**1 Introduction**
In the design of RF amplifier circuits, impedance matching between the input and output is a common challenge. Designing a matching network is essential to ensure optimal performance. When the required impedance for the network is known, RF design software like RFSim99 can automatically generate a matching network, making the process efficient and straightforward. However, in many cases, especially when the impedance requirements are not strict or other parameters are prioritized, engineers often approximate the input and output impedances of the device. This approximation may also consider the parameter variations of the device due to manufacturing tolerances. As long as the design error remains small, this approach is acceptable.
Nevertheless, in the design of RF power amplifiers, achieving high gain and efficiency in the driver stage and power output stage is crucial. Accurate knowledge of the input and output impedances at specific frequencies and power levels is necessary. These values are usually provided in the device manual for power transistors, serving as a reference for engineers. However, due to factors such as temperature, bias voltage, operating frequency, and power levels, the actual parameters can differ significantly from those listed in the manual. To reduce power consumption and improve efficiency, it may be necessary to measure the input and output impedance of the power transistor under real working conditions. While a network analyzer is the ideal tool for this task, it can be expensive. In its absence, engineers can use more common instruments such as oscilloscopes or impedance meters. The following section introduces a practical method for measuring the input and output impedance of an RF power transistor using standard equipment.
**2 General Methods of Impedance Measurement**
There are three main methods for impedance measurement: bridge method, resonance method, and voltammetry. The bridge method offers high accuracy and is widely used for precise measurements. However, applying it to active nonlinear devices like RF power transistors under real working conditions presents significant challenges. Similarly, the resonance method is not well-suited for nonlinear large-signal environments, as the waveform is typically not sinusoidal. Voltammetry, the most traditional method, relies on Ohm’s Law, where impedance is calculated as the ratio of voltage to current. However, in RF power transistors, the base and collector currents and voltages are not purely sinusoidal, making accurate measurement of fundamental components and phase differences difficult. Therefore, these conventional methods have limitations when applied to RF power transistors under actual operating conditions.
To address these challenges, an indirect method based on transfer function analysis has been developed. This method avoids the need for a network analyzer and effectively handles harmonic filtering while ensuring the power transistor operates under real conditions. It has proven to be simple, reliable, and suitable for practical applications.
**3 Indirect Impedance Measurement Using Transfer Function Method**
As shown in Figure 1, the networks HA, HB, and ZX form a test setup, with HC representing the equivalent network in Figure 2. HA and HB are passive linear two-port networks that serve to match, isolate, and filter signals, allowing a cleaner sine wave to be observed at bb'. The transfer function of HC can be expressed as:
$$ H_C = \frac{U_{aa'}}{U_{bb'}} e^{j\theta} $$
Where $ U_{aa'} $ and $ U_{bb'} $ are the effective values of the voltages at aa' and bb', and θ is the phase difference between them. By measuring these values, the transfer function HC can be determined. Since HA and HB are known linear networks, the unknown impedance ZX can be calculated accordingly.
**4 Principles of Test Network Design**
First, the design of HA and HB should be as simple as possible based on the application requirements. A more complex network increases computational effort and potential errors.
Second, component selection should prioritize resistors, capacitors, and inductors that closely resemble ideal models. Inductors should be used sparingly because their quality factor (Q) is limited, and their real-world model is complex. Before use, all components must be accurately measured with a precision impedance meter, and parasitic effects should be minimized during circuit assembly.
Third, the power transistor must operate normally during testing, ideally in a resonant or near-resonant state. The measured parameters will then be meaningful for specific operating conditions.
Finally, the probe capacitance at bb' should be as small as possible, and the input resistance of the probe should be as high as possible. Only the probe's capacitance needs to be considered in calculations, and its size should be measured before testing.
**5 Example of Measuring Input and Output Impedance of an RF Power Transistor**
The application manual of an RF power transistor typically provides input and output impedances under certain operating conditions. If the transistor operates in the typical state described in the manual, engineers can directly use the given values. Although there is some variation in the transistor's parameters, the error is generally small. However, if the operating conditions change—especially the frequency—the manual values may become inaccurate and should only be used as a reference.
For example, the input and output impedance data for the VSC band RF power transistor 2SC2630 from Mitsubishi Electric is: Zin = 0.8 + j1.2 Ω, Zout = 1.5 - j0.6 Ω, at Po = 60 W, VCC = 12.5 V, f = 175 MHz. Another example is the 2SC1971 RF power transistor operating in the VHF band, with Zin = 0.8 + j3.2 Ω, Zout = 6.2 - j3 Ω, at Po = 6 W, VCC = 13.5 V, f = 175 MHz. These values provide useful guidance but should be verified under actual operating conditions for optimal performance.
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