688 BELL SYSTEM TECHNICAL JOURNAL 



Two methods of measurement have been found useful. The first is 

 a null method capable of good precision over a wide frequency range. 

 The second is a visual method in which the transfer factor polar dia- 

 gram is traced on the screen of a cathode ray oscillograph. This 

 method is not capable of very great precision and, in the model used, 

 the frequency range is somewhat restricted. However, it permits of a 

 rapid survey of the situation for which its precision is adequate, before 

 proceeding with the slower and more precise measurements of the null 

 method, where the latter are required. By making such a preliminary 

 survey the critical frequency ranges can be mapped out for precise 

 measurement, thereby eliminating a large amount of unnecessary labor. 



Null Method 



In the more precise measurements extending over a wide frequency 

 range, special care is required to ensure freedom from errors in the 

 measurement of phase angles and amplitudes. Much of the difficulty 

 associated with direct measurement over wide frequency ranges is 

 avoided by the use of a simple demodulation scheme. In this scheme, 

 the potentials to be compared are modulated down to a fixed frequency 

 (in actual use 1000 cycles) regardless of the frequency at which the test 

 is being made. In this way a minimum portion of the circuit carries 

 the high frequency. Further this permits the use of voice frequency at- 

 tenuators, phase shifters, and amplifiers which in fact require calibra- 

 tion at only a single frequency. 



In this arrangement, as shown in Fig. 5, demodulators are shunted 

 across the input and output terminals of the circuit under test. A 

 single oscillator supplies the carrier to both demodulators, its frequency 

 differing by 1000 cycles from the frequency supplied to the circuit 

 under test. The demodulated outputs are connected through attenua- 

 tors and phase shifters to a common amplifier detector. The attenua- 

 tors and phase shifters are adjusted until the detector gives a null read- 

 ing. When this condition obtains the difference in the attenuator set- 

 tings in the two branches is equal to the gain or loss of the circuit 

 under test, and the difference in the phase shifter settings is either 

 equal to or the negative of the phase shift of the circuit under test. 

 To show this, denote the amplifier output voltage by Po cos {livft — (p), 

 and the beat frequency voltage supplied to the demodulators by P cos 

 27r(/ ± 1000)^. The demodulated output, proportional to the product 

 of the two applied waves, is then 



PPoCOS (27r-1000/ T </)). 

 Correspondingly, the demodulated output from the other demodulator 



