From: Paul
Date: Mon, 25 Mar 2002 12:14:01 +0000
Subject: Re: Ready :-)) - Re: [TSSP] short H/D and stuff
I wrote:
> I should have enough info in the waveforms, and from the model,
> to determine the value of the resistance that you use.
Starting with
2*pi*f*Lee/R = Q0 * Qs/(Qs - Q0)
derived in a previous post, in which Q0 is the measured Q with
R in the base connection, and Qs is the normal Q of the coil
without added R.
>From the data, we have for each frequency,
f1/4 f3/4 f5/4 Origin
Qs: 464.44 185.29 106.80 (3-24/TEK00000.CSV)
Q0: 283.93 168.62 102.70 (3-24/TEK00001.CSV)
f: 229.91 kHz 578.09 kHz 904.58 kHz (3-24/TEK00000.CSV)
f: 231.61 kHz 583.92 kHz 939.46 kHz (tssp tfcp1.in)
Lee: 51.77 mH 50.05 mH 38.07 mH (tssp tfcp1.in)
Applying R = 2*pi*f*Lee*(Qs - Q0)/(Q0 * Qs) and using the model's
value for f, rather than the measured (so that it is consistent
with the modeled Lee), we get
f1/4 f3/4 f5/4
R: 103.1 ohm 98.0 ohm 84.0 ohm
Since the formula for R is most sensitive to the difference Qs-Q0,
the error in the estimate of R will be at least the fraction
sqrt(2) * Eq * sqrt( Qs*Q0)/(Qs - Q0)
where Eq is the fractional error in the Q determination. Eq is
typically around 0.3%, so an error estimate from measurement error
alone is
f1/4 f3/4 f5/4
Q err: +/-0.9 % +/-4.5 % +/- 11 %
Since we are using the model's predicted values for the product
Lee * f, and f at least has the known errors
f1/4 f3/4 f5/4
F err: +0.7% +1.0% +4.0%
and if Lee has a similar error, then we can put forward the final
result for R:
f1/4 f3/4 f5/4
R: 103.1 ohm 98.0 ohm 84.0 ohm
+/-2.3 % +/-6.5 % +/-19 %
For this short coil, the ratio Les/Ldc is greater than unity:
f1/4 f3/4 f5/4
Ldc: 39.18 mH 39.18 mH 39.18 mH
Les: 44.34 mH 54.00 mH 58.61 mH
Les/Ldc: 1.13 1.38 1.50
and the measured current profile now stands as a convincing
demonstration of why the effective series inductance at resonance
usually differs from the DC value.
If you were to stand another secondary on top of this short coil,
say 10" diam by 30" long, then you would have a 39"x10" secondary
with the lower 25% available for current profiling. With this
arrangement you could demonstrate the elevated current max of a
normal h/d TC secondary.
This trace analysis method of extracting Q values seems to be
working very well. I can now think of about a million experiments
that can be done now that we can measure Q accurately.
One interesting point is that the measured Q is rather higher than
the predicted Q for this coil. I'm not used to seeing this -
usually its the other way around. The Q measurements are now
precise enough for me to tackle this part of the software.
The calculated winding resistances are
DC: 32.91 ohms
AC: 37.83 ohms (DC + skin effect)
Proxy: 155.45 ohms (DC + skin effect + proximity loss)
Obviously, finding a way to gauge the proximity loss properly
is going to make a big difference.
As regards the errors in the current profile comparisons - up to
20% in the current peaks at f5/4, this looks like it is due to
poor determination of internal capacitance by the model. Cint is
being under-estimated at short range by about 10%, enough to give the
frequency error we see at f5, and this accounts for most of the f5
current profile error. I'll re-run the model with coil former
dielectric compensation turned on to see if that fixes it.
How long did it take to capture the 12 CSV files? Was it likely that
the temperature in the room changed by more than a degree during
the run. In future I think we may have to ask for temperature
readings, since the Q will change by about 0.4% per degree C, which
is more than the precision of the Q extraction.
--
Paul Nicholson,
--
Maintainer Paul Nicholson, paul@abelian.demon.co.uk.