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Adventures in Electronics and Radio
Elecraft K2 and K3 Transceivers
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Measuring High Q
Inductors
Steve, AA7U, and I recently collaborated on methods of
accurately measuring Q of very high Q inductors.
Steve was asked to measure the Q of an inductor wound with
660/46 Litzendraht (Litz) wire. That's 660 strands of no. 46 AWG wire,
each wire separately insulated. This is equivalent, in terms of DC resistance,
to about AWG No. 18 copper wire.
At low frequencies, say a couple MHz or less, Litz wire
has considerably less AC resistance than an equivalent diameter solid copper
wire because of skin effect and proximity effect. I won't go into the details
here as the interested reader can find a good summary at the Wikipedia entry.
http://en.wikipedia.org/wiki/Litz_wire
The particular inductor is 36 turns of Xizi 660/46 Litz,
wound on a 4.5" diameter styrene former, solenoid style. It's pictured in the
photo below, on top of Steve's HP 4342A Q-meter.
Related Web Pages:
I've written about related topics at:
Measuring Distributed
Capacitance
Self-resonant frequency of
Inductors
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The problem measuring the Q of this inductor is that it is beyond the direct
reading ability of the HP4342A Q-meter. The HP4342A's maximum meter range is a Q
of 1000, and this inductor at frequencies around 1 MHz has a Q well in excess of
1000.One detail first - the 4342A has an analog
meter to display measured Q, with a maximum scale of 1000. It also has a
buffered DC voltage output on the rear panel proportional to Q, with Q 1000
corresponding to 1.000 volts. This voltage is not limited to 1.000V and can be
measured with an external digital voltmeter as an indication of Q above 1000.
The photograph shows the analog meter pinned against the right hand limit on the
1000 scale, with a digital multi-meter displaying 1.433 volts on the buffered
output, theoretically corresponding to a Q of 1433.
So, how to measure a "super Q" inductor is the question.
Steve tried three methods to extend the Q range of his 4342A Q-meter:
- Use the buffered DC output, as read with a digital
multi-meter, as a direct Q indication.
- 3 dB Method. Vary the frequency above and below
resonance, measuring the frequencies at which the indicated Q drops to 70.7%
of the peak value, using the digital multi-meter to read the indicated Q.
The Q is then fc/(fupper-flower)
where fupper
and flower are the upper and
lower -3 dB points and fc is the center frequency.
- A "delta C" method using 4342A's ΔC adjustment. (More
details on this later.)
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As a preliminary matter, we must first consider that all
inductors have some distributed capacitance, which represents capacitance from
turn-to-turn and stray capacitance from the inductor under measurement to the
test equipment, the operator, etc.
In order to accurately model the measured inductance, we need to know the
"true" inductance, the "true" Q and the distributed capacitance. Knowing the
three factors allows us to use the simple three element inductor model
illustrated below. L is the true inductance, C is the distributed capacitance
and R is the loss element (resistance loss, core loss and other losses)
transformed into a single series resistance. (In some cases, a parallel resistor
model makes more sense, or a more detailed model may use both series loss and
parallel loss.)
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In addition to distributed capacitance within the inductor, stray capacitance
between the Q-meter and the inductor also exists, such as those illustrated
below. These strays will not be considered in this analysis, but will limit the
accuracy of Q-meter readings for high impedance devices, such as a high Q
inductor. The HP4342A manual explicitly notes:
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The relationship
between "true Q" or Qt and Q as indicated on the Q-meter, Qi, where the inductor
under test has distributed capacitance Cd and resonating capacitance C is given
below.
A similar correction to indicated inductance is necessary
to determine true inductance, Lt:
Finally, the series loss resistor in the model is
determined from the Q measurements:
These particular formulations are extracted from the 4342A
Operating and Service Manual, but are not unique to the 4342A.
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Steve measured the test inductor at four frequencies, using
the three methods mentioned earlier:
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Q Measurement Method |
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Frequency (KHz) |
DMM Extension |
Delta C |
3 dB |
|
605 |
1314 |
1297 |
1284 |
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805 |
1450 |
1347 |
1427 |
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1305 |
1348 |
1313 |
1355 |
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1705 |
1127 |
1355 |
1181 |
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Steve's comments on the various test methods are:
DMM Extension
I have replaced the analog output zero pot (on the A6
board) with a 10 turn trim pot, drilled a hole in the Q meter cover and
positioned that pot next to the cover so it's easy to adjust it when needed for
precise 0.000 zero. My Q meter still drifts around for the zero a little bit
even after hours of warm-up, but usually only 1 or 2 millivolts and is easy to
reset to zero. (The 1 volt adjustment doesn't drift at all, thank goodness.) I
rechecked the 0 and 1 volt adjustments today too, and the 1 volt is fine, just
the zero drifts around slightly. I've been checking the zero before every new
frequency now and readjusting to 0.000 if necessary.
Delta C
I think the new "delta C" method using formula (2) is
proving to be useful too as another check for Q, as well as the DMM reading
alone, and the 3dB method; certainly the delta C method is easier to do than the
3dB method--it takes a very steady hand on the frequency knob to adjust for the
3dB DMM reading--it's not as hard to do with the fine tuning variable capacitor
knob.
3 dB
No comments, other than it is difficult to accurately adjust the 4342A's
frequency precisely at the -3 dB points.
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The "Formula 2" method mentioned in Steve's Delta C comments is a reference to
the Boonton Notebook No. 4, Winter 1955 article "Check
Your Q Meter Readings by the Delta C Method" Step by step instructions to
measure Q using the Delta C method from this article are:
Formula (2) used by Steve is:
A slight variant on this is to use the 3 dB points, or 0.707 Q.
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Steve's conclusions are:
So, which method is the most accurate? That's the big
question!
I do believe the analog output zero adjustment has to be very close to zero,
within 1 or 2 millivolts, to give an accurate measurement at each frequency;
and of course the analog output 1 volt adjustment has to have already been
set, per the calibration information in the Q meter manual. As noted, the 1
volt adjust doesn't drift, only the zero drifts; and it drifts extensively
during warm-up. I use a simple shorting bar so the zero can be checked at
any time, even with the coil attached. (I adjust the zero and 1 volt
settings using the 1000 Q scale, not the 10 scale, if it makes any
difference. I've also checked the 0 and 1 volt settings at 500 kc, 1Mc and
1.7 Mc, and they are the same as at the calibration frequency of 100 kc.
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Steve also provided a series of measurements of resonating
capacitance versus frequency for the inductor. Using the 1/ω2
method discussed at
Measuring Distributed
Capacitance, I plotted the measurements and computed the true inductance and
distributed capacitance. Cdist = 4.97pF
Ltrue = 139.5uH
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