RESISTANCE AND CAPACITANCE IN SERIES 



A less fearsome expression which deals with the area under the phase-shift 

 curve, rather than the phase shift itself, is 



•+00 



I 



IT 



where u = loge ojIm^, cOj. is any convenient reference frequency, and (A as — 

 Aq) is the difference between the transmission factors of the filter at infinite 

 and at zero frequency, measured in dB's. Thus in the filters whose trans- 

 mission characteristic exhibits symmetry about a vertical axis — the Wien 

 bridge and the parallel T — A a, is equal to Aq and the value of the integral is 

 zero; hence the phase characteristic lies equally above and below the line 

 cf) = 0. Again, in limited phase-shift filters, the equation shows that for a 

 given degree of filtering, A^— Aq, there is an inverse relationship between the 

 phase shift encountered and the length of the transition band (i.e. the band 

 over which the transmission factor is changing). In other words, one cannot 

 have filters which cut-off sharply and exhibit small phase shift at the same 

 time. 



53 



