a 0.8dB maximum error in the estimated SNR. If the amplifier transfer function has a single pole response, it is easy to show that: NPBW = (π/2) · f2, Single pole transfer function (23) High-order filters will have: NPBW ≈ f2, high-order filters (24) The approximation formula includes both of these cases. The above results hold for the lower corner -3dB frequency (f1) with minor modifications. When the corner -3dB frequencies do not interact (f1 << f2 ), we obtain: (25) It is easy to extend this result when there is more than 3.0dB of peaking, but it is better to reduce the peaking, or to numerically integrate the output noise. 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