Design Con 2015

All-pass filter phase shifters

-June 20, 2012

All-Pass Filter Phase Shifters  -  John Dunn, Consultant, Ambertec, P.E., P.C.

We're all familiar with low-pass filters, high-pass filters, band-pass filters, band-stop filters and other filter types, but the all-pass filter is perhaps less well known.

All-pass filters have no amplitude roll-off properties, but they do have phase-shift properties that can be of use. The basic all-pass transfer functions when using op-amps are as follows: 

One application of these things is to arrange a group of them as sketched below where each filter has its own particular frequency "corner" and those corner frequencies are put into particular ratios.

The underlying mathematics is discussed on various web sites, but I would recommend looking at this link

Using all of the capacitors as 0.01 µF and choosing the eight resistors to cover the audio speech spectrum, taken here as 300 Hz to 3 kHz, we find nominal resistor values as shown below. Each nominal resistor is then replaced by that parallel pair of standard 1% value resistors that gets us as close as possible to each nominal value as follows: 

With these resistor pairs, we obtain the following results:  

The tabulated results for 300 Hz to 3000 Hz for the nominal resistor values are as follows: 

The tabulated results for 300 Hz to 30 kHz using the parallel pair resistors values are as follows:

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