[Elecraft] Q

[Jack Smith]

Paolo:

Continuing our discussion on measuring RF inductors, I tested an 
inductor I wound on a powdered iron core this morning. 29 turns of #22 
wire on a T50-2 (red) core. Nominal value is 4.2 uH if I recall correctly.

HP4342A Q-meter, measured at 7.9 MHz:
Lp = 4.30uH, Q=212

HP4320A RLC Bridge @ 1 KHz:
Auto:  1.5uH Q: N/A
Ls (manual) L=2.0uH, Q=0.98
Lp (manual) cannot be measured as Lp requires Q > 8

General Radio GR1650A RLC Bridge @ 1 KHz:
Lp=10uH, Q=0.98
Ls=5uH, Q=5uH

Leader LCR740 RLC Bridge
L=4.50 uH Q=0.98

The Q-meter values are the ones I regard as "correct."

I also measured the DC resistance of the inductor, using an HP3468A 
multi-meter in 4-wire ohms mode: 28 milliohms.

We can compute the approximate Q of this inductor at 1 KHz, assuming its 
true inductance is 4.3 uH (powdered iron has a very flat relative 
permeability versus frequency relationship, so we should expect the true 
inductance to be 4.3 uH at 1 KHz.)

Xl = 2*pi*L = 27 mOhms. 

In series model, Q = Xl/Rs = 27/28 = 0.96

Note that both the GR1650A and LCR740 match this Q value almost exactly. 
(We can safely neglect the core loss and other losses in this 
approximation, as the inductor's loss is dominated by the DC resistance 
of the windings.)

If you read the instruction manuals on the RLC bridges (GR1650A manual 
is much better in this regard than HP's 4260A manual in my view) you 
will see that low Q inductors are difficult to accurately measure. You 
will also see how to convert the series model to parallel and vice versa.

What about that 10uH Lp value from the GR1650A?  To compare it with the 
same instrument's Ls reading, we must convert to consistent models. In 
this case, we'll use the series model and compute Ls from the Lp 
measurement:

GR1650A Lp=10uH

Ls = LpQ^2/(1+Q^2) =>  Ls = 10uH*0.98^2/(1+0.98^2) = 4.99 uH.

Thus, we see that the series model inductance is 5uH, whether measured 
with the bridge in Ls or Lp mode.

The GR1650's accuracy rating is +/- 1uH when on the lowest inductance 
range (100 uH full scale) at the bottom of the dial, which is where this 
inductor reads.

Hence the measured value of the inductor at 1 KHz is 5 uH +/- 1uH, so we 
see that the "true" value of 4.3 uH is within the measurement accuracy 
of the GR1650A bridge.


The measurement accuracy at 1 KHz can be improved by calibrating out the 
residual inductance and some other tricks that are mentioned in the 
manuals.

The GR1650A bridge, by the way, is the same model I used in Electrical 
Engineering labs when I studied EE in the mid 1960's. Still a good 
bridge and I find it preferable to the HP4620A.

Jack K8ZOA
www.cliftonlaboratories.com - home of the Z90/91 digital panadapter.