Let's also look at the high-Q stage of the MFB implementation in this same way. We'll skip right to the Monte Carlo analysis. Figure 17.

View the full-size image

View the full-size image

As with the Sallen-Key circuit, the 100MHz GBWP op amp shows no perceivable difference from the ideal op amp. The 10MHz op amp deviates from the ideal by about 0.35 dB with about 0.1 dB variation, slightly more than with the Sallen-Key. The 1MHz op amp peak deviates in frequency from ideal by about nine percent and about 3dB in amplitude, with about 0.9dB in amplitude variation, again, slightly more than with the Sallen-Key.

The earlier Monte Carlo analyses show that the MFB and low-sensitivity Sallen-Key filters frequency responses varied with their passive components by about 3dB. Therefore, the 1MHz op amp would cause a substantial shift in the response and add moderately to the variations. The 10MHz op amp would not significantly modify the response over the ideal op amp. While some applications may be able to allow the increased variations caused by the 1MHz op amps, a 10MHz GBWP should be adequate for any application using this filter.

Overcoming capacitor value limitations for high-Q stages
As discussed before, the low-sensitivity Sallen-Key and the MFB topologies have allowed us to implement this filter with low sensitivities. The main trade-off is that the capacitor values for the high-Q stages vary over more than a 100:1 range, from 82pF to 10nF for the Sallen-Key and 68pF to 12nF for the MFB. If we needed a higher Q stage, the capacitor values for both topologies would spread even further, making it difficult to implement using capacitors with reasonable properties at reasonable prices.

In such cases, the high-Q stages (usually only one stage) can be implemented with other, more complex topologies, which can provide higher Q stages while using reasonable capacitor values. There are several three-op amp topologies that can do the job. These include the KHN (Kerwin-Huelsman-Newcomb or State-Variable), the Tow-Thomas and Akerberg-Mossberg topologies.^1,2,3,4

Interestingly, despite their increased complexity and ability to implement higher Q stages with practical component values, they are no better in terms of component sensitivity than the MFB and low-sensitivity Sallen-Key. While tripling the number of op amps for a single stage is not desirable, typically this only has to be done for one stage. The rest can be done with the topologies we have been discussing.

By being aware of component sensitivity for filter circuits we can at least chose to tighten up on tolerances for components to which the circuit response is most sensitive. By using this sensitivity information intelligently we can often configure circuits to be inherently less sensitive. Understanding the limitations of these less sensitive circuits, we can chose to use more complex circuit topologies only when necessary while using simpler, but more limited in usability, insensitive circuits for the majority of needs.

The definition of and methods for using circuit sensitivity presented here have uses beyond that of analog filters. Similar insights and improvements in designs can be made for virtually any circuit.

For the last five years, Mark Fortunato has been the Southwest Analog Field Applications Manager for Texas Instruments. When not working with customers, Mark enjoys reading, coaching youth sports and listening to his son perform live Jazz and Latin music. Mr. Fortunato has not written a line of code since the fall of 1992.

Endnotes:

1. Sallen, R.P. and Key, E.L., "A Practical Method of Designing Active Filters," IRE Transactions on Circuit Theory, vol. CT-2, pp.74-85, March 1955.

2. Huelsman, L.P. and Allen, P.E., Introduction to the Theory and Design of Active Filters, McGraw-Hill, New York, 1980.

3. Budak, Aram, Passive and Active Network Analysis and Synthesis, Houghton Mifflin company, Boston, 1974.

4. Ghausi, M.S. and Laker, K.R., Modern filter Design: Active RC and Switched Capacitor, Prentice-Hall, Englewood Cliffs, N.J., 1981.

5. Fortunato, M., "Circuit Sensitivity; With Emphasis On Analog Filters," Texas Instruments Developer Conference 2007, March 2007: http://focus.ti.com/general/docs/tidc/general.tsp?templateId=6180&navigationId=12622&path=templatedata/cm/tidcgeneral/data/am_landing/ww_07presentations