A bridge for the determination of the frequency of an alternating current in the audio-frequency range
Geoffrey D Pegler · Proceedings of the Physical Society · 1934
When the secondary of an air-cored transformer, of inductance N , is closed through a total resistance Q , the effective resistance P ' and the effective inductance L ' of the primary are given by ( P ' - P ) = p 2 M 2 Q /( Q 2 + p 2 N 2 ), ( L - L ') = p 2 M 2 N /( Q 2 + p 2 N 2 ), where M is the mutual inductance between primary and secondary, and p is 2π times the frequency. If Q is varied and p is kept constant, P ' becomes a maximum when Q = pN , and under this condition ( P ' - P ) max . = pM 2 /2 N , which is proportional to the frequency, while ( L - L ') max . = M 2 /2 N = a constant. The above equations form the basis of the proposed method of determination of frequency, the maximum change in P corresponding to any frequency being measured by the Owen a.-c. bridge. The changes of resistance necessary to satisfy the third of the above equations may be effected with a single control, since both ( P ' - P ) max . and the corresponding value of Q are proportional to the frequency. The change required to satisfy the last equation is effected by the mere closing of a switch. The effect of residuals is discussed also.