23cm Stepped-impedance coaxial LPF

I’ve been trying to design a stepped-impedance coaxial LPF for 23cm using the tool at http://www.changpuak.ch/electronics/Stepped_Impedance_Lowpass_Coax.php

Plan is to use ordinary 28mm plumbing pipe with 0.9mm walls, plus 7/8 inch round bar for the low-Z sections and 3mm round brass rod for the high-Z sections as I don’t currently have a lathe.  I chose 28mm pipe to make it easier to fit 7-16 DIN connectors, the idea being that this will fit directly on the output DIN of my hybrid combiner.  Early days in the thought process so far though.

Stepped Impedance Coaxial Lowpass Filter Designer
http://www.changpuak.ch/electronics/Stepped_Impedance_Lowpass_Coax.php
Version : 09. November 2014
---------------------------------------------------------------------
Cutoff Frequency : 1600 MHz
System Impedance : 50 Ohm
Low Impedance : 9.87 Ω , cap.
High Impedance : 129.88 Ω , ind.
Order of Filter : 11
Filter Topology : Chebyshev, 0.0100 dB
Return Loss, S11 : 26.44 dB (approx)
Tube is round. Center is round.
Tube inner diam. / width : 26.20 mm, respectively 1.0315 inch
Overall Length : 154.0 mm, respectively 6.0627 inch
Depending on your connectors, you may need additional length !
---------------------------------------------------------------------
Section #0
Z (Ω): 50.0
Length : as required ...
Diameter : 11.39 mm, respectively 0.4483 inch
---------------------------------------------------------------------
Section #1
Z (Ω): 129.88
β*l (deg) : 18.16
Length : 9.46 mm, respectively 0.372 inch
Diameter : 3.00 mm, respectively 0.118 inch
G[1] : 0.8235
---------------------------------------------------------------------
Section #2
Z (Ω): 9.87
β*l (deg) : 16.34
Length : 8.51 mm, respectively 0.335 inch
Diameter : 22.22 mm, respectively 0.875 inch
G[2] : 1.4442
---------------------------------------------------------------------
Section #3
Z (Ω): 129.88
β*l (deg) : 40.36
Length : 21.02 mm, respectively 0.828 inch
Diameter : 3.00 mm, respectively 0.118 inch
G[3] : 1.8299
---------------------------------------------------------------------
Section #4
Z (Ω): 9.87
β*l (deg) : 19.73
Length : 10.28 mm, respectively 0.405 inch
Diameter : 22.22 mm, respectively 0.875 inch
G[4] : 1.7437
---------------------------------------------------------------------
Section #5
Z (Ω): 129.88
β*l (deg) : 43.13
Length : 22.46 mm, respectively 0.884 inch
Diameter : 3.00 mm, respectively 0.118 inch
G[5] : 1.9555
---------------------------------------------------------------------
Section #6
Z (Ω): 9.87
β*l (deg) : 20.20
Length : 10.52 mm, respectively 0.414 inch
Diameter : 22.22 mm, respectively 0.875 inch
G[6] : 1.7855
---------------------------------------------------------------------
Section #7
Z (Ω): 129.88
β*l (deg) : 43.13
Length : 22.46 mm, respectively 0.884 inch
Diameter : 3.00 mm, respectively 0.118 inch
G[7] : 1.9555
---------------------------------------------------------------------
Section #8
Z (Ω): 9.87
β*l (deg) : 19.73
Length : 10.28 mm, respectively 0.405 inch
Diameter : 22.22 mm, respectively 0.875 inch
G[8] : 1.7437
---------------------------------------------------------------------
Section #9
Z (Ω): 129.88
β*l (deg) : 40.36
Length : 21.02 mm, respectively 0.828 inch
Diameter : 3.00 mm, respectively 0.118 inch
G[9] : 1.8299
---------------------------------------------------------------------
Section #10
Z (Ω): 9.87
β*l (deg) : 16.34
Length : 8.51 mm, respectively 0.335 inch
Diameter : 22.22 mm, respectively 0.875 inch
G[10] : 1.4442
---------------------------------------------------------------------
Section #11
Z (Ω): 129.88
β*l (deg) : 18.16
Length : 9.46 mm, respectively 0.372 inch
Diameter : 3.00 mm, respectively 0.118 inch
G[11] : 0.8235
---------------------------------------------------------------------
Section #12
Z (Ω): 50.0
Length : as required ...
Diameter : 11.39 mm, respectively 0.4483 inch
---------------------------------------------------------------------

GB3MHZ strength

Signals from GB3MHZ feel a bit down on a few months ago. Conditions are flat, but this used to be a lot louder.  Note that the GPSDO is having one of its periodic wandering sessions.

Later capture shows the GPS lock is good again:

The mechanics of aircraft scatter – dF/dt of Doppler

OK, I sort-of answered my own question originally posted below. I just ran a numerical simulation which calculates the rate of change of path length from station A to the plane and the plane to station B using simple three-dimensional geometry. It then uses the bistatic doppler equation to find the instantaneous doppler shift at +-30s from the crossing point. As the plane height is potentially significant, at least on shorter paths, I took the height of the plane above the direct line from station A to station B – which obviously goes through the earth to the depth of the earth curvature on the path – along with the angle of the plane to the direct path and the speed of the plane, and found that the rate of change of the rate of change of the path length is indeed just about constant over a 200-600km path with an offset of 10-15km from the direct path for constant plane speed when the angle to the path is around 90 degrees. At sharper angles, it all gets a bit asymmetric and leads to curved tracks on the waterfall, particularly where the angle is less than 30 degrees or more than 160, and when the crossing point is less than 15% from either end of the direct path.

Magically, it works out to be within a few percent of the measured value of the rate of change of frequency on a real A/S reflection from a plane using the velocity vector reported on Flightradar24. For the example below, it gives 4.65Hz/sec, against a measured 4.9+-0.2 which is probably within the error margins for speed and heading and location of the plane.

Now all I have to do it turn the numerical model into an analytical one, so I can enter the frequency, path length, distance from A to B, distance of A to the plane, angle of the plane to the direct path, plane height and speed, and it will tell me the expected rate of change of frequency.

Next level is to use the rate of change of doppler and the zero-shift time to work out unambiguously which plane caused which reflection when there are 3-5 planes in the zone as reported by Airscout, and try to extract from that historic data some way to prioritise which path to try next, when there are five potential DX stations to work and ten possible planes in the next fifteen minutes. It would be good to know that the 21:35 crossing of the Reykjavik flight to a station in GM is likely to be better than the 21:34 Bratislava flight for a path into DL.
On 29/01/2017 03:00, Neil wrote:
>
> Tonight, I watched as a plane crossed the patch between me and GB3ZME on 13cm. Plane’s path was at about 70 degrees to the direct line between me and ZME, and was within 2km of the midpoint of the path. Plane was at a constant height of 8530m and travelling at 169m/s. I saw the reflection as usual, with the doppler changing by 4.9Hz/sec over the 21.5 seconds of the reflection. That inspired me to do the trigonometry and see if I could understand why the rate of change of frequency was constant and had that particular value.
>
> Now back in the day I remember doing something at college for the doppler effect from a moving mirror. So long as you aren’t at relativistic speeds it looks simple enough if you treat the plane as a mirror travelling perpendicular to the line of sight path between you and the source. The equation looks like:
>
> where v is the plane’s ground speed, c is the speed of light and α is 90 degrees minus the angle between the plane and the direct line of sight. Now v^2/c^2 is very very close to zero for a plane at 328 kts, so the doppler shift is very nearly just (2fv/c) cos(α) where f is frequency (in the paper that equation comes from, the author used omega instead of nu or f, but I *think* he meant frequency not angular frequency as it comes from the photon energy with Planck’s constant)
>
> So, working out using the full equation for 10 seconds either side of the line of sight, ignoring the height of the plane and the fact it isn’t at 90 degrees, the rate of change of doppler shift should be a constant 2.7Hz/sec. That is a lot different from the measured 4.9Hz/sec. I took the plane’s speed from Flightradar24, so it is possible that it was wrong, for example if it was really doing about 440kts, the rate of change would be just about right.
>
> However, it would be odd for the site to be that far wrong. I am pretty sure the component of velocity of the “mirror” along the line between me and the source must cancel out for the two halves of the path, but perhaps the angle between the source-plane and plane-me paths matters.
> Can anyone point me at a paper or reference which will fill in the missing elements of the height of the plane and its angle to the direct path and put me out of my misery please? All the papers on passive bistatic/multistatic radar seem to be behind paywalls or only talking about the path-loss implications of the bistatic radar equation and forward-scatter, and don’t have anything quantitative about the doppler shift.
>
> Neil G4DBN
>
> https://arxiv.org/pdf/1207.0998.pdf
>
> http://www.vk3hz.net/aep/vk7mo_2000.pdf
>
> http://www.nitehawk.com/w3sz/W3SZ-NEW-AirCraftScatterNEWS2014.pdf
>
>

Learning about the mechanics of aircraft scatter

So far I have ignored the problem of calculating the *amplitude* of the reflection based on the computed scattering cross-section, mostly because after a couple of trial calculations, it feels like what I am seeing from the beacons is more like a specular reflection, perhaps 10-20dB more signal than simple forward scattering would suggest. On 23cm, the amplitude variations seem to be either very slow or very fast, so either they are of a similar period to the reflection duration, or the averaging of the waterfall is probably smearing them out. They are certainly not as apparent as they are on A/S on 2m. I’ll have to try it with GB3DUN, where the reflections are a decent strength.

I guess the three-dimensional picture will be something like the fringing patterns discussed by DJ5HG for MS reflections, but from a point source.

I certainly see the beating effect of interference between the tropo and A/S path from the beacons I can hear directly, and that does look like the Lille transmitter tests in the G3BGL 1966 RSGB Bulletin article.

There are some Czech research papers about using passive bistatic and multistatic radar, but it looks like the majority of this work is probably classified.

The tests I have done with off-axis aircraft scatter using QRO with G4BAO and others have signal levels about the same as those of the direct-path reflections from the beacons. As the stations are using beams and QRO, I reckon the off-axis path loss must be 30dB or so higher than the direct forward reflections from the beacons.

Once I’ve got the analytical equation for the doppler sorted, I’ll try plugging in the actual signal levels to the bistatic radar scattering equation for a typical plane cross-section and see what it suggests the signal levels should be for the JO02 path to here via a scattering point near Newbury (about 60 degrees off-axis for JO02 station and 40 degrees for me) versus direct. I can see there is a problem of variation of the effective cross-section of a plane depending on its orientation and whether it is off-axis or directly in line or beyond the beacon – I seem to get a fair number of reflections when there are no planes shown between me and the beacon, they can’t all be military flights. However I haven’t been able to identify a specific case where the reflection came from a plane beyond MHZ or DUN, so at the moment that is still just surmise.

One thing I have found is that the angle to the plane from here is very important, same as for EME without elevation, owing to the deep nulls between the lobes of my yagi on 23cm. Some large planes close to me at an elevation of 2 degrees show no reflections at all, whereas a much lower or higher plane at the same range produces a very good reflection. Guess I need to map the vertical lobes against an EME signal, as I have done on my 2m antenna with KB8RQ’s mammoth signal as the moon sets from 20 degrees downwards. The same probably applies to the vertical pattern of the beacon, but I’ve not been able to verify that. I can certainly see the curved doppler trace of planes approaching Doncaster airport as they decelerate in their final apprach and map that against the actual airspeed from the ADS-B feeds.

I’ll re-read the VK7MO paper and see if I can lift some of the DJ5HG Matlab code to use in simulations based on those scattering cross-sections. However, first job is to get the new 6m/4m PA built, then the synth LO for the 9cm gear. Oh, and the mounting brackets and airline for the second SCAM12 pump-up. So many projects, so little time….

Musings about disciplined OCXO hold-over

I have been trying to fix a minor shortcoming in my locked 100MHz OCXO project.  If the reference signal is lost, the PLL either starts hunting in a sawtooth pattern, so the output frequency swings a few Hz either side of the free-running frequency, or it goes to one end of the VCO range and jams there.  I have a sort-of-OK workaround, which is to put the PLL charge pump into power-down mode on loss of reference (or loss of lock signal of that reference when it is the 10MHz GPSDO), and trickle a fixed DC level to the loop filter.

I have a 22-turn 5k pot across the low-noise reference supply, with a 10M resistor from the wiper to the junction of the charge pump output and the loop filter input.  Under normal operation, this has negligible effect, but when the charge-pump goes tristate, the voltage on the loop filter capacitors settles to the value set by the 5k pot. The time-constant is very long (CR=10M x 22u, about 3 mins) so there is no sign of a step when the thing goes tristate, and if I’ve tweaked it correctly, the 100MHz output just stays rock-solid to a few parts per billion.

However, there are some measurable variations of reference voltage over each 24 hour period (measured using a 6.5 digit Fluke DVM with GPIB), I guess the cause could be the slow diurnal variation of room temperature, despite the thick expanded polystyrene insulation around the OCXO.  The variation is tiny though, so I wouldn’t be able to measure it easily using a 10-bit ADC in a PIC unless I used an amplifier with x10 to x100 gain and a DC offset.

I sort of imagine a solution where I store the last 24 hours of measured voltage changes at the VCO pin, with an FET-input precision opamp zeroed to the mean lock voltage, then measure the output of the opamp with a 12-bit ADC in a PIC with Flash/EEPROM.  When the lock is lost and the charge-pump goes tristate, I would feed the same voltage from a DAC or PWM output into the loop filter through a 10M resistor.  It would then start to follow the delta pattern from the previous 24 hours, but starting from the current measured value.

The thing would be rather like the current manual solution, but trimmed every ten minutes or so to ensure the holdover voltage is always just about right.  It would automagically compensate for ageing and adapt to seasonal changes, although not to weird weather events. I guess it might be necessary to use an amplifier with a gain of 0.1 to 0.01 and a trimmable offset to get sufficient resolution from a typical PIC DAC/PWM, or perhaps it would be possible to use software dithering for interpolation?  I’d worry about spurs then, but if the time constant is 220s, then a 1Hz randomised dither rate won’t cause any fixed spurs that matter.

I can see it might be necessary to do something a bit cleverer than just outputting the “right” value in the hope that it might give the desired voltage on the loop filter caps.  It might be better to have a simple digital control loop to set the output voltage so that the measured voltage matches the required value.  Just a detail really.

The U-Blox LEA-M8F implements holdover somehow, does anyone have any references for other ways to implement PLL holdover?  The only recent refs I can find are all behind IEEE paywalls.  Does anyone have access to the full text of the Bourke and Penrod paper “An Analysis of a Microprocessor Controlled Disciplined Frequency Standard” ( 37th Annual Symposium on Frequency Control; 1983, p485-491)? [sorry it is behind the IEEE paywall]

Yes I *KNOW* this is overkill for this application and that <10ppb holdover is fine for all practical purposes.  This is about striving for a bit of engineering magic to make me happy.  Fun beats boring old “It’ll do” practicality every time.  In terms of hardware, it will only need an SOT23 op-amp and a slightly better-spec PIC than the one I am using already for monitoring and display, so the additional physical complexity is minimal.