Stability of feedback circuits is generally quantified as phase margin, a function of the phase of the system loop gain evaluated at the frequency where loop gain magnitude goes to one. Introductory analysis uses ideal blocks having low output impedance and uni-direction signal transmission where finding loop gain is relatively straight forward. Real systems have real elements and suffer from loading and bi-directional signal transmission leading to loading and feed forward effects in addition to the desired feedback effects. Finding the loop gain function becomes more difficult for real systems and even more difficult yet for systems with multiple and embedded loops. This paper develops a process for finding the proper loop gain in real systems, single and embedded loop designs using driving point impedance and signal flow graph analysis. While simple systems using simplified device models can be solved in closed form, the algebra for complex models quickly becomes unmanageable. A method for obtaining loop gain terms from simulation is shown allowing for complex algebra to be performed by the simulator.
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