EXPLANATION OF PUPPI MIXER GROUP DELAY MEASUREMENT
	  

INTRODUCTION:

The PUPPI mixer can be switched in just ahead of the PUPPI back end, for the
purpose of making the PUPPI back end's useful input frequency range be the
band 1.1 - 1.9 GHz for compatibility with the 1 - 2 GHz IF from the existing
IF/LO system.  This also requires using PUPPI in its 2nd Nyquist zone.

Physically what the mixer does, then, is to translate the input band of
1.1 - 1.9 Ghz down to an output frequency range of 0.8 - 1.6 GHz.  However,
the bandpass filters in this unit are set to be about 20 dB down at the nominal
band edges to assure that aliased noise from the filters' soft transitions does
not excessively corruput the effective signal passband. 

In doing this work the mixer uses two conversion stages, first up and then back
down.  The reason for this arrangement was to assure that the effects of
RF -> IF leakage characteristic of a single-stage mixer will not appear in the
final output.  This could otherwise be a serious problem because the ouput
frequency band greatly overlaps the input band.  Both stages use high-side LOs;
thus there is no frequency inversion as a result of using this mixer.


THEORY OF OPERATION (see the diagram 'PUPPI_MIX_group_del_meas_block.FC7'
or its PDF version):

This system differs from the usual method of using a standard Vector Network
Analyzer with an external mixer and filter(s) because I was seeking a way to
avoid the hassles of getting more precision filters, characterizing them, and
then trying to incorporate those filter characteristics into the overall test
result (necessary because those filters would add appreciable group delay and
non-flatness of their own in very significant amounts).

This scheme reduces the external filter requirement to a non-critical BPF or
LPF to pass a very narrowband 300 MHz IF but block LO (and harmonics) and
sum-frequency signals from overloading the post-mixer amplifier stages.  The
filter used is the Mini-Circuits SLP-450, an inexpensive 450-MHz lowpass filter
available from stock.  Because of the very narrowbandedness of the 300 MHz IF
signal, group delay flatness is trivial and mostly doesn't appear in the final
result in any case.  Static phase delay of this filter is of exactly zero
consequence.
  
However, there is a price to be paid:

> The system as described is inherently uncalibrated for amplitude in that the
  directional coupler and mixer's non-flatness will first-order affect the
  amplitude of the 300 MHz IF output.  
  
  But since we are mainly interested in the group delay and can easily measure
  the PUPPI mixer's ampiitude response in other ways, I felt that this "defect"
  could safely be overlooked (swept under the rug, as it were).
  
In operation, the output of a swept oscillator covering the PUPPI mixer's input
frequency range is split into two parts by a directional coupler.  The higher-
level straight-through output of the coupler serves as the LO for a "test
mixer".  The lower-level (coupled) signal is further reduced in amplitude to a
quite comfortable input level for the PUPPI mixer (albeit moderatly higher than
the normal signal level).  The output of the PUPPI mixer then goes to the RF
port of the test mixer.  Since the RF & LO are always tracking, the output of
the test mixer is a fixed 300 MHz signal, except for some small and quite slow
phase variations arising from group delay (and non-flatness thereof) in the
PUPPI mixer unit itself.  This IF signal is gained up to a suitable level and
applied to the CH1 vertical input of a DSO having sufficient bandwidth to
capture the 300-MHz signal.

If the PUPPI mixer were entirely free of group delay, the 300 MHz IF would be
exactly constant in frequency and phase as each sweep progresses.

If the PUPPI mixer were afflicted with a fixed group delay (independent of the
frequency), then the swept frequencies presented to the LO and RF inputs of the
mixer will be slightly out of time step because of the added delay in only one
path, leading to a constant frequency "error" in the test mixer's IF output.  
This is exactly equivalent to a phase ramp referred to a 300 MHz reference.
The slope will be the frequency slew rate of the applied swept signal times
delay amount.

I should mention at this point that if the sample rate of the DSO used is not
exact, the apparent IF frequency will be slightly in error, which masquerades
as a static error in the PUPPI mixer's group delay.  Unfortunately our DSO does
not possess an input for an external reference, so we must deal with the error
in some other way if we want to measure absolute group delay as opposed to
merely group delay non-flatness.  As this is an important part of the overall
measurement, this must indeed be dealt with.  I address this problem by taking
simultaneous samples of an exact 300-MHz signal from a separate but locked
signal generator, via the DSO's CH3 vertical input.  This can be used to
directly measure the error in the DSO's sampling rate as of the same time as
the important signal data is taken.

Also, I take samples, via CH2 of the DSO, of the frequency-modulating wave-
form from the sweeping generator to facilitate accurately locating the start
and end of a single full sweep in the CH1 signal after the fact.

But I digress; now let's get back to the mainstream discussion:

If the PUPPI mixer filters have group delay non-flatness, there will be some
associated phase variations in the PUPPI mixer's output phase versus frequency
(or equivalently time, since we know the sweep parameters from the sweep
generator's settings).  These phase variations will also be conferred upon the
300-MHz IF signal being recorded by DSO CH1, so that the phase history of that
IF signal can be used to calculate the group delay variations across the band.

As described, the data processing can be done by a three-time application of
an existing signal analysis program written by Dana: 'isf_md13.exe', followed
by a simple manual scaling with the help of a scientific calculator.  The first
run is merely to examine the CH2 waveform and pick off accurate array indices
for the start and end of the RF frequency sweep.  The second application is to
measure the apparent IF frequency compared to the theoretical 300 MHz.  The
numbers from the first two runs should be written down on paper for reference
during the 3rd run in which the real, meaningful processing finally occurs.

During the 3rd run of the program, using the data file from CH1, the array
indices obtained from the 1st run will be used to restrict the time scope of
the analysis.  For the recommended sweep setup of 100 sweeps per second, this
will be about 8 msec.  The remaining 2 msec or so is used for sweep generator
retrace and is of no significance to this measurement.  Then it is necessary to
examine the spectrum plot and choose frequency limits on both sides of the peak
at about 300 MHz: wide enough to encompass virtually all of the signal energy,
but not much wider, so as to exclude excess noise.  Also at this step one must
pick a central location of the signal peak and enter that.  The program will
provide guidance in how to make these selections.  The next step will show only
the amplitude envelope, then the next step will show (mainly) the phase versus
time.  In this plot there will be a frequency shown in the lowerleft part of
the plot.  It should be near 300 MHz, but will, in the absence of a miracle,
not be quite the right frequency.  Use the hotkey <shift F> to enable entry of
the exact correct frequency, which is the number recorded from the 2nd run of
the program.  Upon doing this the program will next display the correct phase
versus time waveform.  Save this data to a file by the hot key <s> and giving
a desired filename, then bail out of the program.  But before bailing out, take
a moment to write down the array size indicated for the next step.

At this point one needs to view and plot the frequency versus time waveform,
then scale the result to group delay by computing, point by point, the
frequency / sweep rate, giving group delay in seconds.  This is most readily
done by running the program 'consplyt.exe', which first asks for the maximum
expected array size, then the filename to process.  It will then offer a menu
of possible things to do.  Feel free to explore; however, the one you really
want is choice #6.  Vertically pan and zoom until you obtain a reasonable-
looking plot.  Use the cursor to measure the highest values within the bandpass
of the PUPPI mixer, as well as the lowest value which should be near the center
of the bandpass.  But better yet, simply use the hot key <c> to force creation
of an EasyCAD plot with relevant scaling information.  Then builld a graticule
in the EasyCAD environment, to show the group delay.  This will require taking
the vertical scale info drawn at the bottom of the plot and modifying it 
according to the frequency sweep rate (about 125 GHz / sec, if you use the
general setup I suggest).  The overall result should be a nice plot of group
delay versus time; then modify the horizontal scale by the sweep rate and the
CF setting for the sweep to make the graticule show group delay versus input
frequency.

A more elegant way of doing the processing, including dynamic correction for
DSO sample rate error, could be done by writing new software just for this
situation.

However, this is seen as a one-time set of measurements, with no justification
for extreme accuracy given that this measurement ignores all the unknown group
delay aspects of the remainder of the Arecibo telescope.  Therefore the effort
required to write a special program seems unjustified at this time. 

However, depending on how things go with the FRBs, it is possible that a
whole-telescope calibrated group delay measurement might become desirable in
the future.  This will probably prove to be a daunting task, especially when
one considers the uncalibrated state of virtually the whole system with
respect to delays.  To my knowledge, this small effort for the PUPPI mixer is
the first time that instrumental group delay has been seriously taken into
account for passive single-dish observations.  With luck, a variation on this
theme should provide a useful foundation for whole-telescope measurements if
ever called for.


Dana Whitlow
19 Nov 2016
PUPPI_MIX_group_delay_meas_TOO.txt