696 BELL SYSTEM TECHNICAL JOURNAL 



operated in a nonlinear region — let us say by impressing upon the cir- 

 cuit a sufficiently large alternating potential provided by an external 

 independent generator. 



To answer this question we may consider the response of the am- 

 plifier, loaded by the independent generator, to a small alternating 

 potential introduced for test purposes. Since the response of the sys- 

 tem is known to be linear from the theory of perturbations, we might 

 attempt to apply the linear criterion to the small superposed force. To 

 do this it is necessary to measure the transfer factor for the small super- 

 posed force over the frequency range at a particular load of interest. 



Application of the experimental technique to this extended criterion 

 introduces difficulties since the opening of the feed-back loop for meas- 

 uring purposes disturbs to a certain extent the distribution of these 

 loads, particularly the harmonics, and modulation products in general. 

 This makes it difficult to get the same loading effect when the loop is 

 opened for measuring purposes as obtained when the loop is closed. 

 Another consideration is that the response to the small component 

 may be expected to vary in general at different points on the loading 

 wave, so that the measuring procedure averages the response over a 

 cycle of the loading wave. A method of measurement analogous to 

 that of the flutter bridge would be required to evaluate the transfer 

 factor at points of the loading cycle. Further, the measuring appara- 

 tus is affected by the presence of the loading currents when these are 

 sufficiently large. In the present case in which the loading frequency 

 (60 kilocycles) was far removed in the frequency scale from the test 

 frequencies, it was found possible to approximate the necessary meas- 

 urements by the insertion of selective circuits. 



The curves of Fig. 1 1 represent portions of the transfer factor polar 

 diagram for an amplifier similar to the one previously described, meas- 

 ured by the visual method with different loading amplitudes. The 

 effect of the load on this particular amplifier is to change both phase 

 shift and amplitude so that the curves shrink both radially and tan- 

 gentially, pulling the loop back across the zero phase axis until, at the 

 heaviest load, the two low-frequency crossings are completely elimin- 

 ated. If the extended criterion is valid, we should expect the ampli- 

 fier to be stable at any setting of the feed-back attenuator. As the 

 load is decreased from this value, the crossings occur at successively 

 higher gains so that the start of oscillations would occur at progres- 

 sively higher settings of the feed-back attenuator. 



The curves of Fig. 12 show the attenuator settings predicted by the 

 extended criterion and those determined by direct observation of the 

 attenuator setting required for oscillations when the feed-back circuit 



