Band Pass Translation

Changing to a Band Pass Filter

A translation from a low pass prototype requires three steps. The first of which is to do a resistance translation (q.v.) and second to do a low pass frequency translation using this conversion factor.

delta frequency

where fc, normally the corner frequency in a low pass or high pass filter, is replaced by the difference between the upper and lower corners, (f uc - f lc) times 2 * pi.

Having done those two translations, find the geometric mean of the two frequencies f uc and f lc by using

geometric mean

The geometric mean and the arithmetic mean are only a few percentage points different when pass bandwidths are small, but become larger as bandwidths increase.

The Translations:

In the case of the bandpass filter, prepare a low pass prototype according the the information above and find the geometric mean as shown. To complete the bandpass transformation, each capacitor becomes a parallel resonant circuit which is resonant at the geometric mean frequency. Each inductor becomes a series resonant circuit which is resonant at the geometric mean frequency. To translate from the previously prepared capacitance values, perform this mathematical manipulation:

capacitor to parallel
where CP is the prepared capacitance, LN is the inductance and CN is the capacitance after the translation.

To translate from the prevoiusly prepared inductance values to the series resonant circuit, perform this mathematical manipulation:

inductor to series
where LP is the prepared inductance, CN is the capacitance and LN is the inductance after the translation.

A Final Word About Band Pass Filters

When designing band pass filters, keep an eye on the percentage bandwidth. This is defined as the bandwidth divided by the center frequency (either) and multiplied by 100. If the percentage bandwidth exceeds 80% to 100%, consider cascading a low pass filter with a high pass filter. The number of reactances will be the same, but the filter should perform better.

If, on the other hand, the filter has an extremely narrow bandwidth calling for a filter of very high order, above 15 or 20, consider a mechanical or crystal ladder filter

Prototype Button Resistance Button LP Button HP Button BS Button

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