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By Allan Waters (auth.)

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10) Selection of op-amps with superior GB and SR is left to the designer, who must choose between cost and suitability of a device for his particular require- 34 Active Filter Design ment. It should be noted that non-ideal op-amps have fmite, (usually) high values of input resistance and non-zero values of output resistance. ; this latter condition is of importance to the filter designer and will be briefly investigated here. In the case of an ideal op-amp, the output voltage will be zero if both input voltages are zero.

15) We must now introduce normalisation into the components and design parameters in order to produce a rationalised design procedure. Let w~ = 1 rad/s, C 1 = C2 = 1 F. 16) Notice that there are six unknowns and therefore a certain degree of component selectivity will have to be made since a unique solution is not possible. 16) we obtain which may be written boR? 17) So far we have normalised the capacitors C 1 , C2 and obtained the normalised values for the resistors R 1 , R 2 • We now have to obtain values for the gain resistors R 3 , R 4 for the good circuit design condition of minimum de offset.

9. 3. 10 where G 1 = - etc. Rt for the circuit Gt} G2 If now all of the components, with the exception of G4 , are fixed resistors of equal value, sketch the variation of V0 /Vi with variation of G4 , assuming that it is a pure resistor. 4. 11 is that of a summing amplifier with inverting gain. The op-amp has an open-loop gain given by AUw) = A 0 waf jw + Wa. 11 37 38 Active Filter Design Show further that the 3 dB bandwidth is given by w 3ds = A 0 w 3 /1 + 2k, stating any assumptions made. 5. 12 is a level-shift network necessary to convert the differential output from the multiplier into a single-ended output relative to earth.

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