Potential error in cauer band(pass|stop) center frequency calculation

[jcolafrancesco]

Context:

1. For bandpass and bandstop filters, the qucsfilter interface is taking as input low and high corner frequencies
2. The qf_cauer filter is, on its end, taking as input an alternative representation: bandwidth and center frequency.
3. In the code, the conversion is done this way: https://github.com/ra3xdh/qucs_s/blob/f9b3441de7d42151d9c004cb7f5de466d5422183/qucs-filter/qucsfilter.cpp#L426C1-L426C73

Issue:
Basically, the center frequency is computed as the arithmetic mean between the two corner frequencies, although I really though we shall use the geometric mean here.

Looking at the transfer function of a generated filter, we can see a slight shift in frequency (1GHz to 2GHz band-pass):

With a small patch implementing a geometric mean, I obtain the following results:

This looks much more satisfying.

I'll prepare a pull request, but in the meantime, I'd be happy to have some confirmation by an RF expert.

[tomhajjar]

It's always best if a tool uses the same definition for variables for all choices.

As I stated before about this tool, in real life, you can't buy components with the values calculated by the tool. Also component "Q" and package parasitics isn't taken into account so the analysis will be flawed. The higher the frequency and narrower the bandwidth, the more the measured results will deviate.

The only way to have accurate simulations is to measure every component on a LCR meter capable of measuring at the actual filter frequency. Components must be measured using a jig replicating the PCB or circuit parasitics. Measured component data is then used to update the schematic. Manufacturers data is always suspect.

Attached is a filter I designed decades ago for an Intelsat satellite receiver. 70MHz BPF with amplitude and group delay equalization.