Asymptotic gain model
The asymptotic gain model (also known as the Rosenstark method) is a representation of the gain of negative feedback amplifiers given by the asymptotic gain relation:
where 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. This form for the gain can provide intuitive insight into the circuit and often is easier to derive than a direct attack on the gain.
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. See Figure 2. The asymptotic gain model is a special case of the extra element theorem.
As follows directly from limiting cases of the gain expression, the asymptotic gain G∞ is simply the gain of the system when the return ratio approaches infinity:
while the direct transmission term G0 is the gain of the system when the return ratio is zero:
Direct application of the model involves these steps:
These steps can be implemented directly in SPICE using the small-signal circuit of hand analysis. In this approach the dependent sources of the devices are readily accessed. 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.
Classical feedback theory neglects feedforward (G0). If feedforward is dropped, the gain from the asymptotic gain model becomes
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