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WHAT'S YOUR ENGINEERING QUOTIENT?

Problem 4—Assuming 1% resistors, what is the largest reasonable number of stages to use?

The use of 1% resistors implies that the cancellation of harmonics is not going to be perfect. The errors will accumulate at a rate roughly proportional to the square root of the number of stages, which means that for an N-stage synthesizer, the overall error will be sqrt(N)×1%.

There would be no point to adding another stage if the level of the harmonic to be cancelled would be less than this error amplitude. Since the harmonic amplitudes are proportional to 1/(2N–1), we simply need to find the value of N for which 1/(2N–1) < 0.01×sqrt(N).

It doesn't take much trial-and-error to discover that this happens at about 13 or 14 stages.

Contributor: Dave Tweed

12-01 — NEXT Q&A