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Problems measuring an inductor

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LAN_403

Avi

Tue Aug 09 2011, 08:10PM

Registered Member #580 Joined: Mon Mar 12 2007, 03:17PM
Location: Melbourne, Australia
Posts: 410

Why are my measurements so far off from calculated values?
my procedure is as follows:
Apply a sine wave signal from a DDS (frequency output has been verified) which is DC biased, though a 470uf capacitor to make it bipolar AC, then to a 12.5 ohm (measured) resistor to the test inductor to ground.
The junction of the resistor and inductor go to an analog oscilloscopes ground, and then the other side of the inductor to ch1 and the other side of the resistor to ch2.
The frequency is then adjusted until the 2 amplitudes match such that it is known that XL=R
This is then placed into the formula XL=2*pi*F*L and then rearranged as L=XL/F/pi/2 or L=12.5/F(DDS set)/pi/2

Note: the frequency generation circuity is floating and ran from a battery.

first air core coil (spiral)
inductor voltage matches 12.5 ohm series resistor voltage when applied frequency=1129khz
XL=2*pi*F*L
12.5=2*pi*1129000*L
12.5/1129000/pi/ 2=L
L=1.76uH

using physical specifications:
Primary inner diameter: 16 cm (6.2992126 inches)
Primary thickness: 2.5 mm (0.0984251969 inches)
Primary turns: 11
L(uH)=((turns*average radius)^2)/((8*average radius)+(11*total coil width))
L(uH)=((11*(6.2992126+(0.0984251969/2))) ^2)/((8*(6.2992126+(0.0984251969/2))) +(11*(6.2992126+0.0984251969))=40.25uH

using
Primary inner diameter: 16 cm (6.2992126 inches)
Primary turns: 11
Wire diameter=2.5 mm/11=0.227 mm (0.00893700787 inches)
turn spacing: 0
46.419uH

second air core coil (helical)
inductor voltage matches 12.5 ohm series resistor voltage when applied frequency=1039Khz
XL=2*pi*F*L
12.5=2*pi*1039000*L
12.5/1039000/pi/ 2=L
L=1.91uH

using
average coil diameter=84mm+((wire diameter/2)*2)=
84+3mm (wire)=87mm diameter
19 turns
wire diameter: 3mm
turn spacing: 0
27.97uH

klugesmith

Tue Aug 09 2011, 08:51PM

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

Your calculations seem to be in order.
I think the L values calculated from geometry are about right --
just figured your helical coil using

& got around 27 uH.
(I think formulas without online calculators are much better than online calculators which don't state their formulas!).

So I'm guessing the low values from the o'scope could be an artifact of your lab setup.
Is your reference resistor a wirewound type? I would not be surprised if its own w*L surpasses its DC resistance at around 1 MHz. Do you know the output impedance of your signal generator?

Here's an independent lab method:
Put a plastic capacitor of about 1 nF in parallel or series with the inductor under test.
Drive with your signal generator and optional resistor, monitor with o'scope, sweep frequency, chart amplitude, find LC resonant freq.

Or simply put L, C, and a switch in series. Connect DC power through a high value resistor, so C is charged when switch is open. Use scope to observe the frequency of ringing each time you close the switch.

Avi

Tue Aug 09 2011, 10:00PM

Registered Member #580 Joined: Mon Mar 12 2007, 03:17PM
Location: Melbourne, Australia
Posts: 410

I put the first coil in parallel with a 470nf capacitor (only small value one i got that had the value directly printed on it without researching capacitor codes).
Peak amplitude occurred at 195Khz.
F=1/(2*pi*sqrt(L*C))
(((1/F)/2/pi)^2)/ C=L
(((1/195000)/2/pi)^2)/(470/1000000000) =L
L=1.42uH

klugesmith

Tue Aug 09 2011, 11:59PM

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

How strange.
If there's any electrical component whose value can be computed from its geometry, it's an air-core coil.
I don't see how your spiral can be much different from 40-some uH, or the helix not 20-some uH.
Could it have so much turn-to-turn capacitance that we are seeing self-resonance?
Could it have a shorted turn?

Can you post a schematic and a physical picture of the setup?
How sharply does the amplitude change as you tune away from resonance?
Do you have a labeled inductor as a reference L element? Need one?
Do the oscilloscope timebase and signal generator agree as to frequency?
What happens if you measure your 2 coils in series or in parallel (with their axes perpendicular) ?

[edit] Someone else must put on the online debugger's lab smock now.

Sulaiman

Wed Aug 10 2011, 12:16AM

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

Measuring inductance can be difficult, mainly due to source impedance of signals
(e.g. is your sig gen << 12.5 ohm output impedance?)
and loading. (is the 'scope input impedance (say 1Mohm//15pF?) >> 2.pi.F.L.Q ? )
my method is;
1) put a capacitor in parallel with the inductor to form a resonant circuit, one end 'grounded'
2) connect the signal source to the resonant circuit using a capacitor <= 1/100th of the resonant capacitor
3) connect the resonant circuit to a detector (meter, 'scope etc.) via a similarly small capacitance
The impedance of the small capacitors at the resonant frequency should be >> source or load impedance.
The total capacitance in the resonant circuit is the main capacitor in parallel with the two small ones.
This allows a very high 'Q' resonant circuit, the smaller the small capacitors compared to the main one, the greater 'Q' achieved.

Avi

Wed Aug 10 2011, 01:25AM

Registered Member #580 Joined: Mon Mar 12 2007, 03:17PM
Location: Melbourne, Australia
Posts: 410

the "first air core coil (spiral)" coil has significant inter turn capacitance, which was the reason for the second test with a more conventional coil.
as for source impedances, there may be an issue that the signal is generated by a current output DAC?
the product page is here:

Do you have a labeled inductor as a reference L element? Need one?

I have a lot of inductors, and know the value of none. :(

Do the oscilloscope timebase and signal generator agree as to frequency?

The time base is not accurate on my scope, i have been using a microcontroller to measure frequency when required.

Here is a photo of the "second air core coil (helical)"
1312940892 580 FT0 Dsc 5201

It is all connected with breadboard and clip leads.

klugesmith

Wed Aug 10 2011, 02:46AM

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

Yup, that looks like a 20-some uH inductor. Here's a 50 uH:

1293071742 2099 FT104049 Lisn Coil 49 Cr

Following Sulaiman's suggestion, put your 470 nF capacitor in parallel with the inductor as close as possible (each lead of capacitor directly touches the corresponding lead of your coil; you can use one end of a clip-lead as a clamp).
The signal and ground connections to your signal generator (with large value DC blocking cap) and to your oscilloscope should each go directly to those same two nodes.

Measure and -chart- amplitude vs. frequency with the LC tank circuit; then replace the LC tank circuit with
your 12.5 ohm resistor and repeat the sweep (to detect any abberations in your setup).
Ideally the amplitude will be flat with the resistor, and be very small with the LC tank except for a sharp peak near resonance.

Your signal generator has a 300 ohm output impedance (current output IC in parallel with 300 ohm load/bias resistor), which is >> the load impedance except, perhaps, with the LC near resonance. Same should go for your scope input. These meet Sulaiman's criteria.

The LC tank circuit will obviously have an impedance near zero at DC and at very high frequencies.
The resonant frequency should be about 45 kHz with the geometrically calculated L value, or 195 kHz based on your previous measurement.
At resonance, the expected load impedance will be real, and >> the value sqrt(L/C)
(which I figure to be about 8 ohms with the geometric L value and about 1.7 ohms with the 1.42-uH value.).

[edit] Are you sure your reference C is 470 nanofarads, not 470 picofarads?
The former is often marked 0.47 or 474; the latter is often marked 471.
27 uH with 470 pF would have a characteristic impedance of 240 ohms, which is comparable to the signal generator impedance. So you'd have a low-Q (broad) peak near [edit edit] 1.4 MHz.

[edit^3] Are you sure that tabletop isn't made of metal under fake wood-grain vinyl? Didn't think you were trying to make an eddyscope.

Conundrum

Wed Aug 10 2011, 06:42AM

Registered Member #96 Joined: Thu Feb 09 2006, 05:37PM
Location: CI, Earth
Posts: 4061

Yeah, have been stung by this problem before..

(re. edit^3)

If its a factor of a round number like 10 or 100 out, the capacitor could be incorrect.
I've had cheaper parts go strange values before, once
had this happen on a CCFL inverter.
Looked OK but inverter wouldn't run with bulb connected, turned out that the capacitor measured about 1Mohm series resistance and nearly four times its marked value.

-A

Avi

Wed Aug 10 2011, 03:40PM

Registered Member #580 Joined: Mon Mar 12 2007, 03:17PM
Location: Melbourne, Australia
Posts: 410

second air core coil (helical)
490nF (470nJ written on it, i measured it at 490nF with a microcontroller)
43.2khz
F=1/(2*pi*sqrt(L*C))
L=(((1/F)/pi/2)^2)/C
L=(((1/43200)/pi/2)^2)/(490/ 1000000000)
L=27.7uH
That is better!

first air core coil (spiral)
490nF
172khz
L=(((1/172000)/pi/2)^2)/(490/1000000000)
1.75uH

2450khz
2.47nf
L=(((1/2450000)/pi/2)^2)/(2.47/1000000000)
L=1.7uH

some pictures of the spiral coil are attached

klugesmith

Wed Aug 10 2011, 06:32PM

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

Good work with the helix. Do you know what was wrong the first time?

As for the spiral coil, you didn't say it was a foil coil. I had interpreted the 2.5-mm primary thickness as an axial dimension (i.e. wire diameter) instead of the radial thickness of 11 turns. Is the 2.5-mm a measured value, so thickness per layer is about 1/11 of that?

Self-capacitance could be a significant contributor here. Have you done the frequency-swept amplitude measurement with no added capacitor?

If you post the missing dimension (axial length), perhaps someone here is equipped to easily reproduce your spiral (at a different scale) and measure its vector impedance vs. frequency.

[edit] I'll wager (without the usual arrogant confidence) that well below its self-resonant frequency,
your foil coil will have about the same inductance as an 11-turn helical coil of the same overall dimensions --
perhaps 6 microhenries? An empirical formula optimized for flat pancake coils could land far from the mark
when length / average diameter ratio is nearly one. This can be a learning experience all around.

We still want to know the width of your foil (i.e., length of your coil).

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