RF & Wireless RF Amplifier Output Voltage, Current, Power and Impedance Relationship put impedance result in a percentage of the forward power being reflected back to the amplifier. In some cases, excessive reflected power can damage an amplifier and precautions that may affect forward power are required. Given these realities, how does one go about determining output voltage, current and power? Again Ohm’s law comes to the rescue, but with the caveat that the actual power delivered to the load (net forward power after the application of any VSWR protection less reflected power) must be determined before applying Ohm’s law. This Application note will highlight some of the major RF amplifier characteristics that impact forward power as well as net power allowing the use of Ohm’s law, even when conditions are far from ideal. Back to Basics: Ohm’s Law Ohm’s law states that the amount of current flowing between two points in an electrical circuit is directly proportional to the voltage impressed across the two points and inversely proportion to the resistance between the points. Thus, the equation Figure 1: Ohm’s Law pie chart Application Note #49 Jason Smith, Manager Applications Engineer Pat Malloy, Sr. Applications Engineer rf/microwave instrumentation www.ar-worldwide.com 64 is the basic form of Ohm’s law where the current I is in units of amperes (A), the How much output voltage, current and power Electromotive Force (EMF) or difference can RF amplifiers provide? This question is of electrical potential E is in volts (V), and often asked by novice test engineers as well R is the circuit resistance given in ohms as seasoned RF professionals. Depending (Ω). Applying the standard equation relaon the application, there is often an under- ting electrical power to voltage and current lying desire to maximize one of the three A parameters: power, voltage or current. While one would think that a simple application of Ohm’s law is called for, this would only cross multiplying and rearranging each of apply given ideal conditions, such as when the variables results in the equations shown an RF amplifier with a typical 50 Ω output in the Ohm’s law pie chart (see Fig 1) shoresistance is driving a 50 Ω load. In this rare wing the various combinations of the four case where the load impedance perfectly variables, I, V, Ω and W. Let’s use Ohm’s matches the amplifier output impedance, pie chart to determine the output voltage, the power delivered to the load is simply current, and power of a 50 Ω amplifier opethe rated power of the amplifier. There is rating under ideal conditions. absolutely no reflected power and thus, there is no need to limit or control the gain Example of the amplifier to protect it from excessive reflected power. Assume we have a 100 watt amplifier with 50 Ω output impedance driving a 50 Ω load. Unfortunately, such ideal conditions rarely This is an ideal situation in that 100% of the apply in actual “real world” applications. forward power will be absorbed in the load Real amplifiers are required to drive varying and therefore there is no reflected power load impedances. The mismatch between in this example.The full 100 Watts will be these “real” loads and the amplifier’s out- delivered to the 50 Ω load. hf-praxis 6/2017 RF & Wireless Selecting appropriate formulas from the tolerate a maximum power of 200 watts Ohm’s pie chart, one can easily characte- (100 watts forward + 100 watts reverse). rize this ideal amplifier: Clearly this is cause for concern and amplifier designers must deal with the very real √ possibility that the amplifier’s output might either be accidentally shorted or the load Substituting known values: could be removed. Consequently, all ampli= 70,7 Vrms fiers should employ some form of protection √ when VSWR approaches dangerous levels. Thus, the output voltage across the 50 Ω The following is a partial list (most desirable load is 70.7 Vrms to least desirable) of some methods used: Substituting known values: = 1,41 Arms Overdesign • All Solid-state devices and power combiners are conservatively designed to provide sufficient ruggedness and heat dissipation to accommodate infinite VSWR. The output load current is 1,41 Arms • No additional active VSWR protection circuitry is required with this approach. As can be seen from the above example, when impedances match, power, voltage, • This conservative approach is found on and current are easily determined by the AR’s low to mid power amplifiers. application of Ohm’s law. Now let’s consider “real life” amplifiers and the effects Active monitoring of VSWR they have on the determination of output resulting in a reduction in voltage, current and power. Impedance Mismatch: The danger of impedance mismatch and methods used to protect amplifiers amplifier gain when VSWR approaches dangerous levels Active monitoring of both output voltage and/or current • Limits are set for both voltage and/or current similar to restrictions placed on DC power supplies. • If either of the two parameters is exceeded, the amplifier is shut down. Many amplifiers are designed with little or no concern regarding load mismatch. It is assumed that the application involves a load that matches that of the amplifier. In applications like electromagnetic compatibility (EMC) immunity testing where impedance mismatch is the norm, care must be taken in selecting an amplifier that can tolerate any mismatch while still delivering the required power. AR solid-state amplifiers have been designed to tolerate extreme load mismatch. They are exceptionally rugged and provide superior protection while delivering maximum output power to any load. Impedance mismatch is discussed in further detail in Application Note #27A, “Importance of Mismatch Tolerance for Amplifiers Used in Susceptibility Testing”. • When VSWR exceeds a safe level the for- What will be the effect of VSWR ward power is reduced. This technique is sometimes referred to as “gain fold-back” protection on forward power, or power available to the load? or just “fold-back”. Maximum power is transferred to the load Let’s first look at the various methods used only when the load impedance matches the • AR’s high power solid-state amplifiers will to protect AR amplifiers from the ill effects fold-back when reflected power reaches amplifier’s output impedance. Unfortunately, 50% of the rated power corresponding of extreme VSWR. this is rarely the case. In these “typical” situto a VSWR of 6:1 and will withstand any • Class A amplifiers designed to tolerate ations, reflections occur at the load and the amount of mismatch. infinite VSWR: This type of amplifier difference between the forward power and will not fold-back or shut off when opethat delivered to the load is reflected back rating into a high VSWR. (Most AR low to the amplifier. A voltage standing wave is Active monitoring of VSWR to medium power amplifiers fit in this created by the phase addition and subtrac- leading to a shut down when category.) tion of the incident and reflected voltage VSWR exceeds a safe level waveforms. Power amplifiers must either be • This is considered a brute-force tech- • With these amplifiers, the forward power capable of absorbing this reflected power or is always the rated power, and is indepennique that can lead to undesirable test they must employ some form of protection dent of load disruptions. to prevent damage to the amplifier. • Example: A 100 watt amplifier will proFor example, an open or short circuit placed • AR does not use this technique in any of vide 100 watts forward power irrespecits amplifiers. on the 100 watt power amplifier discussed tive of load variations above would result in an infinite voltage Active thermal monitoring • Fold-back based on reflected power: standing wave ratio (VSWR). Since This technique is used for high power AR • High VSWR will cause a buildup of for Z0 >ZL and amplifiers where the reflected power is not heat. When a predetermined temperaallowed to exceed 50% of the rated power. ture threshold is exceeded, the amplifier is shut down. • These larger amplifiers provide full rated for ZL > Z0 power to the load for any VSWR up to • Due to the nature of thermal time con6:1. As VSWR increases beyond this level, stants, this approach is relatively slow. it can be seen that VSWR is always ≥1. With fold-back is used to limit the reflected Extreme variations in VSWR may not no active VSWR protection, an open circuit power to no more than 50% of the rated immediately result in shut down. at the load would result in a doubling of the power, regardless of load variations. output voltage to 141,4 Vrms, while a short • AR amplifiers employ some degree of thercircuit would increase the output current to mal monitoring for circuit protection but • In this case, available forward power is equal to the rated power until a VSWR 2,82 Arms. In either of these worst case scedo not rely on this relatively slow method of 6:1 is reached. At this point, 50% of narios, the 100 watt power amplifier must to protect against extreme VSWR. hf-praxis 6/2017 65 RF & Wireless the forward power is reflected. For any VSWR greater than 6:1, the forward power is reduced sufficiently to insure that the reverse power never exceeds 50% of the rated power. • Example: A 1000 watt amplifier will limit forward power to 50% of the rated power for any load mismatch greater than 6:1. Thus, since 500 watts is the maximum amount of reflected power, the forward power is 1000 watts for VSWR 6:1 and somewhere between 1000 and 500 watts for VSWR ≥ 6:1. • Voltage and current limited Figure 2: Power vs. Load Impedance 75A400 For a Voltage/Current limited amplifier, calculations are much simpler. Ohm’s law can be directly applied to find net power, voltage, and load current. The amplifier output impedance is: For load impedance higher than the amplifier output impedance the amplifier is protected by the voltage limit. Regardless of the load impedance the output voltage is clamped near the specified minimum voltage rating. Applying ohm’s law: and Figure 3: Current vs. Voltage 75A400. (The center point of the graph occurs at the point where the load impedance is matched to the output impedance. Maximum power is delivered to the load only at this point) For load impedances lower than the amplifier output impedance the amplifier is protected by the current limit. Regardless of how small the load is, the output current will not exceed a value near the specified minimum current rating. Again applying ohm’s law: = and xΩ The following comments apply to amplifiers that don’t use one of the AR style VSWR protection methods listed above: • Amplifiers that protect by shutting down or turning off the RF output: • Forward power will be 0 if VSWR is excessive. This may occur at a VSWR as low as 2:1, but more often occurs for a VSWR somewhere between 2:1 and 3:1. Figure 4: Power vs. Load Impedance 1000W1000D 66 Clearly, amplifiers that either don’t employ VSWR protection or use this brute force VSWR scheme cannot be used in applicahf-praxis 6/2017 RF & Wireless tions where load mismatches are expected. Amplifiers that employ fold-back schemes at even lower VSWR levels than noted above are also in this category and are unsuitable for applications characterized by high load VSWR such as EMC immunity testing and research applications where load impedance is unknown. Output power loss due to load mismatch We have concentrated on the topic of forward power up to this point. This is the power actually available at the load. Jacobi’s Law, also known as the “maximum power theorem” states that “Maximum power is transferred when the internal resistance of the source equals the resistance of the load, when the external resistance can be varied, and the internal resistance is constant.” This effect Figure 5: Current vs. Voltage 1000W1000D is clearly observed when load impedance differs (greater or less) from the amplifier’s output impedance. As VSWR increases, an ever greater portion of the forward power is reflected back to the amplifier. Since net power is calculated by subtracting the reflected power from the forward power, it is apparent that any VSWR other than 1:1 will reduce the actual power absorbed by the load. The amount of power delivered to the load can be calculated using the following standard RF formulas: Reflection Coefficient: The two impedances are the load impedance and the output impedance of the amplifier. Once the forward power has been determined and the reflection coefficient calcu- Figure 6: Power vs. Load Impedance 800A3A lated, the net power delivered to the load only one point where the power delivered is found by merely substituting values into • 10 kHz – 400 MHz bandwidth to the load is equal to the forward power; the following equation: • 75 Watts minimum RF output the point where the load impedance mat• No active protection is required given its ches the amplifiers output impedance. The fall-off of the power delivered to the load very robust, conservative design Furthermore, given the net power and load • Full forward power is provided into any on either side of the 50 Ω load impedance is the result of load VSWR causing an ever impedance one can then calculate the outload impedance increasing portion of the forward power to put current and voltage using Ohms law. Figure 2 clearly demonstrates the best pos- be reflected back to the amplifier. Recall that sible scenario provided by the 75A400. Pnet = Pfwd - Pref. Real Examples The forward power is constant at 75 watts Now that we have investigated the nuances irrespective of load impedance. The center Figure 3 plots the voltage and current over involved in determining output power, vol- point of the graph demonstrates maximum the entire range of load impedance. The tage and current of RF power amplifiers in power transfer per Jacobi’s Law where center point represents the voltage and curgeneral, let’s look at four existing AR ampli- the 50 Ω amplifier is driving a 50 Ω load rent produced when the load impedance fiers and how they deal with load mismatch. and the blue output power curve clearly matches the amplifiers 50 Ω output impeExample 1: Most low and medium power demonstrates the reduction in net power per dance. Loads greater than 50 Ω are plotted amplifiers are of the Class A design and the maximum power theorem as the load to the right of the center point and loads less have nominal 50 Ω output impedance. A varies from the ideal of 50 Ω. Note that even than 50 Ω appear to the left. The end points typical amplifier of this type is the 75A400 though 75 watts is available independent of demonstrate the two possibilities of a worst the load impedance (orange curve), there is case mismatch; an open where the output power amplifier: hf-praxis 6/2017 67 RF & Wireless matching transformers tend to be narrow band, this approach may prove impractical if the 1000W1000D were to be operated over its entire frequency band. In this case, a series of narrow-band transformers could be switched in to the application as the frequency dictated or simpler yet, the user could opt for a higher power amplifier. The above graph demonstrates that even though fold-back occurs at a VSWR of approximately 6:1, significant output voltage and current are still delivered to the load. Example 3: Much has been said so far regarding the importance of impedance matching. The 800A3A is an example of a unique amplifier that provides the user with selectable output impedance to match a wide variety of applications. Figure 7: Current vs. Voltage 800A3A • 10 kHz – 3 MHz bandwidth • 800 Watts minimum output power rating • An internal user selectable impedance transformer provides 12.5, 25, 50, 100, 150, 200, or 400 Ω to facilitate a closer match to the load impedance • Active protection kicks in when VSWR exceeds 6:1 to reduce the gain • This fold-back protection limits the reflected power to 400 watts maximum The internal impedance transformer of the 800A3A allows this amplifier to have output impedance that matches that characterized by a variety of applications. External transformers are available to extend the usefulness of the 800A3A to include even more applications. Figure 8: Power vs. Load Impedance 350AH1 voltage is at a maximum with zero current, and a short where the current is maximum with zero voltage. The graphs in figure 2 and 3 are based on the minimum rated output of the amplifier across its entire operating frequency range. There most likely will be spots within the frequency range where the output power will exceed the specified minimum rated output power. To avoid unexpected results, always request a copy of specific production test data before placing an amplifier in service. • Active protection kicks in to reduce the gain when reverse power is measured at 500 watts; this is a VSWR of 6:1 when using the amplifier at rated power. Figure 7 clearly highlights the benefits of an amplifier with an internal impedance matching transformer that facilitates a better match with varying loads. The range of output voltage and current is considerably greater than what is provided by a standard 50 Ω amplifier. • This fold-back protection limits the reflected power to 500 watts maximum Example 4: The salient characteristics of high power, broadband, and very low The 1000W1000D is an example of one of output impedance (typically <1 Ω) of the AR’s high power amplifiers that folds-back 350AH1 uniquely appeal to low frequency when reverse power reaches 50% of rated applications. The 350AH1 differs from power. Even though the amplifier does fold- other amplifiers in this class in that it is a back, a considerable amount of power is still full sized bench-top instrument with “realbeing delivered to the load. In many cases, time” graphical color displays of output other manufacturers of high power ampli- voltage and current. It’s extremely robust Example 2: High Power Solid-State ampli- fiers would not be able to handle such con- design ensures that it can stand up to the fiers by necessity employ active VSWR pro- ditions and forward power would either be most demanding applications. tection. Take, for example the 1000W1000D. shut-down completely or reduced drastically. • 10 Hz – 1 MHz bandwidth • 80 MHz – 1000 MHz bandwidth • 1000 watts minimum RF output delivered into a 50 Ω output impedance 68 In power critical applications, an impedance • The minimum rated output power is 350 watts into a 1.8 Ω load. This equates matching transformer similar to the one used to a minimum of 25 volts and 14 amps into in the AR 800A3A could be used to match 1.8 Ω. (Power de-rated above 300 kHz) the amplifier to the load. However, since hf-praxis 6/2017 RF & Wireless • Source impedance is rated at <1 Ω (Since the output voltage and current are specified, output impedance is not used in the forward power calculations.) • Effective source impedance is 1.8 Ω (Zo=Vo/Io= 25 V/14 A) • Output protection limits both the voltage and current at rated values into any load. For loads less than 1.8 Ω, the output current is limited. For loads exceeding 1.8 Ω the output voltage is limited. This is an example of an amplifier with a 1.8 Ω effective output impedance. Due to the voltage and current limiting protection of the amplifier, VSWR does not play a role in lost power delivered to the load. Figure 9 plots the available output voltage and current from the 350AH1. The gray area is provided to indicate a more “typical” output profile. Individual amplifier characteristics will vary and are somewhat influenced by operating frequency and system losses. Figure 9: Current vs. Voltage 350AH1 from my amplifier?” can in rare cases be answered by merely applying Ohm’s law assuming the net power or power delivered to the load is simply the rated power output of the amplifier. In most cases, practical Summary issues such as VSWR and forward power The age old question of “How much out- concerns must be considered before appput voltage, current, and power can I expect lying Ohm’s law. While this application note has provided guidance in this matter, AR firmly believes that the best approach is to apply actual test data when calculating output parameters. If you are the least bit uncomfortable with this exercise, feel free to contact one of our Application Engineers. We would be more than happy to guide you through the process. ◄ News To coincide with Space Tech Expo, taking place in Pasadena, California, USA over May 23 to 25, Knowles Capacitors has produced a new shortform capability guide outlining their range of Space Heritage products. This user friendly guide provides an overview of Knowles’ space heritage and involvement in space grade platforms, as well as illustrating the specialty High REL and approved parts that find use in critical or high reliability environments. Knowles brands Syfer Technology and Novacap have drawn on the experience and expertise gained on numerous platforms to remain a leading supplier of Multilayer Ceramic Capacitors (MLCC) and assemblies for military and commercial space programs. The products detailed in the guide include EMI filters, High Rel and High Temperature Capacitors and Space Grade ranges including leaded & capacitor assembly options. Of particular interest, and on show on booth 2024 at Space Tech, is the catalog range of Single Layer Capacitor (SLC) Filters, Power Dividers and Directional Couplers from Knowles brand DLI. The filter series encapsulates SM Bandpass, Lowpass, Highpass and Cavity Filters, hf-praxis 6/2017 finding typical applications in Microwave Radar, Satellite & Radio Comms, Test Equipment and 5G Base Stations amongst others. These SMD products are designed to work at up to 42 GHz; with temperature stability over -55 to +125 °C: power hand- ling up to 40 Watts and high repeatability thanks to their precision thin film fabrication. The range is also EAR99 approved. ■ Knowles (UK) Ltd. www.knowlescapacitors.com 69

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