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General info:

• Table showing distance along waveguide with the various waveguide sections used.
  

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16jan12: Waveguide measurements

• Setup
• Calibrating the data
• Assumptions made in the calibration
  
• dedispersing the data
• checking vgrp, correcting for waveguide loss
• The data results:
• data results with short at ch.
• data results with waveguide attached to the linefeed
  
• plots:
• dedispersing the data with the short at the end of the waveguide (.ps) (.pdf):
• check the group velocity and compute how much loss we have in the transmission system (.ps) (.pdf):
• the data results with the short on the Ch waveguide (.ps) (.pdf):
• data results with the  Ch waveguide connected to the antenna (.ps) (.pdf):
• Summary
  

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Setup: (top)

    The network analyzer was attached to a waveguide transition where the waveguide exits the transmitter building. The network analyzer measures the reflection coef at each frequency channel (VoltTransmitted/Voltage Received). A reflection at a particular distance will cause a ripple in the spectra. Transforming the spectrum to the time domain will then give the distance for this ripple.
 Measurements were done with the following setups:

• 40 MHz bw (410 to 450 MHz), 1201 spectral channel recorded.
  
• power splitter on platform set to  pass all power to the ch.
  
• astronomy mode (short in waveguide at Y switch)
• radar mode.. waveguide connected to carriage house linefeed.
• Measurements were done at zenith angles of 0,5,10,15,19.6 degrees.

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Assumptions made when correcting the data:

• When computing waveguide loss using the short data, assume that all the power that does not come back is due to waveguide loss.
• The 3.7% loss around 426 was probably not from the waveguide, but  is got thrown into the db loss/100 feet calculation.
• The power reflected vs distance plots are for the 40 MHz bandwidth used.
• Reflected power near 430 MHz could be different (see freq domain spectra).
• For the waveguide reflections, probably not too  much freq dependence.
  
• For the txMode reflections that go through the omt, it probably does make a difference.
• The measurements were made from where the waveguide exits the transmitter room (after the magic T).
• The magic T, harmonic filter, hybrid are not included in these numbersl.
  

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Dedispering the data. (top)

    When measuring reflections (S11) in the waveguide (w2100) we want a large bandwidth to give us high time (distance) resolution.  Since the group velocity in the waveguide is a function of the frequency, each frequency channel will arrive back from a reflection point at a slightly different time. This will smear out the distance measurements. To correct for the smearing we can try to dedisperse the data returned by the network analyzer.

    The plots show an attempt to dedisperse the data with the short at the end of the waveguide (.ps) (.pdf):

• Page 1: Group velocity vs frequency
• top: group velocity vs freq. At 430 MHz Vgrp=.757 c.
  
• Middle: fractional change of group velocity (relative to 430 MHz)
• bottom: Distance  smearing as a function of measured distance.
• The distance resolution at 430 MHz for a 40 MHz band is:
• distRes= 9.3ft =1/40e6 * c/2 * .757 (c/2 since up and back distance).
• As we go out to the waveguide end (about 1400 feet) the reflected signal we be smeared by about 10 channels.
• Page 2: Reflection coef vs frequency:
• top: Real and imaginary reflection coef measured at each frequency bin.
• The high frequency ripple is coming from the end of the waveguide.
• the lower frequency modulation is a reflection around 100 feet.
  
• Middle: reflection coef power vs frequency:
• the network analyzer sends out unity power in each channel.
  
• the return have an average around .6 --> there is loss in the system.
  
• Also notice the added loss of returned power around 425 MHz.
  
• Bottom: blowup real voltage. Spacing of 279 Khz caused by the reflection from the end of the waveguide.
• Page 3: Phase of reflection coef vs frequency:
• Top: phase vs frequency
• Bottom: blowup showing 410 to 412 MHz.
• Each frequency channel is (40MHz/1201 = 33 Khz).
  
• The wrapping every 8 freq channels is from the 279khz ripple caused  by the reflection from the end of the waveguide.
• Page 4: Unwrapping the phase, finding the dispersion:
• How to correct the dispersion:
• With no dispersion, the phase vs frequency for a given refection will be linear in frequency.
  
• With dispersion, the phase vs frequency will be non-linear.
• to correct the dispersion we do a linear fit to the phase vs freq, subtract, and then use the difference to correct the phase at each frequency.
• The phase vs frequency will be different for each reflection distance. We need to do them separately.
  
• Unwrapping the 2pi phase jumps before fitting phase vs freq.
  
• We can't fit phase vs freq until we unwrap the phase jumps.
  
• The  strongest reflection is at the short (about 1400 feet). This is determining most of the phase jumps.
• Top: phase vs frequency after unwrapping the 2pi phase jumps. Each color is a measurement at a different zenith angle.
• Middle: Linear fit to phase vs frequency, the subtract the fit.
  
• za=0,19.6,and 15 deg have jumps in the residual phase. This may be caused by the  "other ripples" in the  spectra that i'm ignoring.
• Bottom:quadratic fit the average of (data-linearfit) for za=5 and 10.
• Subtracting this from the phase at each freq will then correct the data. eg
  
• Let:
•  fc= complex reflection coef.
• ph=atan(fc,/phase) (if using idl)
• phDiff= phase difference  computed above.
• phCor= ph - phDiff (corrected phase)
  
• fcDedisp=abs(fc)*exp(iphCor)
• Computing the distance from the spectra:
• The distance of a reflection is:
  
• reflPower=(abs(fft(shift(fcdedisp,fftlen/2,1)/fftlen)^2
  
• distance=findgen(fftlen)/40e6 * c/2 * Vgrp
  
• Page 5,6: examples of before and after dedispersion: 
• Each color is a measurement at a different za:
  
• top: reflection coef power vs distance 0 to 4000 feet.
• We can have multiple bounces so the length can be longer than the short at 1400 feet.
• The reflection at 1400 feet is spread out
• 2nd: ReflCoefPower after dedispersing using the 1400 foot reflection.
• The reflections at the short have gotten narrower while the reflection at 100 feet has become wider (because the dedispersion we did was for 1400 feet).
• 3rd: Blowup short with no dedispersion.
• 4th: blowup at short with dedispersion.
• The reflections are now close to 1 channel wide.
• The reflection strength has increased since all the power that was smeared out over many channels is now in one channel.
  
• Page 6: 0 to 1300 feet.
• frames 1,3 show no dedispersion
• frames 2,4 show dedispersed data.
  
• The dedispersion widens the reflections at these shorter distances since we are trying to unsmear about 10 channels (the smearing at 1400 feet).
  

Summary dedispersion:

• You can dedisperse the reflection data.
• It needs to be done separately for each reflection distance.
• Unwrapping the data as is and fitting corrects for the main reflection at 1400 feet.
• to correct the data:
• I'll use the dedispersed spectra for 1000 feet and beyond.
• below 1000 feet i'll use the undedispersed data (since it isn't smeared as badly).

Processing: x101/tx430/wgmeas/120116/cmpdedisp.pro

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Checking Vgrp, correcting for waveguide loss.  (top)

    The plots check the group velocity and compute how much loss we have in the transmission system (.ps) (.pdf):

• Page 1: Group velocity vs za.
• We took data with the short in at 5 different zentith angles.
• Since we know the radius of the waveguide (420.078 Meters), we can compute the extra distance the reflection should take for each za.
• Top: the short reflection at each za (after dedispersion).
• Bottom: Align each za reflection with that of za =0.
• Use Radius*theta for the extra distance to remove.
• They all line up to within 1 pixel except za=19.6 degrees.
• The waveguide is not a perfect arc because of the azimuth rail shimming. The shims go from 1 foot at za =0 to close to 0 at za=19.6. I'm not sure if this is the cause of the extra distance..(probably goes the wrong way..).
• anyway, Looks like Vgrp is working pretty well.
  
• Page 2: Correcting reflected power assuming waveguide loss.
  
• The network analyzer outputs unit power at each frequency channel. The returned spectra showed an average value of about .6. So 40% of the power was missing.
• W2100 waveguide has a theoretical loss of  .054 to .034 db per 100 feet for (350 to 530 MHz). This is the one way loss. Our two way reflection measurements would give .108 to .068 db per 100 feet.
• Using .088 db/100 feet at 1400 feet the two way loss is 1.23 db. If this was all the loss then the network analyzer should have read .75(25% of power missing) instead of .6 (40% missing).
• Top: returned power after using different waveguide loss/100 feet (two way).
• Each color is a different za measurement.
• Using the time domain distance, i divided the return  power at each distance by the loss at that distance. When the correct loss is used, the average of the data should be unity.
  
• the two way dbloss/100 feet  ranges from .157db at za=0 to .167db feet at za=19.6. the one way losses are 1/2 of this. I ended up using .162 for the two way loss (.081 for the 1 way loss /100 feet).
  
• Bottom:
• The reflected power vs distance after correcting for the waveguide loss.
• The short reflection peak  is only 50 to 60 %. There is still lots of power coming back from somewhere else.
• Page 3: cumulative reflected power vs distance
• top: the cumulative reflected power vs distance before dedispersion and waveguide loss correction.
• The peak is about 60%
• the transition at 1400 feet is slow since it hasn't been didispersed.
• Bottom: Cumulative reflected power  vs distance after corrections.
• 10% at 100 foot reflection
  
• 12.3% at 1250 feet. So only 2.3% get reflected between 100 1250 feet.
  
• 75% at 1380 feet. this is the end of the short reflection for za=0.
• 85% at 1635 feet. So 10% is reflected after the short.
  
• Part of this may be going out to the end of the az arm and coming back (150' one way).
• 95% at 2664 feet. This is coming down from the short , bouncing off the 100ft reflection and going back up.
• Looking at the different za data at 1300 to 1500 feet might tell us more about how the power is getting through the slotted waveguide.
• Page 4: Loss that is not in the waveguide:
• The above assumed the only loss was in the waveguide. It was distributed evenly as a function of distance.
• Top the reflection coef power vs frequency (uncorrected).
• Each color is a different za.
• The za's have been offset for display.
• You can see a dip in the reflected power around 425 MHz.
• Bottom: smooth reflected power vs freq by 8 channels to get rid of fast ripples.
• You can clearly see the dips and how they move in freq for different zenith angles.
• za=0 425.48 MHz
• za=5, 426.06 MHz
• za=10, 425.75 MHz
• za=15, 426.90 MHz
• za=19.6, 424.80 MHz
• Integrating over the dip at za=0% shows that 3.7% of the power is lost here.
• Not sure where this power is going.

SUMMARY LOSS:

• Vgrp=.757 lines up the za distances pretty well
• 60% of the power is lost somewhere.
• Assuming all the loss is in the waveguide the loss is:
• measured 1 way loss : .081 db/100 feet
• measured 2 way loss: .162 db/100 feet
• theoretical 1 way loss  .054 to .034 db/100 feet (350 to 530 MHz).
• 75% of the power has been returned after 1370 feet. 25% is making an extra bounce.
• about 5% of the reflected power goes up to short, down to 100foot reflection, backup , and the all the way down
• there is a dropout in the reflected power near 425.5 MHz.
• It moves a little in freq when the za is changed.
• at za=0 it absorbs about 3.7% of the power.
  

processing: x101/tx430/wgmeas/120116/wgcal.pro