Active Filter Design

A filter is an electrical network which is designed specifically to modify, in a prescribed way, an electrical signal applied to its input terminals. An elementary example would be a signal having only low-frequency and high-frequency components. A low-pass filter would permit only the low frequencies to be transmitted, the high frequencies being suppressed or attenuated. The converse is true for passing the high frequencies while suppressing the low frequencies by means of a high-pass filter.

Modern filter design is based on the accurate selection of an appropriate input/output relationship which will satisfy the required specification of the filter. The steps involved in any successful filter design may be summarised as follows:

It is useful to consider at this stage the basic theory concerning integrated circuit operational amplifiers, since they are the foundation of most of the filter circuits to be studied. The reader should refer to the more specialised texts for a fuller treatment of the subject matter.

A number of popular circuits will now be considered using the non-inverting (positive gain) and inverting (negative gain) operational amplifier configurations. In both cases, the open-loop gain of the amplifier will be taken to be high (10⁵ or greater) and in the first class of circuits to be considered, the so-called voltage-controlled-voltage-source (VCVS), it will be seen that the circuit gain may be adjusted by means of a resistor ratio. In the second class of circuits where there are two feedback paths, the so-called multiple feedback (MFB) circuits, the operational amplifier is again assumed to be working as an ideal infinite gain device.

It would be misleading to suggest, with the advent of operational amplifiers and digital synthesis techniques, that passive filters have no role to perform in modern circuit applications.

A major problem encountered by filter designers is that caused by the need for inductance at low frequencies. We will now consider a concept which will enable the designer to dispense with inductors for certain applications by using what is referred to in the literature as the passive network simulation method. Central to the basis of the design is a device referred to as a gyrator whose principle of operation was outlined by Tellegan. It will be seen that we fortunately possess an op-amp based gyrator circuit and several such devices are manufactured using IC technology. A distinct advantage of the active simulation approach is that the circuits produced have low sensitivities which are basically those of the passive counterparts. We shall see that a distinct disadvantage of producing synthetic inductance, as it is called, is that being an active device, one of its terminals must be connected to earth. Furthermore, if matched op-amps are used, then the effects of non-ideal amplifier parameters on the inductance realisation are minimised.

Circuits or networks are constructed to produce a specified input/output relationship and since the solution to the design problem may not be unique, a variety of circuits may be constructed to realise the same transfer function.