Low Pass Corner Frequency Translation

Changing the Low Pass Corner Frequency

A change in the corner frequency requires that the impedances of each inductor and capacitor be changed from the prototype's values by a factor equal to the change in frequency. The factor is

omega conversion
where fc is the desired corner frequency.

Conceptually, an adjustment to the reactances of the capacitors and inductors is needed so that the reactances remain the same when the new frequency is applied. Since 1 rad/sec is a very low frequency, most of the time this will involve making the inductors and capacitors smaller. Division is conceptually sound. But even if the frequency were less than 1 rad/sec, a division by a number less than one increases the reactances. This notion is intuitively correct, also.

The Translations:

With multiple translations in store, make the resistance translations first. This is because some of the filters require inductors to translate to capacitors and conversely. Some filters require inductors to translate into a resonant circuit and it would be a difficult chore to determine the original prototypical component's nature.

To translate the capacitance values (which may have been through a resistance translation), perform this mathematical manipulation:

capacitor conversion
where CP is the prototype capacitance and CN is the capacitance after the translation.

To translate the inductance values (which may have been through a resistance translation), perform this mathematical manipulation:

inductor conversion
where LP is the prototype inductance and LN is the inductance after the translation.

Prototype Button Resistance Button HP Button BP Button BS Button


HTML 4.01 Validation