Electronic apparatus for biological research electronicappara00dona Year: 1958 RESISTANCES AND CAPACITANCES From A, draw a dotted straight line to the left and downwards, of slope 6* dB per octave, that is, 6 dB's for a twofold change in frequency. From A, mark the point B, 3 dB's below A. Draw a smooth curve, through B, asymptotic to the dotted hnes. This is the required characteristic curve {Figure ). The transmission curve A Transmission factor 1 Slope: f 6 B's/octave,^ dB's down Frequency ——»- Figure for the low-pass case is, of course, the mirror image of this and the techni
Electronic apparatus for biological research electronicappara00dona Year: 1958 RESISTANCES AND CAPACITANCES From A, draw a dotted straight line to the left and downwards, of slope 6* dB per octave, that is, 6 dB's for a twofold change in frequency. From A, mark the point B, 3 dB's below A. Draw a smooth curve, through B, asymptotic to the dotted hnes. This is the required characteristic curve {Figure ). The transmission curve A Transmission factor 1 Slope: f 6 B's/octave,^ dB's down Frequency ——»- Figure for the low-pass case is, of course, the mirror image of this and the technique for sketching it will be obvious. Finding the phase shift when using j operator—To plot the modulus of the transmission factor for a filter is not to tell the whole story, for we are saying nothing about the relative phase angle between input and output. To find the 'phase shift' when using j operator we employ a process called 'rationaliza- tion'. In general the final expression for Fout/^in has the form {A +jB)l (C+jD) To rationalize this, we multiply numerator and denominator by C —jD, giving Fout _ (A -f JB)iC - jD) _ {AC-V BC)-^ j{BC - AD) Fin ~{C+jD){C-jD) C^-^r D^ The tangeni of the phase shift is now given by they part of the numerator divided by the real part, , BC-AD ^ - *'^ AC-VBC If the phase of the output leads on that of the input, the phase angle will come out positive; if it lags, negative. Thus, for the high-pass filter, we had Fout 1 rationalizing, Fout Fm Fin 1 + 1 J coCR J coCR 1 + coCR 1 - J mCR, 1 + ^r 1+(—V ayCR] ^ [coCRj ♦ 6 dB's loss is almost exactly a transmission factor of ^ (Graph 6). 36
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