From: Paul
Date: Sun, 18 Feb 2001 21:53:35 +0000
Subject: Re: [TSSP] Reactive part of base input impedance
Terry wrote: > For the bare small-coil no top-probe I get: > > Q = 170.03 > > f1 = 358.81 > V = 0.47218 (corrected scope) > I = 2.6234 mA > > f45low = 357.87 > V = 0.48419 (corrected scope) > I = 1.9908 mA > > f45high = 359.89 > V = 0.48419 (corrected scope) > I = 1.8823 mA First, we can extract from these a measurement of Lee, since Rin = w Lee/Q, we have, at f1, Rin = 0.47218/2.6234e-3 = 180 ohms, so Lee = Q Rin/w = 13.58 mH and the predicted value is 13.66 mH, +0.6%. No problem there. Now to check the slope of the reactance. Near f1, Zin(w) = Rin + jwLee( 1 - (w'/w)^2) so at +45 degrees phase, Rin = 2 pi f Lee ( 1 - (f'/f)^2) or Lee = Rin/2/pi/f/(1-(f'/f)^2) therefore, using f45high, Rin = 0.48419/1.8823e-3/sqrt(2) = 181.89 ohms Lee = 181.89/2/pi/359890/599e-5 = 13.42 mH At -45 degrees phase, Rin = - 2 pi f Lee ( 1 - (f'/f)^2) so Lee = Rin/2/pi/f/((f'/f)^2 - 1) and using f45low, Rin = 0.48419/1.9908e-3/sqrt(2) = 171.98 ohms Lee = 171.98/2/pi/357870/526e-5 = 14.53 mH The average of these two is 13.98 mH, +2.3% from the predicted Lee, and -15% from the predicted Les of 16.41 mH. So the result is rather nearer Lee than Les. That's a good result. The small coil and new coupling box are doing quite well there Terry, you've measured and verified Les and Lee in quick succession to quite a decent accuracy. I don't suppose anyone in the coiling community has done these before. Hopefully a few more measurements along these lines will become available - it will all help to establish the validity of these equivalent reactances and demonstrate that they are real and measureable. I'll be preparing a web page summarising your Zft, Les, and Lee measurements, so let me know if you put up any related pages at your end. Althogether, this is a great step forward, as pn2511 is distinctly lacking in references to these kind of results. I expect you'll be glad to know that I'm scheming up a way to measure Cee also. The 45 degree phase readings are going to be most useful, as I try to figure out just what's going on with the base impedance, and why the Qi always seems to be a little higher than Qv. Note the lopsided variation of Rin, I'll be taking a closer look at this to make sure the model reproduces the same values. Incidentally, the 'new formula' predicts an f1 of 356.7 kHz, -0.6%, for this coil. BTW, next time you're playing with the probed small coil, have a look and see if you can see the difference between the frequency of max Ibase and the frequency of max Vtop - it is likely to be very small, with max Ibase lower in frequency than max Vtop. Cheers. -- Paul Nicholson, Manchester, UK. --
Maintainer Paul Nicholson, paul@abelian.demon.co.uk.