Generally to maintain stability, an active filters gain must not be more than 3 and is best expressed as: The Quality Factor, “Q” But a filters gain also determines the amount of its feedback and therefore has a significant effect on the frequency response of the filter. Then Q, the quality factor, represents the “peakiness” of this resonance peak, that is its height and narrowness around the cut-off frequency point, ƒ C. In simple terms, a low pass filter will always be low pass in its nature but can exhibit a resonant peak in the vicinity of the cut-off frequency, that is the gain can increases rapidly due to resonance effects of the amplifiers gain. Both Q and ζ are independently determined by the gain of the amplifier, A so as Q decreases the damping factor increases. In active second order filters, the damping factor, ζ (zeta), which is the inverse of Q is normally used.

However, second order filters can exhibit a variety of responses depending upon the circuits voltage magnification factor, Q at the the cut-off frequency point. The difference this time is the steepness of the roll-off which is -40dB/decade in the stop band. The frequency response bode plot above, is basically the same as that for a 1st-order filter. The Sallen-Key filter design is one of the most widely known and popular 2nd order filter designs, requiring only a single operational amplifier for the gain control and four passive RC components to accomplish the tuning. All these types of filter designs are available as either: low pass filter, high pass filter, band pass filter and band stop (notch) filter configurations, and being second order filters, all have a 40-dB-per-decade roll-off. Most designs of second order filters are generally named after their inventor with the most common filter types being: Butterworth, Chebyshev, Bessel and Sallen-Key. Then we can define second order filters as simply being: “two 1st-order filters cascaded together with amplification”. In this analogue filters section tutorials we have looked at both passive and active filter designs and have seen that first order filters can be easily converted into second order filters simply by using an additional RC network within the input or feedback path. Second Order Filters which are also referred to as VCVS filters, because the op-amp is used as a Voltage Controlled Voltage Source amplifier, are another important type of active filter design because along with the active first order RC filters we looked at previously, higher order filter circuits can be designed using them.

Multisim bode plot voltage gain