Electronic apparatus for biological research electronicappara00dona Year: 1958 RESISTANCES AND CAPACITANCES and by the usual process the phase shift turns out to ht 4 (j> = tan~^ coCR — 1 (oCR (Graph 19) Relationship between transmission characteristic and phase shift It often happens that apparatus contains filters, either of the R-C type we have been discussing or of the R-C-L type to be dealt with in Chapter 5, whose precise natures are not known. If the transmission characteristic is known, or can be measured, then it is possible* to compute the phase shift. If on the transmission cha
Electronic apparatus for biological research electronicappara00dona Year: 1958 RESISTANCES AND CAPACITANCES and by the usual process the phase shift turns out to ht 4 (j> = tan~^ coCR — 1 (oCR (Graph 19) Relationship between transmission characteristic and phase shift It often happens that apparatus contains filters, either of the R-C type we have been discussing or of the R-C-L type to be dealt with in Chapter 5, whose precise natures are not known. If the transmission characteristic is known, or can be measured, then it is possible* to compute the phase shift. If on the transmission characteristic we are considering a region of the curve which is reasonably straight, then the phase shift ^ at frequency a> is given simply by ^' = 15 (^)„ where (d^/dM)^^ is the slope of the characteristic in dB's per octave at frequency co. Thus a tapered 3-section low-pass R-C filter, well above the turn-over frequency, has a slope of 18 dB's per octave and the phase shift is ^0, = 7^ X 18 or 270 degrees If the transfer characteristic is rather less simple, perhaps a low-pass type of curve but containing a 'bump', as shown in Figure , then in the region Frequency Figure of the bump the phase shift is modified and it is necessary to add a correcting term to the expression already given. The equation which follows is due to Bode, and is quoted by F. E. Terman {Radio Engineer's Handbook). If the slope of the curve at the frequency m where the phase shift is required is {dAjdu)^, and the general slope of the part of the characteristic upon which the bump is superposed is (d^)/(dw), as before, then Uu) ~ , 77 (dA\ 1 f loge COth 2r' where u = loge (frequency/frequency co). * Provided there are no 'all pass' sections present, or 52
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