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Fachzeitschrift für Hochfrequenz- und Mikrowellentechnik

RF & Wireless RF

RF & Wireless RF Amplifier Output Voltage, Current, Power and Impedance Relationship Unfortunately, such ideal conditions rarely apply in actual “real world” applications. Real amplifiers are required to drive varying load impedances. The mismatch between these “real” loads and the amplifier’s output 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 How much output voltage, current and power can RF amplifiers provide? This question is often asked by novice test engineers as well as seasoned RF professionals. Depending on the application, there is often an underlying desire to maximize one of the three parameters: power, voltage or current. While one would think that a simple application of Ohm’s law is called for, this would only apply given ideal conditions, such as when an RF amplifier with a typical 50 Ω output resistance is driving a 50 Ω load. In this rare case where the load impedance perfectly matches the amplifier output impedance, the power delivered to the load is simply the rated power of the amplifier. There is absolutely no reflected power and thus, there is no need to limit or control the gain of the amplifier to protect it from excessive reflected power. is the basic form of Ohm’s law where the current I is in units of amperes (A), the Electromotive Force (EMF) or difference of electrical potential E is in volts (V), and R is the circuit resistance given in ohms (Ω). Applying the standard equation relating electrical power to voltage and current A cross multiplying and rearranging each of the variables results in the equations shown in the Ohm’s law pie chart (see Fig 1) showing the various combinations of the four variables, I, V, Ω and W. Let’s use Ohm’s pie chart to determine the output voltage, current, and power of a 50 Ω amplifier operating under ideal conditions. Example Assume we have a 100 watt amplifier with 50 Ω output impedance driving a 50 Ω load. This is an ideal situation in that 100% of the forward power will be absorbed in the load and therefore there is no reflected power in this example.The full 100 Watts will be delivered to the 50 Ω load. 64 hf-praxis 6/2017

RF & Wireless Selecting appropriate formulas from the Ohm’s pie chart, one can easily characterize this ideal amplifier: √ Substituting known values: √ = 70,7 V rms Thus, the output voltage across the 50 Ω load is 70.7 V rms Substituting known values: = 1,41 A rms The output load current is 1,41 A rms As can be seen from the above example, when impedances match, power, voltage, and current are easily determined by the application of Ohm’s law. Now let’s consider “real life” amplifiers and the effects they have on the determination of output voltage, current and power. Impedance Mismatch: The danger of impedance mismatch and methods used to protect amplifiers Maximum power is transferred to the load only when the load impedance matches the amplifier’s output impedance. Unfortunately, this is rarely the case. In these “typical” situations, reflections occur at the load and the difference between the forward power and that delivered to the load is reflected back to the amplifier. A voltage standing wave is created by the phase addition and subtraction of the incident and reflected voltage waveforms. Power amplifiers must either be capable of absorbing this reflected power or they must employ some form of protection to prevent damage to the amplifier. For example, an open or short circuit placed on the 100 watt power amplifier discussed above would result in an infinite voltage standing wave ratio (VSWR). Since for Z 0 >Z L and for Z L > Z 0 it can be seen that VSWR is always ≥1. With no active VSWR protection, an open circuit at the load would result in a doubling of the output voltage to 141,4 V rms , while a short circuit would increase the output current to 2,82 A rms . In either of these worst case scenarios, the 100 watt power amplifier must tolerate a maximum power of 200 watts (100 watts forward + 100 watts reverse). 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 could be removed. Consequently, all amplifiers should employ some form of protection when VSWR approaches dangerous levels. The following is a partial list (most desirable to least desirable) of some methods used: Overdesign • All Solid-state devices and power combiners are conservatively designed to provide sufficient ruggedness and heat dissipation to accommodate infinite VSWR. • No additional active VSWR protection circuitry is required with this approach. • This conservative approach is found on AR’s low to mid power amplifiers. Active monitoring of VSWR resulting in a reduction in amplifier gain when VSWR approaches dangerous levels • When VSWR exceeds a safe level the forward power is reduced. This technique is sometimes referred to as “gain fold-back” or just “fold-back”. • AR’s high power solid-state amplifiers will fold-back when reflected power reaches 50% of the rated power corresponding to a VSWR of 6:1 and will withstand any amount of mismatch. Active monitoring of VSWR leading to a shut down when VSWR exceeds a safe level • This is considered a brute-force technique that can lead to undesirable test disruptions. • AR does not use this technique in any of its amplifiers. Active thermal monitoring • High VSWR will cause a buildup of heat. When a predetermined temperature threshold is exceeded, the amplifier is shut down. • Due to the nature of thermal time constants, this approach is relatively slow. Extreme variations in VSWR may not immediately result in shut down. • AR amplifiers employ some degree of thermal monitoring for circuit protection but do not rely on this relatively slow method to protect against extreme VSWR. 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”. What will be the effect of VSWR protection on forward power, or power available to the load? Let’s first look at the various methods used to protect AR amplifiers from the ill effects of extreme VSWR. • Class A amplifiers designed to tolerate infinite VSWR: This type of amplifier will not fold-back or shut off when operating into a high VSWR. (Most AR low to medium power amplifiers fit in this category.) • With these amplifiers, the forward power is always the rated power, and is independent of load • Example: A 100 watt amplifier will provide 100 watts forward power irrespective of load variations • Fold-back based on reflected power: This technique is used for high power AR amplifiers where the reflected power is not allowed to exceed 50% of the rated power. • These larger amplifiers provide full rated power to the load for any VSWR up to 6:1. As VSWR increases beyond this level, fold-back is used to limit the reflected power to no more than 50% of the rated power, regardless of load variations. • In this case, available forward power is equal to the rated power until a VSWR of 6:1 is reached. At this point, 50% of hf-praxis 6/2017 65

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