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measuring coil inductance with resonance

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LAN_403

Sulaiman

Mon Oct 05 2009, 05:02PM

Registered Member #162 Joined: Mon Feb 13 2006, 10:25AM
Location: United Kingdom
Posts: 3140

For high impedance circuits put L & C in series,
for low impedance circuits put L & C in parallel.
e.g. if at the resonant frequency the tank capacitor and inductor have impedances of 0R346 and the Q is 100, then the tank will 'look' like 34R6, ok to put directly across your sig.gen. ...

klugesmith

Mon Oct 05 2009, 05:05PM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716

Here's another way to measure low impedance (< 1 ohm) tank circuits.
It requires an oscilloscope. It served me very well for a can crusher setup (52 uF and about 2 uH), and would certainly work for a TC primary and 10uF, or 1 uF, or the intended MMC.

Just look at the voltage waveform of a weakly damped oscillatory discharge from, say, 10 volts.
It isn't hard to measure the period and damping ratio, even without a storage scope, if you can get repeatable shots at the push of a button.

My charger was a nominal 8-volt gel cell battery with 1K series resistor.
For the discharge switch, a mechanically-closed spark gap (adjusted for zero gap) or hand-held jumper wire got the job done. Contact bounce was a minor nuisance, and it sometimes took a couple of tries to get a good shot. Peak current was around 40 amps - it's Vpeak / sqrt(L/C).
I got repeatable bounceless closures using a mercury tilt capsule, and a mercury-wetted relay, and a vintage "silent" wall switch that was confirmed to behave as a tilt switch (though its ON resistance significantly increased the circuit damping).

Automatically repeating discharges would be handy for a 'scope that could not capture single-shot events. I'm sure a MOSFET with sufficiently low ON resistance would work. (During the On phase, V_DS will oscillate around zero, but with a very small amplitude. The resistive operating region extends into the third quadrant of I/V chart).

Hope this helps.
Rich

IamSmooth

Mon Oct 05 2009, 05:58PM

Registered Member #190 Joined: Fri Feb 17 2006, 12:00AM
Location:
Posts: 1567

Oh. The current transformer is put in line with the parallel tank. I thought it was coming off of the signal generator line.

Harry, how did you calculate the characteristic impedance? At resonance Xc and Xl cancel out, so where did the 1R1 and 0R346 come from?

klugesmith

Mon Oct 05 2009, 06:27PM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716

IamSmooth wrote ...
Harry, how did you calculate the characteristic impedance? At resonance Xc and Xl cancel out, so where did the 1R1 and 0R346 come from?

Harry won't mind if I answer. And simply Googling for that expression will turn up mostly references to Z_0 of transmission lines.

Characteristic impedance (of an LC tank circuit) is the magnitude of both Xc and Xl at the resonant frequency.
It's the ratio of peak voltage to peak current at that frequency, thus an important consideration in the design of circuits associated with the tank.
Numerically it's sqrt(L/C), while the characteristic time is sqrt (LC). Undamped oscillation period is 2 pi x sqrt(LC).

Proud Mary

Mon Oct 05 2009, 06:51PM

Registered Member #543 Joined: Tue Feb 20 2007, 04:26PM
Location: UK
Posts: 4992

IamSmooth wrote ...

How did you come up with the characteristic impedance of 1R1?

Zo = sq rt L/C

IamSmooth

Tue Oct 06 2009, 12:27AM

Registered Member #190 Joined: Fri Feb 17 2006, 12:00AM
Location:
Posts: 1567

I connected everything in parallel and all I got was a constantly increasing voltage as I increased the frequency to 200kHz.

I measured the output impedance of my signal amp and it was close to 35-40R.

I don't need to measure the inductance, but I would like to do it for the sake of learning how. What are my options? Would some kind of Wheatstone bridge with inductors work?

klugesmith

Tue Oct 06 2009, 01:00AM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716

IamSmooth wrote ...
I connected everything in parallel and all I got was a constantly increasing voltage as I increased the frequency to 200kHz.

Next step for me would be to repeat the frequency sweep a couple of times,
after replacing the LC tank circuit under test with
1) an open circuit and
2) a plain resistor of 10 ohms or so.
If you see a non-flat response then something needs to be fixed.

Knowing that wirewound resistors are inductive, I once measured HOW inductive.
WW R's nominally valued at about 1 ohm, in 2 to 5 watt size,
typically had corner frequencies between 1 MHz and 2 MHz.

teravolt

Tue Oct 06 2009, 01:28AM

Registered Member #195 Joined: Fri Feb 17 2006, 08:27PM
Location: Berkeley, ca.
Posts: 1111

I did what you are doing with your equipment and tried it with my table top DRSSTC with no secondary. when I changed the primary inductor the frequency changed. luckally I have accsess to a comersial bridge so after persisly mesuring the L and C and using the resonant frequency of the drsstc and math there was about a 5% differance.

IamSmooth

Tue Oct 06 2009, 04:06AM

Registered Member #190 Joined: Fri Feb 17 2006, 12:00AM
Location:
Posts: 1567

Voltage response to a 10R resistor is flat as expected.

Ok. Maybe this will work, so all of you up on your EE tell me if this is acceptable. How about a step response? I don't have a digital scope, so what if I feed a square wave into the coil and measure the oscillations? The coil has a resistance, R, and an inductance, L. So, if I know R I should be able to get L if I can measure the period of the oscillations, right? I can look up the equation, but tau is related to the L/R ratio. Can someone fill in the specifics if this is feasible?

What I am shooting for is L = R*tau
I will use a large R in series with the coil to eliminate the very small native resistance of the coil itself. I will measure the time until 63% voltage rise to make the calculation. Does this sound good?

Here is what I get:
Step response to square wave input

Proud Mary

Tue Oct 06 2009, 07:24AM

Registered Member #543 Joined: Tue Feb 20 2007, 04:26PM
Location: UK
Posts: 4992

Smoothie, I can see you're struggling a bit here, so why not connect a much smaller capacitor in series with your coil, say 500pF (hint hint) and look for a resonant dip somewhere between 6 and 7MHz. (If my very approximate calculation of 1.2uH from your description of the coil is correct, 500pF should give a series resonant frequency of 6.5MHz, with an impedance just short of 50R, a healthy match to your signal source. )

If you don't get a dip between 6 and 7MHz increase the width of the sweep until you do - but always be aware of false resonances - none of the components in your experiments are the pure things suggested by formulae. The capacitor has some inductance, the inductor some capacitance, and so on, which can result in a real-world coil-cap combination having several points of resonance, in which you should always choose the largest one as the most likely fundamental.

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