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That secondary harmonic voltage distribution stuff...

Hi All,

	Inspired by Alwyn's questions about secondary voltage, I made the
following measurements.  I took a small (~3 inch) cell phone antenna and
taped it to a wooden stick.  I taped a yardstick on my coil to measure the
distance along it.  The bottom turn of the secondary was at 1 inch and the
top turn was at 31 inches.  Using the insulated tip of the antenna, I was
able to fairly accurately place it at one inch increments along the coil.
I then set the digital scope to take the average of 64 measurements and
find the RMS voltage level.  This proved surprisingly accurate and gave
very stable and repeatable readings.  The coil was driven by a 1Vp-p sine
wave generator with less than 1 ohm output impedance.  The top terminal was
in place and the primary was directly grounded without a cap in the circuit.  

As far as I know, this is the best measurement of it's type ever despite
it's simplicity.  Of course, the math power of the digital scope was
essential to cancel noise and do the RMS stuff...

I adjusted the frequency for maximum output with the probe at a high
voltage spot.  So the relative voltage levels from graph to graph should be
fairly realistic.  The probe no doubt de-tuned the coil a bit but I don't
think it was very significant.

There is a graph at:
	users.better-dot-org/tfritz/VoltDist.jpg

An Excel97 file is at:
	users.better-dot-org/tfritz/voltagedist.xls



There are three surprises.

The 1st harmonic produced 173mV, the 2nd 27.2mV, the 3rd 8.02mV, and the
4th 4.61mV.  So the 1st harmonic has almost 7 times the power of the
second.  Obviously tuning a coil to the 1st harmonic is VERY important!

As I mentioned before, the harmonics or not 1, 3, 5 multiples of the
fundamental, but 1, 2, 4, 6 multiples.

The top of the coil is a node and not an anti-node for harmonics above the
fundamental as we have always assumed.  That does not help the streamer
output of harmonics either ;-)



Pos	1st 	2nd 	3rd 	4th
kHz	82.6	310.2	477.9	636.6

0	0	1.46	1.55	1.19
1	0	2.51	2.28	1.74
2	5.41	3.81	3.19	2.46
3	6.5	5.24	4.26	3.2
4	7.93	7	5.27	3.86
5	8.52	9	6.38	4.43
6	10.8	11.1	7.25	4.61
7	12.4	13.7	7.78	4.5
8	14.2	16.6	8.02	4.05
9	15.8	19.5	7.9	3.29
10	18.2	22.1	7.45	2.39
11	19.9	24.3	6.65	1.29
12	21.9	26	5.64	0.72
13	24.6	26.8	4.16	1.31
14	27.2	27.2	2.94	2.03
15	30.3	27.2	1.5	2.59
16	33.7	27	0.7	2.76
17	37.6	26.5	2	2.58
18	41.6	25.8	3.31	1.95
19	45.6	24.4	4.49	1.15
20	50.6	22.7	5.56	0.62
21	56.5	20.3	6.31	1.43
22	63.7	17.7	6.8	2.32
23	70.8	14.6	6.96	3.19
24	80.6	11.9	6.79	3.91
25	91.9	9.25	6.11	4.23
26	103	7.04	5.32	4.23
27	119	5.18	4.32	3.95
28	136	3.3	3.13	3.31
29	152	1.93	2.1	2.43
30	166	0.3	1.1	1.57
31	173	0.3	0.4	0.87
32	165	0.3	0.3	0.7

I think the "lumped" model can explain all this.  Basically, the coil is
acting like a series of parallel LC sections each of which is tuned to the
input frequency...  I have to think about this more though.  I did not
expect to find this and the theories may need some "adjustement"...  

Much still to do, ponder, explain....

Cheers,

	Terry