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6-2017

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Fachzeitschrift für Hochfrequenz- und Mikrowellentechnik

RF & Wireless Figure 2:

RF & Wireless Figure 2: Power vs. Load Impedance 75A400 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 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: = x Ω and The following comments apply to amplifiers that don’t use one of the AR style VSWR protection methods listed above: Figure 4: Power vs. Load Impedance 1000W1000D • 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. Clearly, amplifiers that either don’t employ VSWR protection or use this brute force VSWR scheme cannot be used in applica- 66 hf-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 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: Figure 5: Current vs. Voltage 1000W1000D 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 following equation: Furthermore, given the net power and load impedance one can then calculate the output current and voltage using Ohms law. Real Examples 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 four existing AR amplifiers and how they deal with load mismatch. Example 1: Most low and medium power amplifiers are of the Class A design and have nominal 50 Ω output impedance. A typical amplifier of this type is the 75A400 power amplifier: Figure 6: Power vs. Load Impedance 800A3A • 10 kHz – 400 MHz bandwidth • 75 Watts 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 amplifiers 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 P net = P fwd - P ref . 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 amplifiers 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 hf-praxis 6/2017 67

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