Circuit Sensitivity Analysis--An Important Tool for Analog Circuit Design: Part 2

In part one, we learned to calculate circuit sensitivities on simple passive circuits. We then did the same for two common active filters, the Sallen-Key lowpass filter, and the multiple feedback (MFB) lowpass filter.

Our analysis showed that the MFB filter provided circuit sensitivities limited to the range of –1 to +1, with most sensitivities being of magnitude less than half. This is similar to that of passive networks and is about "as good as it gets." The Sallen-Key filter, however, had no such limits on sensitivity. In fact, it can result in very sensitive circuits, as we shall see.

Lessons learned from sensitivity analysis
Let's go back to our Sallen-Key filter and see if we can find ways to lower the sensitivities into the same range as the MFB filter. Figure 1 is the same filter schematic for the Sallen-Key as Figure 5 in Part 1.

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The transfer function for this filter, as we learned in Part 1, is:

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(1)

where K is the DC gain, K=1+ R_b/R_a.

The filter characteristic equations are:

(2)

(3)

The sensitivities are:

(4)

(5)

(6)

(7)

(8)

(9)