From: Paul
Date: Wed, 14 Feb 2001 08:25:52 +0000
Subject: Re: [TSSP] Top voltage testing
Hi All, This might be a good time for some transfer impedance measurements, since I've been talking about effective series inductance (Les) on the pupman list, trying to get these ideas into better circulation, and at this time plenty of solid verification would be most appropriate. Les relates directly to the transimpedance by Les = Zft/(2 pi f) For large h/d, Les is around 70% of Ldc, eg for Marc Metlicka's coil #2, h/d = 10.11, Ldc = 29.12 mH, Les = 22.3 mH Terry's recent measurements support this for a more modest h/d, where h/d = 2.94, Ldc = 75.1 mH, Les = 67.8 mH, f1 = 105.087 kHz are the figures for the probed coil, and the last set of measure- ments were Vtop = 53.1V, Ibase = 1.1742 mA, so Zft = 45.2 K ohms. >From this, the measured Les = 45200/(2 pi 105087) = 68.5 mH, which is 1% above the predicted Les, and nearly 8% below Ldc, which is a comfortable result - Terry's measurements here are accurate enough to distinguish clearly which inductance is in effect. The measurement of top voltage using a regular scope probe does not seem to be introducing any uncontrolled error, and by adjusting the probe capacitance representation in the model to match the observed f1 of the probed coil, the resulting predictions of Les seem to agree. Marc informs me that when coil #2 is loaded by a 10 Meg 11.2 pF scope probe, the f1 drops from its bare coil value of around 276 kHz down to 189 kHz. Modeling this I find 13.5 pF of probe C is necessary to match the depressed f1, which is reasonable. For Marc's #2, probed, at 189 kHz, we have Ldc = 29.12 mH, Les = 26.2 mH As you can see, the effect of the probe capacitance is to increase Les above the bare coil value (22.3 mH), so that it is now only 10% below Ldc. A simple way to measure Zft might be to use the arrangement shown in http://www.abelian.demon.co.uk/tssp/tmp/zftmeas.gif in which two almost identical probes pickup the top voltage and the base shunt voltage. The Zft is then just Zft1 = Vtop/Ibase = Rs * Va/Vb where Va and Vb are the two scope probe readings. These two readings will be subject to the unknown calibration factors of the probes and vertical amplifiers in the scope. Therefore the probes should be interchanged, so the probe B (and scope amp B) now measures Vtop and probe A measures the shunt voltage. This time Zft2 = Rs * Vb/Va, and we can then eliminate both of the unknown scope calibration factors by taking the geometric mean of the two readings, ie Zft = sqrt( Zft1 * Zft2) from which Les can then be calculated. Marc, perhaps you can try these measurements on coil #2, and see if you get a Zft of around 31K ohms? For Zft measurements, which are largely independent of Q, the shunt resistor Rs does not need to be very small, up to 150 ohms would be reasonable. This approach disposes of channel-to-channel gain variation of the two probes, but does not allow for gain error within each channel occuring when the range is altered, but hopefully that will be small. The reduction of Les below Ldc is disguised to a large extent in these tests by the effect of the probe capacitance. If we go to the other extreme and look for a coil for which we expect Les > Ldc we might be able to obtain a more equivocal demonstration of Les. If we can find a short, fat coil, equipped with a large toroid, we might expect Les to be getting on for 15% greater than Ldc. I have a coil h/d=1.36 and a toroid made from a tractor tyre, so if by some miracle it ever stops raining for long enough, I'll set it up outside for a test. My predictions are h/d = 1.36, big toroid, Ldc = 40.9 mH, Les = 45.1 mH a +10% increase. I've just finished putting together a new 18 sq m ground plane, made from layers of foil sandwiched between sheets of thick poly, so I'm desperate for a break in the weather. Cheers, -- Paul Nicholson, Manchester, UK. --
Maintainer Paul Nicholson, paul@abelian.demon.co.uk.