Measuring the self resonant frequency of an inductor?

[TimFox]

I originally used this test box to measure inductance (possibly affected by its parasitic capacitance) and coil Q by adding a known good capacitor in series with the coil under test, between the two large capacitors.
Roughly, the relationship between the parallel resistance and reactance, and the equivalent series resistance and reactance (at a fixed frequency for the reactances) is calculated from:

 R_p / X_p = X_s / R_s = Q

Therefore, if Q >> 1

R_s = X_s x X_p / R_p = R_p / Q²  << R_p (since X << R_p );  and X_p = X_s

Go to the textbooks for the exact formula, since X changes for lower Q.

I used the shunt C method to get very low resistance for the original Q measurement, with a slight correction to the known capacitor from the two large capacitors in series with it.
Your circuit works, but has a larger resistance in series with the coil.
Note that C1 and C2 must be chosen for the frequency of interest.

[T3sl4co1l]

Mind, there is no "one" way to measure an inductor.  Any circuit you can make, in which the impedance of the element in question is sensible at the input, output or both, can be used, given appropriate calibration (or the circuit and given values).

Consider these simple methods:
https://www.seventransistorlabs.com/Calc/RLC.html

L/C by divider assumes an ideal reactive component in the divider, and based on the ratio measurement (can be done with any AC voltmeter that reads the driven frequency accurately enough), tells what L or C that would be, given the assumption.

I normally use this when I want a crude measurement of a component, letting R = generator impedance (50 ohms) and adjusting F until drop is in the 10-90% range.

Vector impedance, is basically the same thing, but with a series resistor added (we ignore source resistance because it's measured as reference; this requires a simultaneous measurement, and hence the extra resistor), and using a low distortion sine wave, and the scope's phase measurement function, we get a more accurate value -- also we know unambiguously not just what reactance it is, but its resistance as well; at least to within measurement error: the phase measurement tends to be pretty rough (+/- degree or two), so for element phase near 90° (note, that doesn't mean measurement phase near 90°, it's less due to the modest divider ratio!), resistance is proportional to phase difference from 90° and it can easily be measured near-infinite, or negative.  (Note that, for electrical purposes, real numbers are a ring, i.e. there is a continuum from positive-infinite to negative-infinite numbers.  So this is expected behavior.)

Frequency and Q factor, is practical when measuring higher impedances, and at select (tuned) frequencies.  Because the inductive reactance is canceled out with capacitance, the resistance can be measured accurately, and at a chosen frequency F <= SRF.  Note that, for very high impedances (large divider resistance, small capacitance), and high frequencies, probe impedance itself is a concern, but for modest values at 10s of MHz or below, a typical 10x probe is generally fine.

Note that we can measure Q both ways, i.e. by resistor divider and by fractional bandwidth.  I didn't bother writing a calculator for that, but simply noting the frequencies where amplitude is 70.7% of the peak, and dividing center/peak frequency by that difference, gives the same value.  Same give or take -- if the network is more complex than assumed (repeated/overlapping poles at the frequency, or the resonance of a continuous structure like a transmission line), the methods might differ, which is useful info about the network/element itself, though how one might use this difference, depends on the network.

Capacitance by difference, is adding a tweak and measuring the shift in frequency.  I probably use this most often when measuring switching circuits, the ringing frequency of a stray oscillation I want to dampen.  First introducing a plain capacitor Cx, I determine the in-circuit capacitance; then I use >2C, plus a resistor R = Zo, to dampen the oscillation (which gives a Q factor under 2 or so).

Matching capacitor, is as it says in the description; I use it to measure high-Q inductors at level.  Taking careful measurements, using high-Q capacitors (C0G are practically ideal, they are very good capacitors indeed), I get values as accurate as the measurements themselves.  So, repeatable within some percent, which is enough to see the effect of, say, bits of metal near an airgap in a ferrite-cored inductor.

The above-posted methods are variations on this (or these) approach(es), with parallel or series arrangements instead.  The flanking-capacitors motif effectively swaps series and parallel resonances, so instead of an input dip you see an output peak, etc.  The capacitors skew the response -- reactance is lossless, you don't get a straight-up / naive resistance divider, it's impedance, and the transfer curve contorts as a result.  Ultimately, all we're doing is rotation and translation on the Smith chart; so as long as we haven't completely lost visibility of the test component (which is guaranteed when lossless components are used around it), we're just picking what frequency we want to measure the element at, and what range of impedance it will present to our instruments at that frequency.

Tim

[TimFox]

Lots of ways to do an impedance measurement.
For inductor self-resonance, the important thing about the fixture is to avoid uncompensated parallel capacitance added across the inductor.

[T3sl4co1l]

Or a known amount of capacitance, of course.

Any kind of coupling will do:

In the resistor divider case, you're coupling with a resistor, measuring the peak into the element's resistance (anywhere d|Z|/dF = 0, i.e. at local minima/maxima, the impedance is real), and as long as the resistor divider is a resistor divider (you aren't introducing reactance), then there you go.

For inductors with external field, an inductive link can be used, in which case, as coupling is varied, the notch depth and width vary, with maximum depth and minimum width (jointly that is) occurring at critical coupling.  This is a common way to test loading / choking coils for antenna and matching use, and it used to be there was a specific tool to test this (grid/gate dip meter).  I mean, you can still use one too, but these days you might as well get the cheap(ish) VNA and do so much more.

For the C-coupled case, it's the same way, coupling varies with its value, with the difference that the C loads the tank as well.  So, use the C+Cx calculation to correct for that.  For filters constructed this way (i.e. parallel resonant tanks with small C spanning between their tops), it's why you get asymmetric skirts, a highpass-ish characteristic, for example.

Tim

[LooseJunkHater]

I have always used R1 with a 50 ohm source, to avoid loading the generator with a seriously reactive load.
If you are testing around 1 MHz, then you need to increase the capacitor value by a factor of 10 from that used at 10 MHz.
Ceramic capacitors above 100 nF tend to be bad dielectrics: X7R or worse, that may give bad results in a measurement jig.
At or above 100 nF, your best bet might be a polypropylene film capacitor, although C0G/NP0 are available at 100 nF.

I made a [Falstad circuit](https://www.falstad.com/circuit/circuitjs.html?ctz=CQAgjCDsB0AcYCYCsBTAtAThA6TIYAYBmIjDMSMDIggNlpABYGkQkC30wwAoIyDrUYg0RBOASwRY8CA4EeAJwlTR4igzVy2CgMYgawrYZAYGHMNALWbtu2HSQRBK5MgJGsT0iTVGjAmo5KwJeAHMDAmEzSOFEKXkeABtwSE0ZZHTxeStWNBdbBFp3DCRGDEh+IiRaL2EFZUzpcRMtDnYeCI1TBm747T1UrKGe7Us7CdsHNCcXBAQxHwCCBGIMWGsEkN4KQSMZMGH1cAnZF14AezYQITH58mDrf1qfMwRCdw96kNDtcVYiDwrhZtAEyOBoB4yNCYWRyt8VuUMJJ4ARYEVaMQ4thtICgA)

and it appears that at 1v out of the AWG, the load could potentially be 20ma (but I think it would actually be more, because as you increase frequency, the resistance of an inductor increases?). I can't find the max current output of the AWG Uni-T UTG932E. If the AWG can only output 20ma, will that effect the measurement accuracy of the inductor?

[TimFox]

You want to make sure that the generator can drive 50 ohms to the desired amplitude without distortion.
I just obtained a Rigol DHO914S with a (somewhat wimpy) AWG capable of 5 V pk-pk into an open circuit, and verified that it delivers 2.5 V pk-pk into a 50 ohm load.
Most generators with 50 ohm source impedance are designed to drive a 50 ohm load:  some audio generators are rated for 600 ohms.
My circuit as drawn presents a minimum of 50 ohms to the generator:  that's why I included R1.
The reactance of an inductor increases with increasing frequency:  therefore, the current through it (not the same as the current into my left BNC connector) decreases with increasing frequency.

[LooseJunkHater]

My circuit as drawn presents a minimum of 50 ohms to the generator:  that's why I included R1.
The reactance of an inductor increases with increasing frequency:  therefore, the current through it (not the same as the current into my left BNC connector) decreases with increasing frequency.

Sorry, can you explain this in further (simpler?) detail? I'm still not very knowledgeable with electrical engineering.

[joeqsmith]

Paper from Coilcraft:

https://www.coilcraft.com/getmedia/8ef1bd18-d092-40e8-a3c8-929bec6adfc9/doc363_measuringsrf.pdf

[TimFox]

My circuit as drawn presents a minimum of 50 ohms to the generator:  that's why I included R1.
The reactance of an inductor increases with increasing frequency:  therefore, the current through it (not the same as the current into my left BNC connector) decreases with increasing frequency.

Sorry, can you explain this in further (simpler?) detail? I'm still not very knowledgeable with electrical engineering.

With R1 = 50 ohms between the BNC and everything else, the minimum impedance seen by the generator will be 50 ohms.
With large C1, whose reactance is much less than 50 ohms, the actual impedance will not be much higher.
A generator is characterized by its output resistance (50 ohms for most high-frequency generators):  in most generators, that is a physical 50 ohm resistor between the guts and the output connector (often with an attenuator in between).  It is rare for such a generator to be incapable of driving an external 50 ohm load, so the output current capability is enough to drive it (although the maximum voltage across a 50 ohm load is 1/2 the maximum voltage into a high impedance load).

Do you have access to any of the Spice variations, such as LTSpice?
Rather than work through all the algebra, the ".AC" mode will do all the algebra for you on a linear circuit (no diodes, etc.).

The equivalent series-parallel conversion is very useful in RF design.
For a two-terminal network with one resistor and one reactor (capacitor or inductor), at a single frequency, there is no difference in the impedance of the two networks.
Of many on-line articles, see  https://aaronscher.com/Circuit_a_Day/Impedance_matching/series_parallel/series_parallel.html

[LooseJunkHater]

With R1 = 50 ohms between the BNC and everything else, the minimum impedance seen by the generator will be 50 ohms.
With large C1, whose reactance is much less than 50 ohms, the actual impedance will not be much higher.
A generator is characterized by its output resistance (50 ohms for most high-frequency generators):  in most generators, that is a physical 50 ohm resistor between the guts and the output connector (often with an attenuator in between).  It is rare for such a generator to be incapable of driving an external 50 ohm load, so the output current capability is enough to drive it (although the maximum voltage across a 50 ohm load is 1/2 the maximum voltage into a high impedance load).

So my generator can output 20v, does that mean it can actually *likely* output 20v @ 400ma (as 20v/50ohm = 0.4A)?

Do you have access to any of the Spice variations, such as LTSpice?
Rather than work through all the algebra, the ".AC" mode will do all the algebra for you on a linear circuit (no diodes, etc.).

The equivalent series-parallel conversion is very useful in RF design.
For a two-terminal network with one resistor and one reactor (capacitor or inductor), at a single frequency, there is no difference in the impedance of the two networks.
Of many on-line articles, see  https://aaronscher.com/Circuit_a_Day/Impedance_matching/series_parallel/series_parallel.html

I primarily use Falstad. I've tried LTSpice before but it's quite complex, so it'll take a while for me to learn. Is there a reason I should be using a simulation tool, and what for if I'm seemingly "just" testing for the SRF of an inductor?

[TimFox]

With R1 = 50 ohms between the BNC and everything else, the minimum impedance seen by the generator will be 50 ohms.
With large C1, whose reactance is much less than 50 ohms, the actual impedance will not be much higher.
A generator is characterized by its output resistance (50 ohms for most high-frequency generators):  in most generators, that is a physical 50 ohm resistor between the guts and the output connector (often with an attenuator in between).  It is rare for such a generator to be incapable of driving an external 50 ohm load, so the output current capability is enough to drive it (although the maximum voltage across a 50 ohm load is 1/2 the maximum voltage into a high impedance load).

So my generator can output 20v, does that mean it can actually *likely* output 20v @ 400ma (as 20v/50ohm = 0.4A)?

Do you have access to any of the Spice variations, such as LTSpice?
Rather than work through all the algebra, the ".AC" mode will do all the algebra for you on a linear circuit (no diodes, etc.).

The equivalent series-parallel conversion is very useful in RF design.
For a two-terminal network with one resistor and one reactor (capacitor or inductor), at a single frequency, there is no difference in the impedance of the two networks.
Of many on-line articles, see  https://aaronscher.com/Circuit_a_Day/Impedance_matching/series_parallel/series_parallel.html

I primarily use Falstad. I've tried LTSpice before but it's quite complex, so it'll take a while for me to learn. Is there a reason I should be using a simulation tool, and what for if I'm seemingly "just" testing for the SRF of an inductor?

If your generator can deliver 20 V into an high-impedance load, then it probably delivers 10 V into a 50 ohm load.
If both of those voltages are peak-to-peak, then 10 V pk-pk = 5 V pk, so the current into a 50 ohm load would be 100 mA peak.
I believe AWGs are typically specified for peak-to-peak output voltage into high-impedance loads:  check your manual.
The AWG built into my recently received Rigol DHO914S is rated for a (wimpy) 5 V pk-pk, so the maximum current into 50 ohms is 2.5/50 = 50 mA peak.
My boatanchor Wavetek 98 1 MHz synthesized generator is capable of driving a 50 ohm load to 5 V rms (14 V pk-pk), or 7/50 = 140 mA peak.

My recommendation for Spice was to help you understand the algebra:  you don't need it for analyzing SRF data.

Note that some of the other replies deal with compensating for capacitance added across the inductor under test.
For example, if you connect a normal oscilloscope (digital or analog) directly across the inductor, you probably add at least 15 pF of capacitance.
An expensive active probe might add only 1 pF.
Whether that is too large for an accurate measurement is a quantitative question.

[joeqsmith]

Datasheet for a Coilcraft 0805CS-821XJL:
https://www.coilcraft.com/getmedia/dd5f20e4-1ff7-43df-8317-b693eb2dce3e/0805cs.pdf

S-Parameters may be found here:
https://www.coilcraft.com/en-us/models/spice/?seriesName=0805CS

Touchstone file for the above part is attached (.txt). 

Shown using the LiteVNA to measure the parts SRF.   From the Coilcraft paper I attached,

Because SRF measurements are so sensitive to fixture
effects, we specify the SRF for our low inductance RF chip
inductors as a “minimum” value, approximately 15% to
20% below the actual average measurement of a repre-
sentative sample. Since fixture effects become negligible
for higher inductance values, SRF for our power inductors
is specified as “typical.”

Datasheet shows SRF of 310MHz for this part.   +15% is 356.5.   We measured the phase shift at 333MHz.  For a homemade fixture and low cost VNA, it's close enough. 

[joeqsmith]

Here I am using the LiteVNA to measure an 821, 391, 151 & 820 and comparing it with Coilcraft's data.     I've made no attempt to characterize the standards and am using an ideal model.  I have an old 4-receiver Agilent VNA that supports more complex calibrations which could do a much better job making these measurements but still, for $120 the LiteVNA does a reasonable job making these SRF measurements.

[joeqsmith]

Looking at smaller parts, things start to brake down.   Here is a 15 & 10nH inductor.  The LiteVNA was specified to work to 6GHz.  Beyond this it can use harmonics and I can get some sort of somewhat meaningful data out of this one up to about 8GHz. 

The fixture is nothing more that a section of ridged coax that I cut and polished sitting inside a block to keep the ends aligned.  It's now spring loaded to make it easier to insert parts but you can see it is not easy to align them.  In this case, the parts are just sitting in air.  To use the fixture with the Agilent, I use the unknown thru (and somewhat better standards). 

For large inductors, simple clip leads could possibly be used.  All depends what you are after.

[MrAl]

Hello there,

I think another way to measure the resonance is to simply connect a series resistor Rs to the inductor, then apply a sweeping frequency while measuring the voltage across the inductor alone.  You should see a peaked response if Rs is high enough in value.

To understand how the series resistance Rs works, there is something called the discriminant, and if that is either positive or negative it either makes the response sinusoidal or damped.  The idea is to choose a series resistor Rs such that you get a sinusoidal response, which isn't too hard to get I don't think because the discriminant becomes more favorable for a peaked response when Rs is somewhat large.  It depends on the values of L and respective C though, as well as the ESR of the inductor, so it would be hard to calculate.  In an experiment however, you could just vary Rs making it smaller then larger, see what you get.  When you get a peaked response indicating some kind of resonance, that means you have Rs set to a good value.  There is a tradeoff however.  That is, if Rs is too large although you still get a peaked response, the amplitude may be harder to measure as it could be too low at that time.  In that case try to decrease Rs to get a larger amplitude while keeping it large enough to maintain that peaked response we look for.

Just to note, the resonance you see that is indicated by the peak may not be physical resonance, but it could still be useful to know.  To figure out if you are seeing physical resonance you'd have to measure the phase as well as the amplitude.  You may or may not be interested in that.

If someone wants to try this that would be cool.  You need a variable sine wave generator, scope, and I guess you can use a potentiometer for Rs but it depends on the frequency range you may have to use a fixed resistor and perhaps try a few different fixed values.

[TimFox]

Again, if you drive the inductor under test from a suitable resistor, while the inductor is connected to a voltmeter or oscilloscope high-impedance input, you need to deal with the input capacitance of the meter/scope.
Some suggestions above involve measuring with two load capacitors, using math to calculate the inductance and self-capacitance of the DUT to get its inherent SRF.

[RoGeorge]

This is a brief review of most used Q measuring methods, also shows why a low Z generator is needed:
https://www.arrl.org/files/file/QEX_Next_Issue/Jan-Feb_2012/QEX_1_12_Audet.pdf

Another way to identify the self resonance frequency is to use a grid-dip-meter https://en.wikipedia.org/wiki/Grid_dip_oscillator, or to improvise a dip-meter from an existing generator, or from an AWG, like seen in any of the attached examples.

The coil in the schematics is the coil that produces the field, not the one to be measured.  The inductor to be measured has to be put in the nearby of the coil from the schematic, then the frequency must by swiped with the generator.  Instead of the analog uA-meter, can be used a normal DMM.

The schematic captures are from the book "How to use Grid-Dip-Oscillators" by Rufus P. Turner, 1960.
https://www.worldradiohistory.com/BOOKSHELF-ARH/Technology/Servicing/How-to-use-Grid-Dip-Oscillators-Rufus-P-Turner-1960.pdf

[joeqsmith]

Here is a 0805CS-050XJL 5.6nH 5% part.  The datasheet shows a typical SRF of 5.9GHz but when you look at their S-parameter data, they measured 9.5GHz.  Much higher than the 15-20% number they provided.  You can  imagine, the smaller the part, it gets more difficult to measure.   Coilcraft's paper states they used an Agilent 8720D VNA to measure SRF with a in-house fixture.  For this test, I am using a homemade frequency extender.   Consider I am using the cheap standards that came with the LiteVNA and the ideal model, I'm surprised it shows anything close. 

[LooseJunkHater]

I'm trying to measure the SRF of my capacitor but it DOES NOT look like other SRF graphs that others have posted.

Image 0. shows my basic schematic.
Image 1. shows the ceramic capacitor (100nf) that I'm measuring (no datasheets available; just a generic ceramic capacitor).
Image 2. shows my AWG, log sweeping between 1KHz --> 30MHz, sinewave, 10Vp/p, 1second sweep time
Image 3. shows the FFT (with MAX-HOLD, 50ohm load) as well as what the spectrum looks like (neither of these look like the other SRF graphs that I've seen)
Image 4. shows what my overall measuring setup looks like (as I'm not sure if the coils of wire and it all being physically on the ground would mess up the measurement).

Can someone explain what I'm doing right & wrong with measuring the SRF of the capacitor (so that I can then determine if this is an appropriate capacitor to then measure the inductor)?

[joeqsmith]

Its a cap, which is basically open to DC.  As frequency increases, so does the loading.   You are basically shorting out the signal generator.  Pretty much what is expected. 

[LooseJunkHater]

Its a cap, which is basically open to DC.  As frequency increases, so does the loading.   You are basically shorting out the signal generator.  Pretty much what is expected.

So do I just add a 1k resistor in series of the AWG or...?

[LooseJunkHater]

Its a cap, which is basically open to DC.  As frequency increases, so does the loading.   You are basically shorting out the signal generator.  Pretty much what is expected.

So do I just add a 1k resistor in series of the AWG or...?

I tried adding a 47ohm resistor as well as decreasing the AWG output voltage to 1V/p and it shows nearly an identical waveform.

[joeqsmith]

Its a cap, which is basically open to DC.  As frequency increases, so does the loading.   You are basically shorting out the signal generator.  Pretty much what is expected.

So do I just add a 1k resistor in series of the AWG or...?

Then you have just made an RC filter.  Roll off or how fast the signal attenuates will increase with frequency, as after all the RC filter is a low pass.   

[TimFox]

Remember that the (lowest frequency) self-resonant mode of a capacitor is a series resonance (parasitic series inductance), while the lowest-frequency SRF of an inductor is a parallel resonance (parasitic parallel capacitance).
For that purpose, using a 50 ohm spectrum analyzer, I merely ran the generator output through 50 ohm resistor in series with the capacitor (to ground) followed by a 50 ohm resistor to the analyzer input.
SRF for the capacitor is the frequency where the minimum signal occurs on the analyzer.

For leaded capacitors, the parasitic inductance is dominated by the total length of wires plus body.

[LooseJunkHater]

Its a cap, which is basically open to DC.  As frequency increases, so does the loading.   You are basically shorting out the signal generator.  Pretty much what is expected.

So do I just add a 1k resistor in series of the AWG or...?

Then you have just made an RC filter.  Roll off or how fast the signal attenuates will increase with frequency, as after all the RC filter is a low pass.

OH RIGHT. Woops that makes total sense. Okay then, how am I suppose to measure the SRF of the capacitor than? Maybe a diagram would help me?