Discussion in 'General Technical Questions and Answers' started by S21RC, Jun 12, 2021.
If you can measure the complex impedance of the inductor with a VNA, can't you calculate Q directly?
Thanks, can you please suggest the connection (hardware side). I am new with VNA as well.
I'm not entirely sure if I'm right yet -- would love for a smarter person to confirm! But if you know the resistance (R) and reactance (X), shouldn't it be X/R?
If your Mini-VNA shows the impedance in series equivalents, then Q is defined as X/R.
However, it takes a quite good VNA to get more than a "order of magnitude" indication of Q, as the impedance of a high-Q load travels very close to the rim of the Smith-chart.
If you had, say, a very accurate ohmmeter, could you use that to get a good DC resistance measurement, then use the VNA to confirm inductance (and thus reactance) at frequency to calculate Q? Or are there AC characteristics that affect the real component or something I don't know enough about?
Yes, there are skin effect and core losses that increase
the equivalent RF resistance of the inductor.
This may be orders of magnitude higher than the DC resistance.
The Q-meter was invented to get around this problem, and to provide an accurate measure of inductor losses.
The difficulty of Q-measurement with a VNA, that SM0AOM describes, is summarised in this diagram;
When measuring Q values in the hundreds, Gamma changes slowly, ie the line is almost vertical, and the VNA has difficulty in determining its exact value; a tiny error can greatly affect the reported Q value.
There is, however, a method for which a VNA is very much suited; the "3dB bandwidth" method. A signal generator and power meter were used in the "olden days" but a VNA is today's preferred instrument.
The procedure is fully described in W7ZOI's paper to which I linked in an early post.
As an example, here is a VNA sweep of a parallel-resonant LC circuit; I built it and other component combinations as reference objects to verify proper VNA setup & operation;
The W7ZOI paper shows how Q is determined from a centre frequency of 30.56 MHz and a -3dB bandwidth of 0.69 MHz.
Some notes on Elsie and her relationship with Q (seems like a good foundation for a spy novel : ) )
I am using a computer other than my "main" one this morning; it did not have Elsie so I downloaded her from Jim Tonne's site.
Thanks again to Jim for a wonderful and free program.
I reproduced S21RC's design and realised that, in a fresh installation, Elsie assumes impossibly-high Q values; 234 for inductors and 3456 for capacitors.
These values are used in plots and calculations of loss and, unless changed to more realistic values, give misleading results.
They can be changed, as Jim intended, in the Analysis section of the program; I'd forgotten this as it's years since I installed Elsie on my main computer.
I think that I have inductor Q of 100 and capacitor Q of 500 set in that computer; they are more realistic figures, perhaps even on the low side.
It's a quiet day here in Lake Wobegon so I did a little experiment; nothing precise but a good illustration of capacitor Q and its effect on resonant circuit Q.
I found two 1000pF capacitors in the collection; one was a blue 3kV ceramic type, the other was a dipped-mica type.
I also found a T50-2 toroid with five turns on it; calculation indicated a resonant frequency of about 12 MHz with 1000 pF.
The toroid was coupled in parallel with the mica capacitor and then with the ceramic capacitor and a transmission sweep done;
It's immediately apparent that the inductor/mica cap combination (black trace) has a much sharper and deeper resonance than does the inductor/ceramic cap combination (red trace), indicative of higher Q.
Data from the markers is;
Inductor with mica cap; resonant frequency 10.99 MHz, -3dB bandwidth 0.05 MHz, Q = 220;
Inductor with ceramic cap; resonant frequency 11.79 MHz, -3dB bandwidth 0.95 MHz, Q = 12.
Whilst I knew that the mica would out-perform the 3kV ceramic, I found the above results difficult to believe but there it is.
The perils of mental arithmetic or, perhaps,careless typing; the -3dB bandwidth in the first dot-point above should be 0.09 MHz (11.03 - 10.94).
Q is, therefore, 122.