Optimizing Impedance Measurement: Bridge vs. Sine Wave Generator Method?

[damosuz]

Why don't we just connect a sine wave generator in series with a DMM and the coil, set the amplitude Δv₀ to a given value on a scope, measure the RMS current I on the DMM and use Z = 0.707Δv₀/I?

 

[2milehi]

Not that simple. The reactance of the coil is frequency dependent (jωL). Less current will flow as frequency goes up. There is also the resistive part of the coil which could affect results.

 

[damosuz]

Yes, I know that Z depends on f, L and the resistance R of the coil. But you could measure Z by the method I described above and then find L (let's say) from the measured values of f and R. But nobody seems to do it like that.

 

[meBigGuy]

Yes, I know that Z depends on f, L and the resistance R of the coil. But you could measure Z by the method I described above and then find L (let's say) from the measured values of f and R. But nobody seems to do it like that.

Of course that only works if you care about Z in a frequency range that your DMM can deal with, and you don't care about DMM resistance or lead inductance. The DMM resistance could be more than your inductor. You should try it in the lab with a few inductors and see what the practical issues really are.

Easier to stick an R in series and measure with the scope.

 

[damosuz]

Of course that only works if you care about Z in a frequency range that your DMM can deal with, and you don't care about DMM resistance or lead inductance. The DMM resistance could be more than your inductor. You should try it in the lab with a few inductors and see what the practical issues really are.

In the lab I used a 2.5 mH inductor (measured with a LCR bridge) having a 20 Ω resistance. Working in the frequency range of the DMM, the impedance I obtained from Z = 0.707Δv0/I was always significantly higher than the one I calculated from f, L and R. Could it be due to the fact that R is higher than 20 Ω when current flows, either because the coil wire is not ohmic or because of the skin effect ?

 

[zoki85]

Do you want to measure coil inductivity or just coil impedance at some frequency? There's big difference. Coil impendance (at low enough frequencies) you can always measure as IZ I=V_rms/I_rms if current and voltage waveforms are clear sine waves. But, if you measure ferromagnetic core coil's Z by simple V-I method, you may run into problems due to nonlinear features of magnetizing current. And to accurately determine inductivity (L) of nonferromagnetic coil by this method you need to know angluar shift between current and voltage wave or resisistance R_ω=f(ω) of coil wire (phase shift will not be exactly 90°due to loses). Only if skin and proximity effects can be neglected (ie. low ω) you have R_ω= R_DC. Therefore, it is recommended you measure real power to the coil during measurement. Measured inductivity is then:

 

[damosuz]

Thank you zoki85. So if I understand well the IZ I=V_rms/I_rms method will only allow me to determine L accurately for a nonferromagnetic coil and low frequencies.

Now, would the IZ I=V_rms/I_rms method allow me to determine the capacitance of a capacitor from Z = 1/2πfC, using the frequency I like ?

 

[zoki85]

So if I understand well the IZ I=V_rms/I_rms method will only allow me to determine L accurately for a nonferromagnetic coil and low frequencies.
Now, would the IZ I=V_rms/I_rms method allow me to determine the capacitance of a capacitor from Z = 1/2πfC, using the frequency I like ?

If you can neglect loses, yes. Otherwise, you need to now R_ω or φ or P. There could be also other issues like parasitic capacities if you go too high with frequency.
Same kind of considerations holds for capacitor msms.

 

[damosuz]

Thank you! How can you measure P?

One last question: with the coil connected directly to the generator, I noticed that for high frequencies a DMM measured a RMS voltage that was less than the amplitude (as measured on the scope) divided by √2. Do you have an explanation for that?

 

[zoki85]

One last question: with the coil connected directly to the generator, I noticed that for high frequencies a DMM measured a RMS voltage that was less than the amplitude (as measured on the scope) divided by √2. Do you have an explanation for that?

Most likely, such frequency is too high for yor DMM to be accurate enough. Trust your scope.

 

[2milehi]

Thank you! How can you measure P?...

Aim into a graduated quart/liter container. :w

 

[zoki85]

I see I didn't answer power msm question. If you arrived at conclusion power factor isn't negligible, especially at higher frequencies, here's what you can do. Since you already have o-scope you can use it to simultaneously capture voltage and current sinusoids through the inductor. See this video how current probe is used for this. Then you can find angle shift φ between voltage and current. And calculate P=V_rms⋅I_rms⋅cos φ

 

[sophiecentaur]

If you have a variable frequency source and a meter or scope (plus a few odd, cheap components) then you can find the inductance of a coil be resonating it with a known parallel capacitor. In the days before posh readily available RF equipment, the Q Meter technique was used to find component values. That wiki link and others could help you make do without an expensive Impedance Bridge.
It all depends upon the accuracy you require, though.

 

[zoki85]

Or, he could make Hay's Bridge , with relatively small budget

 

[Mike_In_Plano]

In antiquity, a high input impedance transformer would be used in place of the meter and the secondary of the transformer would then drive headphones. The operator would then sweep around in the audible range looking for a null in the tone. Very crude, but sounds like fun to build.

 

[meBigGuy]

Thank you! How can you measure P?

One last question: with the coil connected directly to the generator, I noticed that for high frequencies a DMM measured a RMS voltage that was less than the amplitude (as measured on the scope) divided by √2. Do you have an explanation for that?

Sweep the frequency lower and see what happens. Put another way, measure the frequency response of your meter.

 

[Mike_In_Plano]

With a true-RMS meter, you usually get a good response to 10kHz. Some of the old Fluke handhelds could even go to 100kHz - if calibrated properly. Cheap hobby meters are random. Many don't have a true-RMS function to save cost and those that do may have a poor frequency response.

In any case, if you use a bridge, you would be more interested in the null than the accuracy of the meter.