Amplifier designers have so far learned about the use of the unilateral gain design approach as well as a method for achieving simultaneous conjugate matching of a stable transistor's input and output ports to its source and load. This month, the article series focuses on a method corresponding to the operating gain design approach in which particular load impedance is specified for an amplifier design.

For the 50-Ω loaded amplifier, for the unilateral amplifier designs, and for the simultaneous conjugate match design, the transducer gain (GT) definition was applied. For a network described by S-parameters, two other commonly used gain definitions are used (p. 213 of ref. 1): the operating gain (GP) and the available gain (GA), which are special cases derived from the transducer gain:

where:

and

and

The three gain definitions (Fig. 1) can be expressed in terms of the S-parameters and the reflection coefficients of the network, source, and load.^1,2

The transducer gain is provided by

or

The operating gain can be calculated by

The available gain can be determined by

where:

and

The operating gain design is used with a matched source and optional load. The design is exact, and S₁₂ is not neglected. The operating gain procedure consists of selecting a Γ_L value from constant gain circles (to be presented shortly) and then finding the corresponding input match, Γ_S.

The operating gain method is particularly useful in the case of power amplifiers, for which a specific load impedance for the transistor is often required for maximum power output. The load, Z_L, is typically specified by the transistor manufacturer as that which was found empirically to yield the highest power output for the device at a given frequency. Other applications for this method arise in which the Z_L is predetermined, perhaps by the input impedance of a subsequent filter.

Unlike the unilateral gain and simultaneous conjugate match designs, the mathematics of the operating gain method do not require an unconditionally stable network. However, if the amplifier is not unconditionally stable, care must be taken that the chosen Z_S and Z_L values do not lie within or too near the impedances that cause potential instability. Furthermore, if the design is applied with a potentially unstable network, there will be no safeguard against the network oscillating when the designed Z_S and/or Z_L may be absent, as might occur when the intended source or load is disconnected. Therefore, while the operating gain method can be used with potentially unstable networks, good engineering practice suggests that one first make the network unconditionally stable if this can be done while satisfying the amplifier's performance requirements.

The operating gain can be rewritten as¹

where:

and