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The asymptotic gain model[1][2] (also known as the Rosenstark method[3]) 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: Block diagram for asymptotic gain model[4]
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.
Figure 2: Possible equivalent signal-flow graph for the asymptotic gain model
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:
^Middlebrook, RD: Design-oriented analysis of feedback amplifiers; Proc. of National Electronics Conference, Vol. XX, Oct. 1964, pp. 1–4
^Rosenstark, Sol (1986). Feedback amplifier principles. NY: Collier Macmillan. p. 15. ISBN 0-02-947810-3.
^Palumbo, Gaetano & Salvatore Pennisi (2002). Feedback amplifiers: theory and design. Boston/Dordrecht/London: Kluwer Academic. pp. §3.3 pp. 69–72. ISBN 0-7923-7643-9.
^Paul R. Gray, Hurst P J Lewis S H & Meyer RG (2001). Analysis and design of analog integrated circuits (Fourth ed.). New York: Wiley. Figure 8.42 p. 604. ISBN 0-471-32168-0.
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