274  Other Lowpass and Highpass Filters

Multiple-Feedback 2nd-Order Highpass Filters

The multiple-feedback highpass filter is the multiple-feedback lowpass filter with the resistors and capacitors interchanged.Apractical version of an MFB highpass filter is shown in Figure 10.3, once more designed for a Butterworth characteristic (Q = 0.7071), a cutoff frequency of 1 kHz, and unity passband gain.

This time we have three identical capacitors which can be conveniently chosen from the E6 series, dealing with the awkward resistor values in the usual way; as it happens, in this case R1 comes out as the E24 value of 750 Ω. There may be three capacitors, but this is still a 2nd-order circuit. Given the relatively high cost of capacitors compared with other components, this is not a particularly appealing configuration.

Multiple-Feedback 3rd-Order Filters

Filters of higher order using MFB stages can be made in the same way as for Sallen & Key stages; the appropriate cutoff frequencies and Q’s for each stage are taken from Chapter 7 and the stages placed in series, in a suitable order that minimises headroom restrictions due to gain peaking. Buffer amplifiers are used as required to make sure that 1st-order circuits are not loaded by succeeding stages.

Figure 10.3: A 2nd-order highpass Butterworth multiple-feedback (MFB) filter with the analysis equations. Cutoff frequency = 1 kHz, Q = 0.707 and passband gain is unity.

Other Lowpass and Highpass Filters  275

As for Sallen & Key filters, these buffer amplifiers can be dispensed with if the loading effects are taken into account in the design; this does however make the process much more difficult and is likely to make component sensitivities worse. I have never used these filters myself, and I think caution should be the watchword. Clearly an amplifier is saved; however, you can also make both lowpass and highpass 3rd-order Sallen & Key filters in one stage and therefore using only one amplifier. Examples of 3rd-order Butterworth lowpass and highpass filters are given next, which can be scaled for different cutoff frequencies.

Multiple-Feedback 3rd-Order Lowpass Filters

A3rd-order lowpass MFB filter can be made by placing an additional 1st-order lowpass circuit R4-C4 just before the 2nd-order MFB filter. In Figure 10.4 R4 = R1 = R2 = R3/2.

Multiple-Feedback 3rd-Order Highpass Filters

A3rd-order highpass MFB filter can be made by placing an additional first-order highpass circuit C4-R4 just before the 2nd-order MFB filter. In Figure 10.5, C4 = C1 = C2 = 2C3. There is a clear temptation to make C3 the preferred value of 47 nF. If you do, the cutoff frequency and the later roll-off are unaffected, but the gain in the passband is increased from 0 dB to +0.54 dB; you can probably live with this.Although there are four capacitors, this is still a 3rd-order filter, in the same way that Figure 10.3 has three capacitors but is only a 2nd-order filter. Given the relatively high cost of capacitors, this is not an economic circuit.

Figure 10.4: Third-order Butterworth lowpass MFB filter. Cutoff 1kHz.