High-speed components such as opamps and analog- to-digital converters (ADCs) are now typically available at RF and microwave frequencies for use in 50-Ohm systems. But since they are often at different impedances, parameters such as power gain and noise figure can be misused during a circuit analysis. To better understand the integration of baseband components into high-frequency circuits and systems, it may be helpful to review the concepts of voltage power gain as they apply to two-port networks, and then apply these concepts, along with additive noise models, to show how noise performance can be computed when there is no consistent system impedance.

Consider a general case where there is no consistent system impedance. The power source might be a high-impedance source, the amplifier could be an operational amplifier configured for a finite voltage gain, and the load could be an arbitrary resistance. A modest amount of circuit analysis will reveal the voltage and power gain of the amplifier with specific source and load resistances.

This set of three basic elements can be analyzed by using the method of Thevenin (or Norton) equivalents. The power source can be represented by a simple equivalent circuit (Fig. 1). The amplifier can similarly be modeled by a set of Z parameters as shown in Fig. 1. Assume the amplifier is unilateral. The parameters of this network are the input and output resistances and the Thevenin voltage gain a.

To compute the power gain from source to load, first compute the power absorbed by the input of the amplifier:

Compute the power absorbed by the load by means of

The power gain is then shown by Eq. 2:

To compute the voltage gain, first compute the input voltage, V_in. The input impedance of the amplifier is equal to R_in, so voltage V_in is:

Now compute the voltage at the output of the amplifier:

The voltage gain is then given by Eq. 3:

Usually the amplifier is specified in terms of its available power gain G_A, which is defined with the source and load impedances equal to the input and output resistances, R_in and R_out, respectively. Equation 2 can be used to give the Thevenin voltage gain in terms of the available power gain G_A. Set the source resistance, R_s equal to R_in, and the load resistance, R_L, equal to R_out, and solve for parameter a:

Using this substitution, the power gain and voltage gain can be expressed in terms of G_A:

If the input, output, and load resistances are all equal, the insertion power gain reduces to the available power gain. The voltage gain becomes the square root of the available power gain.

It is also useful to know V_s in terms of P_AVS. For this purpose, Eq. 1 can be used, with the assumption that the load impedance is equal to R_s:

When the source, load, and port impedances of the cascade are all the same real value (R_o), the traditional power-based method of cascading elements can be used.

This method almost always uses the decibel (dB) as a unit of measure. In the most general terms, the decibel is defined as the logarithm of a ratio. A parameter such as power gain is a ratio, so it can be converted to dB as follows:

A parameter such as power is not a ratio, but it can be expressed in terms of its relation to a reference power level; typically 1 mW is used as the reference level:

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