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Creating a frequency plan

19 Dec 2013  | Tom Burke

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A common question then is "The series is infinite; how many terms should we use?" My answer is one I heard from a professor and it seems to be a pretty good rule of thumb for most cases, which is "Five is a sufficient approximation of infinity." Note that the fifth harmonic (5f/5) has just only 20% of the fundamental frequency (f) amplitude. That amplitude may too much for your application, or it may not be so bad after all.

Figure 3: Frequency spectra of a square wave of frequency f.

So how do we use all this? I usually use Excel to generate a table of all my frequencies and their sums and differences. Assume we're testing a 1MHz ADC, but our system is driven by a 20MHz clock that is also divided to a 5MHz clock. We'll also excite our ADC with an 800kHz sine wave. So, the primary frequencies in our system are 20MHz, 5MHz, 1MHz, and 800kHz. These frequencies plus their harmonics out to the 5th are shown in table 1.

Table 1: Initial frequency table for a hypothetical circuit.

Of course, table 2 simplifies quite a bit.

Table 2: Simplified frequency list from Table 1.

This plan is used in two major ways. First, use it to best ensure that no trace or straight segment of a trace on a PCB is close to an integer multiple of one of the ¼λ numbers. That's because ¼λ conductors are pretty good antennas for the frequency of that wavelength. Knowing the frequencies and their wavelength's in your system can help for predicting EMI emissions. The same thing applies to test leads, as these "tones" can couple back into your test equipment, giving you false information.

A frequency plan tells you most of the frequencies of concern. Make sure that your analogue front-end circuits reject all but the frequencies of interest. Make sure that your power-supply filters and other back-end components are protected from these frequencies.

Simple, right?

About the author
Tom Burke is a Senior Systems Engineer.

To download the PDF version of this article, click here.

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