[Gb-ccb] Minutes from 07jul03 videocon

[Martin Shepherd]

On Fri, 11 Jul 2003, Brian Mason wrote:
> In connection with the filters, perhaps this summary will be useful.
> The basic choice being made is between a wider post-detection
> bandpass, which allows higher time resolution at the ADC input and
> thus less time lost to blanking, and a narrower post-detection
> bandpass, which will alias less noise into your measurement.  Both
> effects are at the few percent level.

Not quite.  The choice that is being made is actually between using a
filter designed for its frequency-domain characteristics and a filter
designed for its time-domain characteristics. This isn't the pedantic
correction that it might seem. Two filters with identical 3dB
bandpasses can have orders of magnitude different time-domain settling
times.

I think that it is worth explaining this in a bit more detail for the
non-EEs among us (myself included). First, from the perspective of
amplitude frequency response curves. A few octaves above the cutoff
frequency, the amplitude gain of all the standard classes of low-pass
filter goes down at a rate of n*6dB per octave, where 'n' is the order
of the filter. Thus the difference between the amplitude responses of
different classes of filter are localized in the curves that connect
the flat response below the cutoff frequency, and the -n*6dB/octave
response above the cutoff frequency.

In a filter designed for its time-domain response, a smooth
gaussian-like function connects the flat pre-cutoff response of the
filter with the -n*6dB/octave post-cutoff response. The smoothness of
this transition results in a similarly smooth response in the
time-domain, without any ringing (ie. it is critically damped).

In a filter designed for its frequency-domain response, however, the
curve connecting the flat pre-cutoff filter response and the
-n*6dB/octave post-cutoff response is closer to a sharp step. In the
time domain, the most obvious effect of this step is ringing.

Looking at things from the amplitude response curves neglects half of
the story. The phase response of a filter is just as important.
Filters that are optimized for their time-domain response are designed
to have constant delay as a function of frequency. This translates to
a phase shift that varies linearly with frequency. Thus if you put a
square wave through a time-domain optimized filter, it will retain its
shape, apart from a bit of rounding due to the loss of the higher
frequencies. Since all frequencies in the input waveform are delayed
by the same amount, the response to a step-function input is a rounded
step-function output. The output rises and settles as fast as is
possible, given the frequencies that remain in the output.  This is
what we want for the CCB.

On the other hand, the phase response of a frequency-domain filter
tends to be all over the shop.  If you put a square wave signal
through a frequency-domain optimized filter, the shape of the signal
that comes out is distorted by dispersion and rings at each
edge. Incidentally, it is this kind of dispersion effect that is the
explanation for the otherwise puzzling fact that makers of high-end
audio equipment advertise bandpasses that encompass frequencies well
beyond the limits of human hearing. The phase responses of the
unintended low-pass filters inherent in any analog circuit tend to
suffer far earlier than the amplitude response.

In our case it is important to use a time-domain optimized filter, so
that all frequencies needed to retain the edge of the phase-switch
step function are delayed by equal amounts. The best of this class of
filter is the Bessel filter.

> We see no problem with the 2 MHz 8-pole filter; a 1/2 usec settling
> time out of 25 usec is quite good, and with 10 MHz sampling at the
> ADC we have a comfortable margin ofoversampling. In particular 20 dB
> at the Nyquist frequency of 5 MHz is not unreasonable.

Note that higher frequency ADCs are available (up to about 80MHz), so
in principle I could sample even faster and have a higher frequency
low-pass filter. This would have a better settling time, and thus give
us a bit more of a margin. The reason that I haven't suggested this,
is that the higher the input frequency, the greater the likelihood of
radiation from PCB tracks and cables causing crosstalk and RFI, the
harder it becomes to find op-amps with sufficient slew rates to avoid
creating unintentional dispersion, the more important parasitic
capacitance and inductance becomes, and the denser the FPGA
becomes. So although I would be willing to consider doubling the
sample rate to 20MHz, if this is what people at NRAO would prefer, I
would be reluctant to go much higher. My design goal has been to find
the lowest frequency ADC for which a suitable anti-aliasing filter
doesn't degrade the step response much beyond 0.5us.

>...
> A question (not meant to cause havoc): does the precise filter have
> important impacts on other aspects of the system?  Thus can we swap
> them out based on tests later?

Some aspects can be varied, some not.

1. It is important to use a Bessel filter, for the reasons outlined
   above. A Chebyschev or Butterworth filter would be disasterous, and
   a Gaussian filter simply doesn't have any advantages that I can
   see.

2. A lower order filter can be used if need be, and this may turn out
   to be advantageous, because although this would degrade the noise
   response a bit, it would reduce the temperature dependence of the
   filter delay. According to Dave Woody at NRAO, 7th order is the
   "sweet spot" for low-pass filters, above which one gets diminishing
   returns, due to component precision and temperature instabilities.

3. The choice of case style can be changed.

4. The cutoff frequency could be reduced to get better anti-aliasing
   response in the 3mm receiver, if the phase-switches turned out to
   operate slowly. Note that this is an argument for placing
   the low-pass filters in the receiver rather than the backend, since
   the backends are supposed to be interchangeable.

> Should we do lab tests with a few different filters at first, and
> order the rest later (or are they expensive/long lead items?)?

I got TTE to give send me a quote and lead times for their model
LT8-2M-50-1245 filter (8-pole, 2MHz cutoff, 50 ohm impedance, PCB
mounted case). They quoted me a lead time of 6 weeks. The prices were
unfortunately a lot more than I had been expecting.

 Quantity    Price
  1-4         $230
  5-9         $170
  10          $140
  25          $117
  50          $98

Thus for 32 filters, we would end up paying $3744. Is this too much?

Dave Hawkins at OVRO suggested that we could build active filters
using ast op-amps. Personaly, I suspect that the amount of time needed
to design a 6-8 pole active Bessel filter, the cost of high-precision
components to implement it, and the amount of board space that would
be required for 16 of these, would negate any cost gains, but I
haven't really looked into this, so he might have a point.

Martin