RF and Microwave Amplifier Output Voltage, Current, Power, and Impedance Relationship of RF & Microwave Amplifier
By Jason Smith, Supervisor Applications Engineer and Pat Malloy, Sr. Applications Engineer, AR

How much output voltage, current and power can an RF amplifier 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.

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 article 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 proportional to the resistance between the points. Thus, the equation I=E/R is the basic form of Ohm’s Law where the current I is in units of amperes (A), the Electro-motive 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 (P=V•A), cross multiplying and rearranging each of the variables results in the equations shown in the Ohm’s Law pie chart (see Figure 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
• Selecting appropriate formulas from the Ohm’s pie chart, one can easily characterize this ideal amplifier.

The output load current is 1.41 Arms

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 ZL>ZO 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 Vrms, while a short circuit would increase the output current to 2.82 Arms. 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 shutdown 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 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.

Output power loss due to load mismatch
We have concentated 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 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: where 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 calculated, the net power delivered to the load is found by merely substituting values into the equation:

Furthermore, given the net power and load impedance one can then calculate the output current and voltage using Ohm’s Law.

Real Example
Now that we have investigated the nuances involved in determining output power, voltage and current of RF power amplifiers in general, let’s look at one AR amplifier and how it deals with load mismatch.

Example 1: Most low and medium power amplifiers are of the Class A design and have a nominal 50 Ω output impedance. A typical amplifier of this type is the 75A400 power amplifier:

• 10 kHz – 400 MHz bandwidth
• 75 W minimum RF output
• No active protection is required given its very robust, conservative design
• Full forward power is provided into any load impedance

Figure 2 clearly demonstrates the best possible scenario provided by the 75A400. The forward power is constant at 75 watts irrespective of load impedance. The center point of the graph demonstrates maximum power transfer per Jacobi’s Law where the 50 Ω amplifier is driving a 50 Ω load and the blue output power curve clearly demonstrates the reduction in net power per the maximum power theorem as the load varies from the ideal of 50 Ω. Note that even though 75 watts is available independent of the load impedance (orange curve), there is only one point where the power delivered to the load is equal to the forward power; the point where the load impedance matches the amplifier’s output impedance. The fall-off of the power delivered to the load on either side of the 50 Ω load impedance is the result of load VSWR causing an ever increasing portion of the forward power to be reflected back to the amplifier. Recall that
Pnet=Pfwd-Pref.

Figure 3 plots the voltage and current over the entire range of load impedance. The center point represents the voltage and current produced when the load impedance matches the amplifier’s 50 Ω output impedance. Loads greater than 50 Ω are plotted to the right of the center point and loads less than 50 Ω appear to the left. The end points demonstrate the two possibilities of a worst case mismatch; an open where the output voltage is at a maximum with zero current, and a short where the current is maximum with zero voltage.

Figures 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.

Summary
The age-old question of “How much output voltage, current, and power can I expect 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 issues such as VSWR and forward power concerns must be considered before applying Ohm’s Law. While this article 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.

Reference
Application Note #27A: Importance of Mismatch Tolerance for Amplifiers Used in Susceptibility Testing Application Note #49: RF Amplifier Output, Voltage, Current, Power and Impedance Relationship

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