Topband: Group delay distortion in receiver filters

[John Kaufmann]

Tom Rauch wrote:

> Other than group delay, what do you suppose the difference is between the
> 751's 250Hz  455kHz filters that are terrible for signals in the noise and
> the 250 Hz filters in Drakes that are excellent on weak CW, even with
> Drake's notoriously poor AGC? The passbands are similar, neither are poorly
> shaped so far as cheap mass produced filters go.

Tom and all,

When you mention the 751, I assume it's the IC-751.  I am not familiar with that radio, so it's difficult for me to comment without knowing more information.  I do wonder if the 751 uses the same 250 Hz filters as the IC-781 which I am familiar with.  The 781 actually uses two 250 Hz filters in cascade in the 9 MHz and 455 kHz IF's.  I've never encountered any weak signal reception problems in the 781 that could not be fixed with careful AGC adjustment.  In fact, I use the 250 Hz filters very frequently and for weak signals, they always improve the quality of reception.

I know the 18 msec group delay distortion you measured sounds like a large number, but it is not way out of line for group delay distortions in multi-pole narrowband filters.  For example, refer to the filter characteristics shown at http://www.freqdev.com/guide/amp_phase.html for 8-pole Butterworth, Chebyshev, and elliptic lowpass filters.  Keep in mind that these filter plots are normalized to a cutoff frequency of 1 Hz, where the cutoff is defined as the -3 dB point.  Also, remember these are lowpass filters, so the equivalent bandpass filter has twice the bandwidth.

Now assume the lowpass cutoff frequency is scaled to 125 Hz, which corresponds to 250 Hz for a bandpass equivalent.  The group delays need to be divided by the cutoff frequency to scale properly.  If I did my math correctly, I compute the differential group delay errors (maximum group delay minus minimum group delay) as follows:

Butterworth: 6 msec
Elliptic:  13 msec
Chebyshev: 18 msec

The shape factors (ratio of -60 dB bandwidth to -6 dB bandwidth) of these filters are approximately as follows:

Butterworth: 2.4
Elliptic: 1.6
Chebyshev: 1.8

All these filters exhibit nearly flat response in their passbands. 

A good crystal filter has a shape factor of 2 or better, so the elliptic and Chebyshev filters are perhaps reasonable representations of crystal filter responses.   As you can see their group delay errors are in line with what you measured for the "bad" 250 Hz filter.  With the 250 Hz crystal filters I've used, I haven't observed the kinds of problems you describe.

I don't doubt that there is an audible problem with 751.  I just don't know exactly what it is without knowing more about the radio. 

I have mentioned the possibility of AGC issues.  Also, if the filter passband is not flat, the distortions could be the result of the frequency amplitude errors.  Reception of very weak signals involves SNR's that can be well below 0 dB in the bandwidth of the receiver filter.  At these SNR's noise masking effects can become very pronounced.  A frequency response error that enhances noise by as little as 1 or 2 dB relative to signal can result in a huge perceived difference in signal readability.  This is because the signals are at the threshold of detectability and are easily masked.  It's not unusual for crystal filters to have several dB of passband ripple.  Again I admit I am not familiar with the 751 filters, so this is just speculation.

Here are some other related observations, based on work I did some years ago in the audio field.  A square wave can become horribly distorted by passing it through an all-pass filter that alters phase but not frequency amplitude response.  The filtered waveform can exhibit very high peak to average ratios.  However, I can assure you that an audio square wave that is corrupted this way is absolutely indistinguishable from the uncorrupted one.  I have heard this with my own ears and otherwise I would not believe it, based on what the waveforms look like.  However, if the same corrupted square wave is passed through a nonlinear system (an AGC?) that happens to distort on the high peaks, then audible distortion can be produced.

In any event this is all very interesting stuff and clearly there is more to learn.

73, John W1FV