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The feedback gain at low frequencies and for large A OL is A FB ≈ 1 / β (look at the formula for the feedback gain at the beginning of this section for the case of large gain A OL), so an equivalent way to find f 0 dB is to look where the feedback gain intersects the open-loop gain. (Frequency f 0 dB is needed later to find the phase margin.)
Phase margin and gain margin are two measures of stability for a feedback control system. They indicate how much the gain or the phase of the system can vary before it becomes unstable. Phase margin is the difference (expressed as a positive number) between 180° and the phase shift where the magnitude of the loop transfer function is 0 dB.
Figure 5: Bode gain plot to find phase margin; scales are logarithmic, so labeled separations are multiplicative factors. For example, f 0 dB = βA 0 × f 1. Next, the choice of pole ratio τ 1 /τ 2 is related to the phase margin of the feedback amplifier. [9] The procedure outlined in the Bode plot article is followed. Figure 5 is the Bode ...
The root locus plots the poles of the closed loop transfer function in the complex s-plane as a function of a gain parameter (see pole–zero plot). Evans also invented in 1948 an analog computer to compute root loci, called a "Spirule" (after "spiral" and " slide rule "); it found wide use before the advent of digital computers .
Randomly varying channel gains such as fading are taken into account by adding some margin depending on the anticipated severity of its effects. The amount of margin required can be reduced by the use of mitigating techniques such as antenna diversity or multiple-input and multiple-output (MIMO). A simple link budget equation looks like this:
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The loop gain is calculated by imagining the feedback loop is broken at some point, and calculating the net gain if a signal is applied. In the diagram shown, the loop gain is the product of the gains of the amplifier and the feedback network, −Aβ. The minus sign is because the feedback signal is subtracted from the input.
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