Dual-Resonance Coil Testing - John Dunn, Consultant, Ambertec, P.E., P.C.

If you need to measure a transformer winding inductance in situ, while the transformer is all hooked up to its operating circuitry, that surrounding circuitry may interfere with getting the measurement done if there is a large capacitance present across the winding in question. An LC meter I once tried to use in that way simply could not ascertain a transformer winding's inductance because there was a large capacitance being reflected into that winding from the transformer's other windings.

However, there is a way out of this problem using the test fixture as sketched below. 

This test fixture is an amplitude controlled LC oscillator where "L" is the unknown inductance and "C" that inductance's unknown shunt capacitance value.

The fixture is used by connecting the unknown winding, or coil, as shown, selecting C3a, then C3b, then C3c and then C3d and adjusting S2 and R15 in each case to obtain a linear sinewave output which will be AGC controlled to an amplitude of one volt peak. You'll find in most cases that this is not a critical thing to do. The AGC sets and holds the signal level quite easily.

For some unknown value pair of L and C, the inductance and capacitance at the "unknown" winding, we consider two selected capacitance values for which two oscillation frequencies are obtained. Hence the term "dual-resonance".

We will call these Cx and Cy yielding frequencies Fx and Fy. From the basic LC resonance equation, we obtain the following two equations:

L = (  (1/Fx)² - (1/Fy)² ) / ( 4 * pi² * ( Cx - Cy ) )    and    C = ( Fy² * Cy - Fx² * Cx ) / ( Fx² - Fy² )

With four values of test capacitance selectable via S1, we get four test frequencies which we then use in six paired combinations to obtain redundant calculations of "L" and "C". If those redundant calculation values are essentially alike, we can have confidence that we've taken all of our readings properly.

The following are some typical results:   

In the second case shown, trying to directly measure the 25.5 µHy in the presence of 0.86 µF could be quite problematic.

 

GWBASIC code for doing these calculations is as follows:

 

10 CLS:SCREEN 9:COLOR 15,1:PI=3.14159265#:DIM CT(4),FT(4):ON ERROR GOTO 180

20 PRINT "save "+CHR$(34)+"dualres.bas"+CHR$(34):PRINT

30 PRINT "save "+CHR$(34)+"a:\dualres.bas"+CHR$(34):PRINT:PRINT

40 A$=" ###### Hz  ###### Hz  ########.## uHy  #.#### uF"

50 B$=" ###### Hz  ###### Hz  ####.###### mHy  #.#### uF"

60 C$=" Averages = #####.### uHy  #.##### uF"

70 FOR XX=1 TO 4:READ CT(XX):CT(XX)=CT(XX)*.000001:NEXT XX

80 DATA .0230,.0349,.0492,.1039:REM These CT values are the test fixture caps.

90 READ F(1),F(2),F(3),F(4):CSUM=0:LSUM=0

100 FOR XX=1 TO 4:F(XX)=F(XX)*1000!:NEXT XX

110 FOR X=1 TO 4:FOR Y=X+1 TO 4

120 L=1000000!*(1/F(X)^2-1/F(Y)^2)/4/PI^2/(CT(X)-CT(Y))

130 C=1000000!*(F(Y)^2*CT(Y)-F(X)^2*CT(X))/(F(X)^2-F(Y)^2)

140 PRINT USING B$;F(X),F(Y),L/1000,C:LSUM=LSUM+L:CSUM=CSUM+C

150 NEXT Y:NEXT X:PRINT USING C$;LSUM/6,CSUM/6:PRINT:GOTO 90

160 DATA 14.41,12.07,10.34,7.310:REM  Coil 1 readings in kHz.

170 DATA 33.56,33.36,33.06,32.14:REM  Coil 2 readings in kHz.

180 END

This code will analyze the frequency readings in each DATA line. Add more lines and you get more analyses. In each analysis, you get the six individual calculations and then you get the average values as a sanity check.

A word about the capacitance values in Line 80.

These somewhat odd looking capacitance values were originally entered as standard values of 0.022 0.033,0.047 and 0.1 µF. An air wound test coil was made whose inductance would not change with varying excitation and frequency readings were taken for that coil. These capacitance values were then hand tailored to make the six sets of calculated  L and C values as much alike as possible.

One last point is that this test fixture needed to be inside a metal box. It was not possible to make it work properly when unshielded.

 

 

Comments

[John Dunn]

Just to mention:

This device was used on transformer windings of roughly 1 to 2 mHy of magnetization inductance in parallel with reflected capacitances from high voltage secondary windings, capacitances that approached 0.1 µF. The inductance meter I had at the time was thrown hopelessly off by that combination.

These dual-resonance equations are the same as in the "Dip Oscillator and Dual Resonance" item:

http://licn.typepad.com/my_weblog/2012/03/dip-oscillator-and-dual-resonance-john-dunn-consultant-ambertec-pe-pc.html

[William Ketel]

This system must be intended for smaller transformers, it seems. At first I was thinking that it would be for the larger power transformers in the multiple KVA class.
The winding being checked must be shielded because both ends are connected to relatively high impedance points and both ends have AC signals present. So it is quite susceptible to noise. That must be included in the considerations for the circuit's use. In order to have one end grounded the circuit would become a bit more complex.
It is also possible to do the same test using an external oscillator and oscilloscope and capacitor substitution box. That would be much less convenient but it would not need the shielding enclosure.

[david pacholok]

Clever idea indeed!
BUT:
In my experience with 60 Hz xfmrs the inductance changes with excitation level due to the nature of the slope of the B-H curve in Silicon Steel, and even with frequency due to lamination eddy current losses among other things. So if your goal is to look for variences in L from a production lot - great!
But if you need to get closer to the operating L when the transformer is energized a method we like is solving the simple differnential equn:

V = -LdI/dT + IR

With a DC power supply, fast switch like a MOSFET, a DC current probe and a DSO you can choose your core H excitation level at which you wish to measure inductance by direct examination of I vs. T slope. You can actually watch permability change with this method, then flip the polarity to see what is hapening near the B/H orgin, and look at core retentivity as well.
The paralell capacitance is rapidly charged at the moment of switch turn-on and is effectively not there for the test, given a low Z DC supply.
Safety Note: Use a clamp (MOV, Zener) to safely dissipate energy in L when switch opens!

[John Dunn]

You're quite right, David. This worked on ferrite core transformers and coils and with the grid dipper, on slug tuned and air wound coils. When I tired to use this on 60 Hz transformers, the winding inductance made large values shifts with only small changes of excitation.

As to capacitance, the biggest challenge, the problem that actually brought this whole idea about, was the reflected capacitance from several thousands of turns on the secondary windings of high voltage transformers plus capacitance effects of voltage multipliers that went as high as x20.