Feedback Stage Transfer Functions

Note In defining transfer function H(s), we have not included negative sign 

So its output will always be greater than its input (gain 1). This restriction on the dc gain has been known to cause some strange and embarrassing situations in the field, especially under certain abnormal conditions. Therefore, a non-inverting error op-amp is generally not favored. 

Lastly, note that by just using an inverting error amplifier, we have in effect also applied a — 180° phase shift right off the bat We will see in the following section, that this increases the possibility of oscillations by itself. 

We are now in a position to start tying all the loose ends together For each of the three topologies, we now know both the forward transfer function G(s) (control-to-output) and also the feedback transfer function H(s). Going back to the basic equation for the closed-loop transfer function, 

Note When doing the tan-1 operation, we may often need to visualize where the number is actually located in the complex plane. For example, in this case, tan of 0° and tan of 180° are both zero, and we wouldn t have known which of these angles is the right answer — unless we visualized the number in the complex plane. In our case, since the number was minus 1, we correctly placed it at 180° instead of 0°. 

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