Asymptotic gain model

is the return ratio with the input source disabled (equal to the negative of the loop gain in the case of a single-loop system composed of unilateral blocks), G∞ is the asymptotic gain and G0 is the direct transmission term.

Figure 1 shows a block diagram that leads to the asymptotic gain expression.

The asymptotic gain relation also can be expressed as a signal flow graph.

The asymptotic gain model is a special case of the extra element theorem.

In contrast, for experimental measurements using real devices or SPICE simulations using numerically generated device models with inaccessible dependent sources, evaluating the return ratio requires special methods.

The small-signal equivalent circuit is shown in Figure 4, where the transistor is replaced by its hybrid-pi model.

It is most straightforward to begin by finding the return ratio T, because G0 and G∞ are defined as limiting forms of the gain as T tends to either zero or infinity.

In Figure 5, the input current source is set to zero, By cutting the dependent source out of the output side of the circuit, and short-circuiting its terminals, the output side of the circuit is isolated from the input and the feedback loop is broken.

In addition, a large first term reduces the importance of the direct feedthrough factor, which degrades the amplifier.

This amplifier is often referred to as a shunt-series feedback amplifier, and analyzed on the basis that resistor R2 is in series with the output and samples output current, while Rf is in shunt (parallel) with the input and subtracts from the input current.

It frequently is ambiguous just what type of feedback is involved in an amplifier, and the asymptotic gain approach has the advantage/disadvantage that it works whether or not you understand the circuit.

The circuit to determine the return ratio is shown in the top panel of Figure 7.

In Figure 7, the output variable is the output current βiB (the short-circuit load current), which leads to the short-circuit current gain of the amplifier, namely βiB / iS: Using Ohm's law, the voltage at the top of R1 is found as or, rearranging terms, Using KCL at the top of R2: Emitter voltage vE already is known in terms of iB from the diagram of Figure 7.

Substituting the second equation in the first, iB is determined in terms of iS alone, and G0 becomes: Gain G0 represents feedforward through the feedback network, and commonly is negligible.