best way to measure Q

[ricko_uk]

Hi,
what is the best (most accurate?) way to measure and inductor's Q at a specific frequency using scope, signal generator and standard lab equipment (but not RF type equipment such as antenna or network analysers)?
Most manufacturers tend to specify it at 1MHz (for most coils) and often also provide a Q vs Frequency chart. But when I use the formula Q = 2 * pi * f * L / R the result I get is nowhere near what is displayed in the charts for that frequency.
Thank you

[Benta]

There's no such thing as an "inductor's Q", unless you're talking about it's self-resonance frequency.

Loss factors in inductors are winding resistance, and if cored, core losses. At higher frequencies, skin effect is also to be considered.

[ricko_uk]

Thank you Benta,
I'm not sure I understand your comment. Could you please elaborate.
Almost all of Coilcraft's inductors include a chart of their Q vs Frequency. This link is just an example: https://www.coilcraft.com/1812ls.cfm
The Q is always specified at 1MHz for all values and that is nowhere near the inductor's SRF which clearly also varies for every inductor's value.
Could you please explain what you mean.
Many thanks

[TimFox]

Yes, inductors have a Q factor.  At a fixed frequency, the Q is the ratio
Q = (reactance of series inductance) / (series resistance).
Things get messy when you are close to the self-resonant frequency of a physical coil, since the measured series inductance will increase due to the parallel self-capacitance of the winding.
The tabulated values are ordinarily measured at a frequency well below self resonance.
Even after correcting for self capacitance, neither the Q nor the equivalent series resistance is independent of frequency.

[chris_leyson]

Q = wL/R = 2*pi*f*L/R has nothing to do with the SRF. You can measure Q at any frequency you like depending on the inductor and/or the circuit application. Q of a parallel resonant circuit is defined as q = f_r/BW where f_r is the resonance frequency and BW is the 3dB bandwidth. You could make a parallel resonant circuit with a good quality capacitor and couple into and out of the tuned circuit with very small capacitors and tune a sig gen either side of resonance to find the 3dB bandwidth. Another method called the ring down method applies a step or pulse to start the circuit oscillating and then you measure the time for the oscillation to decay. See: https://www.giangrandi.ch/electronics/ringdownq/ringdownq.shtml

[TimFox]

I was referring to what you measure on  an LCR meter at frequencies that are not far below the self resonance of the coil.  On my DER5000, I can obtain series inductance and resistance, as well as series inductance and Q, at five discrete frequencies.  These values are computed from the real and imaginary components of the measured impedance.

[ejeffrey]

There's no such thing as an "inductor's Q", unless you're talking about it's self-resonance frequency.

Loss factors in inductors are winding resistance, and if cored, core losses. At higher frequencies, skin effect is also to be considered.

Sure they do.  Inductor Q vs f basically just means "If you pair with a lossless capacitor whose value is chosen such the resonance frequency is f, what is the Q".  For a simple circuit you can just take the formula for the series LCR circuit and then substitute w = 1/sqrt(LC) to eliminate C.  That is how you get the omega*L/R formula.

[ricko_uk]

Thank you all!

[CatalinaWOW]

Yet another lesson in the importance of definitions.  Three different definitions for Q in this thread.  All correct when used appropriately.  All somewhat different.  Communication occurs only when the publisher of Q and the user of the information are using the same definition.

[bob91343]

While I have two Boonton Q meters that can measure inductance and Q over a wide frequency range, my newly acquired low cost nanoVNA does the job very well.

Measuring Q is simple enough with inexpensive equipment.  However, given the nonlinearity of many inductors, the definition of Q gets a bit difficult.  Of course it's the ratio of stored energy to dissipated energy, but the parameters make it a confused mess at times.

Inductor saturation, distributed capacitance, skin effect all are secondary parameters that become important for many measurements.  If there is a magnetic core, the amplitude of the signal used for measurement becomes a factor that confuses the issue.  As the frequency changes, so do the magnetic condition of the core, and the amount of skin effect.

My usual Q measurements are made with air core coils at the frequency where I intend to use them.  So don't expect to paste a label on an inductor that says Q = (whatever you like) unless you also specify the test conditions.

[TimFox]

Yet another lesson in the importance of definitions.  Three different definitions for Q in this thread.  All correct when used appropriately.  All somewhat different.  Communication occurs only when the publisher of Q and the user of the information are using the same definition.

The different equations for Q are intimately related.
When you connect a coil and a capacitor together, it makes a parallel-resonant circuit with a free-resonant frequency f0.  If the coil has a Q value Q_L and the capacitor has Q = Q_C at that frequency , then the Q of the resonant circuit is given by
1 / Q_R = (1 / Q_L) + (1 / Q_C)
neglecting the self-capacitance of the coil and the self-inductance of the capacitor.  The proof is left as an exercise for the reader.  Note that the circuit Q is lower than that of either component.

[CatalinaWOW]

I agree to the intimate relation of the various definitions of Q.  But in the simplest form, defined in terms of the losses in a resonant circuit with ideal capacitors and inductors it is purely a measure of the resistance in the circuit.  There is no frequency dependence in the C or L.  When defined as a property of an inductor as a function of frequency there is an implication of non-ideal performance.  Parasitic capacitance and internal resistance.  Different models for the real inductor will give somewhat different answers.  So to interpret the answers you may need to know the model being used.  Or maybe for the application you are chasing all that is needed is an ohm meter.

[TimFox]

A simple ideal inductor with a constant inductance and constant resistance (independent of frequency) will have a Q proportional to frequency. How is this non-ideal behavior?

[CatalinaWOW]

If that was what they were measuring, why not just report the resistance?  Why bury it in a graph?

[bob91343]

There are always parasitic effects.  A wire inductor will have skin effect as frequency rises, slowing the expected increase of Q with frequency.  An iron core inductor is a whole other matter.

A Q measurement is only good at the frequency at which it is tested, as well as the amplitude (if nonlinear).

A better test is to plot a curve of Q vs frequency to ascertain suitability of the component for use.  You do have an expected use, don't you?  That should help you decide how to measure it.  If you are just measuring for fun, don't mark the part because the value isn't constant.

Temperature is another factor, since the resistance of a coil varies with temperature, and thus Q.

[TimFox]

The original poster referred to a table of manufactured coils from a given vendor that tabulated Q at discrete frequencies because that’s how the maker verified the quality of the coils rolling off the line.  He may have graphs of typical Q vs frequency.

[Stray Electron]

Hi,
what is the best (most accurate?) way to measure and inductor's Q at a specific frequency using scope, signal generator and standard lab equipment (but not RF type equipment such as antenna or network analysers)?

  Depending on the frequency, my favorite is one of the Gen Rad (General Radio) 165x Digibridges!  But the fact is that almost no two companies measure Q at the same frequencies!  Depending on the model of Digibridge they can measure Q at several, more or less, standard frequencies and you can also use an external signal source for other frequencies.  There are plenty of old LCR bridges made by companies like General Radio, Leader, etc that are manually tuned and can be used to measure an external Q by comparing it to an internal (or sometimes external) known resistance using a bridge. I would suggest going on E-bay and seeing what kinds of LCR meters are available to you and then looking up their specs and/or their operating manuals and reading those.  GR for one published a LOT of material about how to do tests like this and the all of theory behind it.  In the end you might not want to use one of those old LCR bridges due to the weight, size and the fact that they are slow to take measurements with since they are manually adjusted but you will at least understand what's involved in the process. 

   A GOOD place to start would be to look up the manual for a GenRad 1657 or 1659 Digibridge and read it.

[uer166]

Okay so was about to make a separate thread but will hijack this one instead since it is relevant. I am trying to measure inductor's AC resistance (losses due to skin effect and copper losses) at specific frequencies. I tried:

• Injecting an AC voltage and measuring current. With some complex plane math can determine real part of the impedance (what I'm after). Unfortunately the results are wildly inaccurate. Probably since the phase shift due to AC resistance is so tiny.
• VNA, same result, unable to measure phase accurately enough
• Ring-down method previously mentioned

Trying to make ring-down method work but have unexpected results. The test jig picture attached. The tank circuit is excited with a one-turn winding attached to a function gen outputting a square wave.
The ringdown voltage waveform across cap is attached, white is the Litz, yellow 14AWG. The capacitor is made from 20 47pF C0G 0.5% caps (0.94nF total) in an attempt to reduce its' AC resistance to much lower values than the inductor is. Foil tape would hopefully help with skin effect. For the experiment I made two ~130uH inductors, one with Litz, other with regular 14AWG. What I expected: litz wire version should have much higher Q since at ~450KHz skin effect losses are substantial. Reality: both have a Q of around ~16. And not only is this much lower than I expected (I thought it'd be something like 100 with Litz), the difference between regular and Litz wire is marginal.

The core is a High Flux material: https://www.mag-inc.com/Media/Magnetics/Datasheets/0058726A2.pdf. Both have 27 windings.

Question that I have is same as OP, what is the best way to measure Q, and if this is the best way, why am I getting unexpected (much much worse) values?

[Stray Electron]

Hi,
what is the best (most accurate?) way to measure and inductor's Q at a specific frequency using scope, signal generator and standard lab equipment (but not RF type equipment such as antenna or network analysers)?
Most manufacturers tend to specify it at 1MHz (for most coils) and often also provide a Q vs Frequency chart. But when I use the formula Q = 2 * pi * f * L / R the result I get is nowhere near what is displayed in the charts for that frequency.
Thank you

   You do realize that in that formula f is in radians per second and not cycles per second, don't you?   1 cycle = 360 degrees = 2 pi radians. So multiply CPS times 2 pi to get "f" in radians per second.

[Weston]

Okay so was about to make a separate thread but will hijack this one instead since it is relevant. I am trying to measure inductor's AC resistance (losses due to skin effect and copper losses) at specific frequencies. I tried:

• Injecting an AC voltage and measuring current. With some complex plane math can determine real part of the impedance (what I'm after). Unfortunately the results are wildly inaccurate. Probably since the phase shift due to AC resistance is so tiny.
• VNA, same result, unable to measure phase accurately enough
• Ring-down method previously mentioned

Trying to make ring-down method work but have unexpected results. The test jig picture attached. The tank circuit is excited with a one-turn winding attached to a function gen outputting a square wave.
The ringdown voltage waveform across cap is attached, white is the Litz, yellow 14AWG. The capacitor is made from 20 47pF C0G 0.5% caps (0.94nF total) in an attempt to reduce its' AC resistance to much lower values than the inductor is. Foil tape would hopefully help with skin effect. For the experiment I made two ~130uH inductors, one with Litz, other with regular 14AWG. What I expected: litz wire version should have much higher Q since at ~450KHz skin effect losses are substantial. Reality: both have a Q of around ~16. And not only is this much lower than I expected (I thought it'd be something like 100 with Litz), the difference between regular and Litz wire is marginal.

The core is a High Flux material: https://www.mag-inc.com/Media/Magnetics/Datasheets/0058726A2.pdf. Both have 27 windings.

Question that I have is same as OP, what is the best way to measure Q, and if this is the best way, why am I getting unexpected (much much worse) values?

The output impedance of the function generator is in parallel with the LC tank and is going to damp the resonance during ringdown and reduce the measured Q.

For linear (air core inductors) you can create a series / parallel resonant circuit and measure the 3db points and calculate Q from that. Given the accuracy range of most VNA's, series resonance is probably more accurate.

For cored inductors, which have loss that changes non-linearly with drive level, the previous method will only give you the small signal Q level, under higher power it is going to be less. For a more accurate test you can drive the resonant circuit with a function generator / power amplifier and measure the voltage / current gain at resonance. By changing the drive level you can measure how Q changes with flux density. This paper details a possible test setup: https://www.rle.mit.edu/per/wp-content/uploads/2016/01/Hanson-Measurements.pdf (Figure 13)

[bob91343]

As I said above, the Q meter does a nice job over a wide range of frequency and inductance.  It works by measuring the resonant rise of a simple circuit.

The VNA has a different method, equally valid.  Using a bridge is misleading because of the many variables involved, especially operator skill.  My GR bridges indicate Q but only for rather low frequencies.  The Q meter takes it from there up to a few hundred MHz.  The VNA indicates R + jX or, in the case of the nanoVNA, R and L.  This, over a very wide frequency range from 50 kHz.

The important thing is to compare apples with apples.  Standardize on a method and stick with it.  Comparison with other methods can be interesting.  The lower the Q, the less important is the frequency.  If the Q is low enough, it becomes a resistor.  A perfect resistor has a Q of zero; a perfect inductor has infinite Q.

You can use a generator and oscilloscope but the 'scope input impedance becomes important for high Q.

There is, as noted above, a wealth of material available on the subject.  One could start with Terman's Radio Engineering.  The old highly competent and respected companies that made inductors are pretty much gone.  They were spearheaded/masterminded by some of the most important people, and their work will never become obsolete.

[TimFox]

Hi,
what is the best (most accurate?) way to measure and inductor's Q at a specific frequency using scope, signal generator and standard lab equipment (but not RF type equipment such as antenna or network analysers)?
Most manufacturers tend to specify it at 1MHz (for most coils) and often also provide a Q vs Frequency chart. But when I use the formula Q = 2 * pi * f * L / R the result I get is nowhere near what is displayed in the charts for that frequency.
Thank you
[/quote
   You do realize that in that formula f is in radians per second and not cycles per second, don't you?   1 cycle = 360 degrees = 2 pi radians. So multiply CPS times 2 pi to get "f" in radians per second.

His formula shows 2 pi correctly.

[Stray Electron]

His formula shows 2 pi correctly.

  Agggg! So he did. I don't know why I didn't see that at the time. I guess that that's what I get for trying to read stuff when I'm too tired.


  OP, take a look at this page http://www.prc68.com/I/GR1657Digibridge.shtml#Description He has a ton of information about LCR bridges and many of the related patents.

   Tim is right, it gets tricky to read Q or L, C, R of D at higher frequencies or with great precision.  The problem is that every R has some L and C, every C has some R and L and every L has some amount of R and C! Not only in the Device Under Test but in every component in the test equipment as well. And to add to the problems the output level of every AC signal source varies somewhat with frequency and the sensitivity of every measurement system also varies with frequency.

[ricko_uk]

I have a LCR45 meter (https://www.peakelec.co.uk/downloads/lcr45-datasheet-en.pdf)
it reads the complex impedance/admittance both real and imaginary part and phase & magnitude of the impedance measurement. And it does so at the frequency of interest 200KHz. Would that help in any way to measure/compute the Q factor of the inductor?
Thank you

[Kleinstein]

For relatively high Q values the ring down method can work well. It does not work well anymore if Q is much below 5. The measurement of the resonance curve with a VNA or similar and thus quasi settled measurements works well for a low Q and gets more an more demanding with a high Q , especially at lower frequency. The non resonant measurements with a VNA or bridge is kind of limited by the calibration / reference for the phase shift. Especially a high Q (low loss) is not so easy to measure off resonance.  So it depends on the Q range (and frequency) which method works best.

A parallel resonance can get pretty high impedance, so the scope probe can cause damping. Another point is the excitation - ideally relatively weak coupling is used for the resonant methods.