Measuring Resonator Q at VHF

Greetings!

I've long enjoyed broadcast FM DX chasing. This post covers the first chapter in my pursuit to design and make a homebrew broadcast (wideband) FM DX receiver.

Traditional FM DX superheterodyne receiver ran single conversion with a 10.7 MHz IF and usually a dual-gate MOSFET mixer behind 1-2 dual gate MOSFET preamplifers embedded in 2-4 doubled-tuned bandpass filters.  To cover 88-108 MHz with decent skirts + bandwidth, the band-pass filters were tuned with ganged, air-variable capacitors that simultaneously tuned the VFO.

Fast forward to this day in time. Following low-pass filters and T/R switch circuitry, some modern narrow band FM transceivers run varactor tuned band-pass filters, 1 or 2 dual gate MOSFET amplifier(s) and a MOSFET mixer in the receiver chain.

I explored varactor tuned band-pass filters for wideband FM and learned a few things along the way.

Above — My first FM band-pass filter that tuned all 20 MHz of the FM band without a double humped filter response. In order to get the BB639's capacitance down to its lowest value (~ 3 pF to tune 108 MHz), you need 28 volts applied reverse DC. I keep a homebrew bench DC-DC converter for just that purpose. The filter's 3 dB bandwidth ran from about 2.2 MHz at 88 MHz to 3.3 MHz wide at 108 MHz

In order to boost the filter low-pass response, I tapped the inductors for the input and output ports. Light loading improved the filter response, but reduced the input/output return loss. Tuning a filter over a 20 MHz span proved a lesson in compromise.

60 nH isn't a lot of L and my coils were 6 turns of bare copper 22 gauge wire wound on a small bolt and then stretched to allow room for tapping and to set the correct measured inductance. I further tweaked them in-situ. Later, I placed this filter after various preamplifiers including a dual-gate MOSFET and a common gate JFET amp.

Above — A snippet of 1 of my amplifier + band-pass filter circuits. I got a better filter response with a 96 nH inductor, although this should technically worsen it.

1 major problem arose with my filters: a horrible insertion loss of 8-9 dB!!  I expected about half that. Later I wrote some great friends for advice and after reading their wisdom, I came up with 2 sane theories: the insertion loss was due to lowered Q and input + output port mismatch.

Resonator Q Measurement

I then realized that I'd never measured resonator Q at VHF. If you own a Q meter such as the
HP4342a stop reading now, get a coffee and go to another blog-site.

As amateur experimenters, to derive resonator Q we may employ 2 techniques: calculate Q after measures with a parallel tuned L C tank, or calculate Q after measuring with the L and C set in a series tuned trap circuit.

I've not enjoyed much success with the latter, so will present the method where our parallel L and C are loosely coupled to a 50 Ω source and load. Please refer to EMRFD page 7.36 for more details.

Supplies:

• Signal generator with level output amplitude,  50 Ω output Z and enough output power to allow measurement with your particular detector.
• 50 Ω detector: spectrum analyzer,  50 Ω terminated 'scope, or measurement receiver etc.
• 50 Ω patch cables.
• A homebrew jig with RF connectors, coupling capacitors and ground plane.
• Frequency counter.
• Through connector.

Setup:

Above — The basic paralleled tuned resonator measurement set up including gimmick probes as the input and output coupling capacitors.

Above — My test jig with the inductor and air variable capacitor soldered in place. I copied this jig from Bob, K3NHI and received advice from Wes, W7ZOI. Bob made a circuit at his QTH, measured the resonator Q and sent me a photo and some measures by email. I re-created his circuit to compare results. The coil = ~ 300 nH or 10 turns on a 1/4 inch bolt. The capacitor to resonate it @ ~100 MHz on my bench = 7.27 pF.

 Method to Set Jig Insertion Loss at VHF

In order to measure a resonators unloaded Q, or Qu, the insertion loss of the jig must minimally be 30 dB. To clarify, join the input and output cables together with a barrel or through connector and measure power. Unsplice and then connect the cables to the jig and measure power once again — power should drop by at least 30 dB at the test frequency.

To create the >= 30 dB insertion loss we lightly couple the jigs input and output with low value capacitors. At HF, we may insert small series capacitors, but this is nearly impossible at VHF unless you own some special microwave parts. Instead of series capacitors, we couple with gimmick wires.  Experiment to find the correct wire distance from the resonator to create the needed insertion loss.

Here are my 2 jig measurements with a DSO plus the IL calculation:

Above — My insertion loss fulfills the require >= 30 dB needed for proper resonator coupling
I calculated the IL in dB with JavaScript Tool G. It's difficult to measure under 50 mV with a 'scope for some; your power meter or spectrum analyzer might work better.

To get the needed IL or measure for Qu calculations, set your signal generator to the desired frequency and then tweak the resonator variable capacitor to give the highest possible AC voltage/power. Then re-tweak your signal generator to ensure you've peaked the signal. You might have to re- tweak the variable cap again and so forth.

Optionally, If your resonator capacitor is fixed, adjust your signal generator frequency to peak the signal.

After properly setting the IL and peaking for the strongest signal, the final measures go quickly:

1. Record the frequency where you measured maximum power: that's FO, or center frequency.
   
   
2. While watching your detector, lower the signal generator frequency until FO power drops by 3 dB [easier to do with an SA or power meter]. Record that frequency.
   
   
3. Bring the signal generator back up to FO and then increase frequency until the power drops by 3 dB. Record that value.
   
4. Calculate Qu as Frequency/Bandwidth.

I'll show my measures performed with a homebrew signal generator with less than ideal tuning resolution; however, you'll get the idea.

Above — FO or center frequency = -25.84 dBm, therefore my 3 dB down target = 28.84 dBm when I change my signal generator below and above FO.

 

Above 2 images — The 3 dB measures below and above FO (getting as close as possible with a homebrew VCO).  My VHF VCO sports a >= 30 dB output return loss from 98 - 149 MHz.

Calculate B or the 3 dB bandwidth by subtracting the lower frequency from the higher.

My calculated resonator Qu = 289. Bob, K3NHI measured then calculated 300 on his. Pretty close.

Above — Bob's homebrew jig and resonator. Bob measures everything: including his breadboard length! 

Varactor Measurement

I removed the air-variable trimmer cap and inserted a small piece of copper clad break-out board to hold a tiny BB639 varactor (size SOD-323). I voltage tuned it to resonance and then repeated the whole resonator Q measurement routine. Q = 174: a drop of 115 which would boost my original FM band-pass filter insertion loss by at least 1.5 dB compared to an air variable capacitor.

Above — Measuring resonator Q with a varactor.

Through experiments with the the aforementioned parallel + series resonator measurement techniques, I learned that carved squares and traces in boards may also lower Q. Even a Manhattan or carved pad nearby may couple to the resonator and drop its Q during measurement. My worse case measure produced a drop in Q of 20 from nearby islands carved in the copper board. Clearly we need board traces, but they can affect resonator Q and thus add to filter insertion loss.

Further, good VHF filter designs stick each resonator in an RF tight compartment. Whatever filter I eventually keep, I'll mind my Qs.


Footnotes

Thanks to Bob, Bob, Wes, Ken, John and others who kept me on track  — I know just enough to act foolishly on the bench.

I made 1 varactor tuned band-pass filter on single-sided copper board and compared it to the double-sided board versions. The single-sided board suffered poor stopband shape and didn't tune as well.

Above — A board set up for a dual-gate MOSFET surface mount circuit where the FET source runs a shunt resistor and capacitor to ground, plus has DC voltage on both G1 and G2. Some via holes connect the top and bottom ground plane.

Above — I placed 22 gauge copper wire in the via holes and soldered them top and bottom.
Grounded parts are placed near a via wire. Sometimes, I'll add more via wires near grounded parts.

Above — A single frequency amplifier carefully matched to see how much gain the BF998 could deliver. 21.2 dB rocks my world.

Above — Some of my (mostly) 50 Ω homebrew bench modules for test and measurement.

Above — My favorite design project of 2014: a return loss bridge with directivity >= 30 dB from 5 MHz to 1.5 GHz.   You may read more about it in the old site pops.net archive: Topics 2012 - 2014 : Caitlyn 310 — UHF Beginnings : 3. Return Loss Bridge Experiments : Bridge #4