We would expect the nominal frequency response to be the same as for the Sallen-Key filter unity gain version. Figure 7a shows the frequency responses of both filters. Figure 7b is a close-up at the peak showing only .02dB difference.

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As we did when comparing the two different Sallen-Key implementations, let's run Monte Carlo simulations on the MFB filter and compare it to the better of the Sallen-Key filters. Figures 8a and b.

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View the full-size image

Notice that at low frequencies the Sallen-Key has significantly less variation. This is because at DC the Sallen-Key filter has virtually no variation. Its gain is one, while the MFB filter has a gain dependent of two real resistors. If we were to cancel out the low frequency variation, we would find that the two circuits have very similar high frequency variation.

Implementing a higher order filter
Now let's implement a significantly more complicated filter using the topologies previously discussed using the following specifications:

1. Seventh-order Chebychev

2. 0.05dB nominal in-band ripple

3. 10kHz nominal passband (highest frequency with at most 0.05dB attenuation):

4. Gain = 10

The poles required to implement such a filter are listed in Table 2:

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The schematic in Figure 9 shows this filter implemented in three different ways:

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1. Multiple Feedback (MFB)

2. Sallen-Key with unity gain and equal-value resistors: low sensitivity variation.

3. Sallen-Key with R=R and C=C: cookbook variation.

The cookbook Sallen-Key version (at the bottom of Figure 9) has capacitor values from 1nF to 2nF, while the low-sensitivity Sallen-Key version capacitors vary from 82pF to 10nF. The MFB capacitors vary from 68pF to 12nF, a bit more than the low-sensitivity Sallen-Key. As with the low-sensitivity Sallen-Key, this topology also requires that the capacitor values spread further apart as Q increases. We can get the capacitor spread to be similar to the low-sensitivity Sallen-Key. To do this requires that we decrease the DC gain of the high-Q stage to about –20dB. This gain is impractical for most applications.