Active Filter Design Techniques

Publisher Summary The simplest design of a bandpass filter is the connection of a high pass filter and a low pass filter in series, which is commonly done in wideband filter applications. Thus, a first order high pass filter and a first order low pass provide a second order bandpass, while a second order high pass filter and a second order low pass result in a fourth order bandpass response. In comparison to wideband filters, narrowband filters of higher order consist of cascaded second order bandpass filters that use the Sallen–Key or the multiple feedback topology. A filter with an even order number consists of second order stages only, while filters with an odd order number include an additional first order stage at the beginning. For low pass filter design, the higher the corner frequency of a partial filter, the higher is its Q. Therefore, to avoid the saturation of the individual stages, the filters need to be placed in the order of rising Q values. To design the first stage of a third order unity gain Bessel low pass filter, assuming the same values for fC and C1, requires a different value for R1. When operating at unity gain, the noninverting amplifier reduces to a voltage follower, thus inherently providing superior gain accuracy. High pass filters use the same two topologies as the low pass filters: Sallen–Key and multiple feedback. The only difference is that the positions of the resistors and the capacitors have changed. As with the low pass filters, higher order high pass filters are designed by cascading first order and second order filter stages. The filter coefficients are the same ones used for the low pass filter design.