[Edit #1: Some of my images (graphs & schematics) shrunk to fit the column width. Just click on images that seem to be truncated to see them full sized.]

Measuring Q is an interesting challenge. With the PHSNA (a DDS calibrated source plus AD8307 RF power measurement instrument plus analysis software), it seems like it should be a piece of cake. I'm already doing it with crystals, after all.

But then I remember that Qs of 100 to 200 or more, even with toroids, aren't unusual, and inductors with reactances in the 50 to 200 ohm range are common in RF / HF designs. Do the math and you see that we may be measuring fractional ohm loss resistances. A bit of a challenge in a 50 ohm system.

One way to increase sensitivity is to put the component being tested in a lower resistance fixture, for example, 12.5

Ω is typical for crystals. Going to extremes, a 1 Ω fixture does a lot. A problem is that two 50 to 1 Ω minimum loss pads back to back have a combined attenuation of 45.9 dB. So we need a strong source or sensitive detector or both. My PHSNA system has about 0 dBm RF output and the detector should go down to say, -60 dBm without much trouble. So I probably don't need an amplifier in line.

I also got into looking at Q measurement methods in EMRFD (page 7.36). Typically, one puts a series resonant circuit for which Q is desired in series between the source and detector. In this example, the test circuit is put in the __shunt__ configuration between source and detector. I wondered how that differs in sensitivity form the series method. So the first thing I did was do the math to solve for loss resistance in both configurations.

I derived the formula in general terms for source (and detector) resistance Rs instead of
just for 1 Ω. Rx is the value of the
loss in the coil (or coil + capacitor).
For attenuation A, I get:

The ultimate purpose of this
exercise though is to find Rx. So
solving the above for Rx **for the shunt
configuration**:

The procedure is to measure power to the detector without the tested circuit installed, then measure it again with it installed in shunt (to ground, between source and detector). 'A' is the dB difference in the two measurements and here is it is a negative value.

To compare this method with the series method, I need to derive the equations for that configuration.

**Series configuration:**

and solving for Rx:

I was somewhat surprised when this result didn't look like the equation I've been using for crystal Rloss measurements. I finally realized it was because my math began with attenuation as a negative number but the other equation entered it as positive. So they are equivalent.

I put the equations into an Excel spreadsheet and plotted the attenuation A against Rx for both configurations. My thought is that the method that produces the greatest change in A per ohm change in loss resistance is the more sensitive.

Below:

1 Ω test fixture

Rx on horizontal axis

dB attenuation on vertical axis

From the above, the series method seems better for "all around" measurements, but the shunt method looks like it would be better for high Q / low loss resistance items. In a one ohm environment.

I repeated the above plot for a 12.5 ohm fixture and again for a 50 ohm fixture and present results below:

12.5 Ω test fixture

Rx on horizontal axis

dB attenuation on vertical axis

Above, the series configuration
gives a fairly constant slope of about 0.3 dB per ohm. The shunt configuration gives much better
sensitivity, up to the source resistance of 12.5 Ω which is the crossover point
again.

Finally for the 50 ohm fixture case:

Below:

50 Ω test fixture

Rx on horizontal axis

dB attenuation on vertical axis

(Above) Again the change per ohm with
the series method is constant but it’s down to 0.08 dB/Ω. With the series method, much more sensitivity
is achieved with about 8 dB/Ω at 1 Ω, decreasing to 0.36 dB/Ω at 15 Ω. It's clear that with higher source / detector resistances, the shunt method is better.

It just occurred to me that if you already have a 50/50 system, by using the shunt method you don't have to go to the trouble of building a lower resistance jig. So EMRFD rules again.

**Some practical results:**

I wanted to go with the 1 ohm fixture first. Below is a schematic of one I got from Bill Carver, W7AAZ. It uses SMT precision resistors from Mouser. Also shown is a 3 dB attenuator. Cut off at the right is matching to the HYCAS amplifier. Bill was showing me how to use it to measure crystal parameters.

And below, we have it in physical form:

**An unexpected problem!**

I did some series method measurements with the tested item installed (as shown) and with a short across the two alligator clips. What a shock to find, in some cases, more power measured through the tested device than with the short. Negative attenuation!

This baffled me for a while but I began to suspect the inductance of the loop formed by the two alligator clips and the shorting wire between them. I measured the attenuation of a loop about
that size on my AADE L/C meter and get somewhere between 0.045 and 0.075 uH. At 8.2 MHz, that’s 2.5 to 3 Ω of reactance. And in a 1 Ω environment, that’s
significant. Using LTSpice, it seems to
add about 7 dB attenuation over a “real” short.

But when I have my series L/C
circuit under test installed, the small loop inductance gets absorbed into my
test coil’s inductance and cancelled when I find the resonant peak. That’s why the circuit under test actually
has a higher power value than the so-called shorted fixture.

I saw a couple of ways around this. One was to resonate out the stray inductance when I did my "shorted fixture" measurements. It's best to do this reasonably close to the measurement frequency, so I needed about 5800 pF. That worked -- I was able to see the peak and measure available power with strays cancelled out.

Another method would be to assume the calculated 45.89 dB attenuation of the fixture is accurate, measure power with source plugged right into detector, and take 45.89 dB off of that for my "shorted fixture" power. The method of resonating out strays seemed to give slightly better accuracy.

Oh, I did use a lowpass filter following the generator. The DDS-60 is pretty well filtered, but notes on measuring Q emphasize the need for very good harmonic suppression.

Now some measurements. I had a couple of iron power toroids wound with turns as noted. One was a T68-7 and the other a T50-2. I measured inductance with my AADE meter and chose a resonating capacitor (silver mica) to resonate at something over 8 MHz.

I made a measurement of the L/C resonant circuit and a second one with some series resistance added, to see if the delta came out close to the resistor value. I also tested a type 61 toroid and a miniature molded choke, just to do some samples with lower anticipated Q. I plug the attenuation and source resistance values as well as inductance and frequency into an Excel spreadsheet and have it crank out loss resistance Rx and Q.

The method is to measure the shorted fixture power as discussed above, then hook up the test specimen and do a response sweep with PHSNA. It finds peak and minimum values. In this case, I want the peak. I take a peek at the plot just to make sure it's not a "false peak". Take the difference of the two dBm readings to get dB attenuation.

So I think my accuracy is probably decent, but could be improved. That may be my next post.

**What about the shunt method?**

I decided not to try that with the fixture I have now, because dealing with the stray inductance is not so simple. It will not be absorbed into the test specimen's inductance but instead will combine with it in a more complex way. Probably making another fixture with minimal strays is a good solution. Also, based on the graphs, the 50 ohm method might be the best overall for the shunt method.

__Notes:__

EMRFD is the ARRL book *Experimental Methods in RF Design*

PHSNA can be found at:

https://groups.yahoo.com/neo/groups/PHSNA/info

... and in an article in the spring 2014 QRP Quarterly magazine.

Nick / WA5BDU

4/1/2015