Calculation of closing impedance in feedback systems based on cut-insertion theorem

The cut-insertion theorem allows one obtain the parameters of one-loop feedback system (i.e. the system of order one) resulting from insertion into a cut the two-port providing preservation of the currents and voltages in the rest of network. Yet practical application of this theorem is limited by calculation of the impedance closing one side of the cut (it should be obtained, in general, from an algebraic equation with polynomial coefficients which are very difficult to calculate). The paper shows how to circumvent this difficulty: using the cut-inserted two-port which includes an independent current (voltage) source on one side of the cut and an independent voltage (current) source on the other side one obtains the signal graph of the feedback system of order two. The closing impedance is then directly calculated using the Mason´s formula and the branch transmissions of this graph. Then other parameters of the equivalent one-loop system such as loop gain, transfer function, etc., can be easily found.