How EMI Analyst Assigns Frequencies

Periodic voltage and current waveforms in the time domain have equivalent representations in the frequency domain.  Fourier transforms are used to convert time domain waveforms to their frequency domain spectrum, and vice versa.  The frequency domain spectrum is comprised of spectral lines at all multiples of the time domain waveform frequency.  Each harmonic (multiple of the frequency) has a value, even if it is zero, which is determined by the shape of the time domain waveform.  At all frequencies other than multiples of the time domain waveform frequency the frequency domain spectrum has no value.

The frequencies at which spectral lines exist are called harmonics.  Stated differently, the frequency domain spectrum of a periodic time domain waveform is comprised of harmonics that exist at integer multiples of the time domain waveform frequency and do not exist at frequencies other than integer multiples of the time domain waveform frequency.

Time domain waveforms and their frequency domain equivalents are entered and calculated using the Source form.

When the Start frequency and Resolution are entered in the Frequency Range form the value of each frequency at which subsequent calculations will be performed is determined based on whether a Linear or Logarithmic frequency scale is selected.  However, these frequencies may or may not be the same as the frequencies calculated by the Fourier Transform in the Source form.

For example, if the values on the Frequency Range form are:

Frequency Scale:                Linear
Start Frequency:                1.00E+04 Hz
Stop Frequency:                 1.00E+09 Hz
Resolution:               3.00E+03 Hz

The frequencies at which subsequent calculations will be evaluated are 10 kHz, 13 kHz, 16 kHz .1 GHz.

Now suppose the time domain waveform on the Source form has a frequency of 24 kHz.  Its frequency domain spectrum will be comprised of harmonics of 24 kHz, i.e., 24 kHz, 48 kHz, 72 kHz .

In this example the frequencies generated by the Frequency Range form do not correspond to the frequencies generated by the Source form.   If calculations are performed only at the frequencies generated by the Frequency Range form the effect of the Source waveform would not be correctly taken into account.  For example, no calculations would be performed at 24 kHz, so the fundamental frequency of the Source would be ignored.

In order to ensure that all harmonics of the Source are evaluated in calculations involving the Source, EMI Analyst adjusts the frequencies generated by the Frequency Range form to coincide with harmonics of the Source.

For the example above the frequencies would be adjusted to:

10 kHz, 13 kHz, 16 kHz, 19 kHz, 22 kHz, 24 kHz, 48 kHz, 72 kHz, ..

Notice that at frequencies above 22 kHz the frequency step changes from 3 kHz, specified on the Frequency Range form, to 24 kHz, the frequency of the source waveform.  There is no point in performing calculations in 3 kHz steps since the Source has no value at frequencies other than multiples of 24 kHz.

More:

Limits