Impedance, LCR, ESR meters

[The Electrician]

About impedance.

I'm going into a fair amount of detail that the EE's won't need, but it's aimed at the beginners.


In the early days, shortly after the discovery of electricity, experimenters used mostly static electricity.

Before long, chemical batteries were invented, and experimenters had a good source of steady electric current.  They applied an electrical stimulus to matter in its many forms, and discovered that some substances conducted electricity better than others.  Apparently, the flow of electric current through matter was opposed in a way that was analogous to mechanical friction.
  It was noticed that when an electric current was passed through various substances, heat was generated; electric energy was converted into heat energy.

A way of measuring the opposition to electricity was to apply a known voltage, and measure the resulting current.  If the substance greatly opposed the flow of electric current, that flow would be small.  If the substance allowed a large current, the opposition was small.  The magnitude of the opposition was given a value by dividing the applied voltage by the amount of current that resulted.

A word was sought to give a name to this property of matter, a word to convey the notion of opposition to electric current.  A number of words could be used for this: resistance, reluctance, reactance, impedance, etc.

In those early days when the source of electricity was just chemical batteries, the word chosen was "resistance", and the letter symbol "R" was used.  This was the opposition to the flow of a direct current of electricity.

Later, when it was discovered how to produce alternating current, it was found that capacitors and inductors opposed the flow of an alternating current, but by a different mechanism.  The name chosen for the opposition to alternating electric current exhibited by capacitors and inductors was "reactance", and the letter "X" was used to stand for it.

It's important to note that whereas the opposition of a resistor to electric current (resistance) gives rise to heat, the opposition of pure capacitors and inductors (reactance) does not.

The basis for the opposition to electric current of capacitors and inductors is due to the defining relationship between the AC voltage applied to them, and the current that results:

For a capacitor, i = C*de/dt.  The AC current through a capacitor is equal to the capacitance times the rate of change of the voltage applied to it.

For an inductor, e = L*di/dt.  The AC voltage appearing across an inductor is equal to the inductance times the rate of change of the current through it.

The expressions de/dt and di/dt may not be familiar to those who haven't studied calculus; they are derivatives and refer to the time rate of change of voltage or current.

Just as in the DC case, where we measured resistance by applying a voltage and measuring the current, then taking the ratio (voltage/current) and calling that "resistance", in the AC case we can do the same thing.  Apply an AC voltage of a particular frequency to a capacitor or inductor, measure the current and calculate the ratio (voltage/current) = X, "reactance".

[The Electrician]

Considering the 3 fundamental components of circuits, resistors, capacitor and inductors, we have 3 equations relating the voltage across to the current through each.  We use upper case for DC voltages, and lower case for AC voltages:

For a resistor, E = I*R

For a capacitor, i = C*de/dt

For an indcutor, e = L*di/dt

Suppose we have a circuit composed of a number of these 3 components, connected in some fashion, and we want to know what the voltages and currents would be if we suddenly applied a DC step of voltage to some part of the circuit.  Because the relationships for capacitors and inductors involve derivatives, it is necessary to solve differential equations to get the resulting voltages and currents.

It is known that the differential equations describing circuits composed of only R, L and C are ordinary differential equations with constant coefficients.  It is also known, that the solution to such differential equations is always a sum of exponentials, where the arguments to the exponentials may be complex, involving the imaginary number SQRT(-1).  Euler's formula:

http://en.wikipedia.org/wiki/Euler's_formula

tells us the the result of an exponential with a complex argument involves sines and cosines.

Thus, the solution to a general circuit with a suddenly applied DC voltage will be decaying exponentials, sine waves, cosine waves, and decaying sines and cosines, and combinations of these.

I can tell you that solving a system of differential equations for a complicated circuit is a PITA.  Fortunately, C. P. Steinmetz:

http://en.wikipedia.org/wiki/Charles_Proteus_Steinmetz

discovered that ordinary differential equations with constant coefficients can be solved with plain old algebra if you allow the arithmetic to include complex numbers, and those numbers stand for the value of sine waves of voltage and current.  The reason they represent sine waves is because that is what the solutions of the relevant differential equations are comprised of.

It turns out that if the reactance of capacitors and inductors are taken to be imaginary quantities, the algebra of circuits is fairly simple.

[The Electrician]

What happens if we connect a resistor and capacitor in series and apply an AC voltage of a particular frequency to the series combination?  We could measure the current and calculate the ratio (voltage/current).  There would undoubtedly be opposition to the flow of electric current, just as we found with a resistor alone, or a capacitor alone.

When this is done, there is indeed opposition to the current, and this opposition is called "impedance", and the letter "Z" is used to represent it.

A new phenomenon is observed in this case.  When an AC voltage of a particular frequency with a sine shape is applied to a resistor, and the voltage and current are displayed on an oscilloscope, it is seen that the voltage wave and the current wave are in phase.  But when a capacitor is in series with a resistor, the voltage wave applied to the combination is not in phase with the current wave.

The use of complex numbers deals with this.  The impedance of the series combination of a resistor of value R, and a capcitor with reactance X is given by the formula:

Z = R - jX  The minus sign is there because the reactance came from a capacitor.  If the reactance comes from an inductor, the minus sign becomes a plus sign.

Notice that Z is a complex number, with a real part (R) and an imaginary part (X).  This way of representing the impedance is called rectangular notation.  A complex number can also be represented with a phase angle like this: |Z|<theta, where |Z| is the magnitude of Z, given by SQRT(R^2 + X^2).  This is called polar notation.

If the voltage applied to the series combination is e, then the current i = e/Z (this is sometimes called ohm's law for AC).  Since Z is a complex number, i is also a complex number, so the current has a phase angle.

If we want the magnitude of i, which is what we would measure with an ammeter, we would divide e by the magnitude of z thus: |i| = e/|Z|, that is, the magnitude of i is given by the voltage divided by the magnitude of Z.

Here's an app note that goes into much more detail: http://www.ietlabs.com/pdf/application_notes/030122%20IET%20LCR%20PRIMER%201st%20Edition.pdf

NOW HERE'S THE IMPORTANT PART OF ALL THIS!

If we have a very complicated circuit of R, C and L, we can pick two nodes in the circuit and measure the impedance at a particular frequency there.  The result will be Z = R + jX.  This impedance will have a real part R, and an imaginary part X.  No matter how complicated the circuit, this will be the form of the impedance.  The real part R will most likely not correspond to any single resistor in the complicated circuit.  It's a result of the many resistors in parallel, series, bridge, delta or wye, etc., in the complicated circuit.  But they all boil down to a single R value, the real part of the measured impedance.

Now, an impedance Z = R + jX also represents the impedance of a series combination of a single resistor and single capacitor (or inductor); R is the resistance of the single resistor and X is the reactance of the single capacitor (or inductor).

Since there will always be a single resistor and capacitor (or inductor) series circuit that has the same impedance as we measured at two nodes of our very complicated circuit, we can say that the EQUIVALENT impedance of our complicated circuit's two nodes is given by the simple series circuit of a resistor and capacitor (or inductor as the case may be).

And the resistance (real part) of our EQUIVALENT series circuit of a resistor and capacitor (or inductor), is the EQUIVALENT SERIES RESISTANCE (ESR) of the impedance measured at the two nodes of our complicated circuit.  We could also refer to the reactance of the capacitor (or inductor) of our simple series circuit as the EQUIVALENT SERIES REACTANCE (also ESR; too bad).

[The Electrician]

What would happen if we used a square wave, or a triangle wave, or some other wave shape that was not a sine wave, to measure the resistance of a resistor to an applied wave of a particular frequency?

Consider a square wave.  It is well known that an ideal square wave is composed of an infinite number of harmonics; if the square wave isn't ideal (rise time is not infinitely fast) the harmonics die off faster.

But, even for a real square wave with very fast rise time, there will be quite a few harmonics.  They vary as 1/n; in other words, if the fundamental has magnitude V1, the third harmonic will have magnitude V3 = V1/3, the fifth harmonic will have magnitude V5 = V1/5, etc.

So if you apply a square wave with fundamental magnitude 1 volt to a resistor, and an important consideration here is that THE VALUE OF THE RESISTOR DOESN'T CHANGE WITH FREQUENCY, you are also applying a 3rd harmonic voltage with magnitude 1/3 volt, and a 5th harmonic with magnitude 1/5 volt.  Since the value of the resistor doesn't change with frequency, the ratio of all the harmonic voltages to the harmonic currents is the same at all frequencies.  That ratio is the resistance, and the value we measure doesn't depend on the measurement frequency.

Each harmonic will result in a current of Vn/R.  The total current will be the sum of the harmonic currents which are all in the same ratio to their corresponding harmonic voltage, namely 1/R.  Thus, the ratio of the sum of all the harmonic voltages to the sum of all the harmonic currents is R, because R doesn't change with frequency.

BUT, it's different for a capacitor or inductor.  Remember, at a particular frequency, the reactance of a capacitor has a certain value, but at a frequency 3 times higher, the reactance is 3 times lower.  This means that the higher frequency harmonics will see a lower reactance and the resulting current will be larger than it would have been if the reactance had remained constant with frequency.

This means that the ratio of the sum of the harmonic voltages to the sum of the harmonic currents will not be the same as we would get if we simply measured with a single sine wave at the fundamental frequency; in other words, we won't get the same value for the reactance measuring with a square wave that we would get if we measured with a single frequency sine wave.

The upshot of this is that we can use any waveshape to measure the value of a resistor that doesn't change value with frequency, but we can't do this to measure the reactance of a capacitor (or inductor), because the reactance of a capacitor definitely changes with frequency!

[The Electrician]

What does all this have to do with measuring ESR?  Why can't we just apply a square wave of some particular frequency (probably 100 kHz) to a capacitor and measure the current, then take the ratio of applied voltage to resultant current and call that the ESR?  ESR is just a resistance, right?

As I showed above, if the resistance doesn't vary with frequency, then we can use any waveshape to measure the resistance.  Why wouldn't the ESR of a capacitor be constant with frequency?

Here's why:

Any impedance, at a particular frequency can be shown to be equivalent to a simple series circuit of a resistor (which is constant with frequency) and a capacitor (or inductor).  But, it's also true that a simple parallel circuit consisting of a resistor in parallel with a capacitor (or inductor) can give the same impedance.  Let's see how that works.

Suppose we have a 1 ohm resistor in series with a capacitive reactance of -j100 ohms.  The impedance is Z = 1 - j100.  What parallel combination of resistor and capacitor is equivalent to that (gives the same impedance)?

Using a calculator that can do complex arithmetic, the answer is a 10001 ohm resistor in parallel with a capacitor whose reactance is -j100.01 ohms.  We can test this by using the standard product over the sum formula for parallel resistances, which also works with reactances if you use complex arithmetic.

(10001)*(-j100.01) = 0 - j1000200.01
(10001)+(-j100.01) = 10001 - j100.01

Now divide those intermediate results:

(0 - j1000200.01)/(10001 - j100.01) = 1 - j100

which is the same impedance as a 1 ohm resistor in series with a -j100 ohm reactance.

The resistor we used in the parallel combination isn't the same resistor used in the series combination.

If we connect up a series combination of a resistor and capacitor and do a sweep of the combination on the impedance analyzer, we see that the resistive part is in fact constant if the sweep is in the SERIES EQUIVALENT mode.  Here's the sweep of a 10 ohm resistor in series with a 2 uF capacitor.  The green curve is the impedance magnitude; the yellow curve is Rs, the equivalent series resistance (ESR):



But here's the surprising fact.  If we sweep that same series combination in PARALLEL EQUIVALENT mode, look what happens.  The yellow curve, which is the parallel equivalent resistance, is NOT constant with frequency!!  Yet, the circuit uses a 10 ohm resistor which IS constant with frequency up to at least 1 MHz; the previous sweep shows that it is:



Why isn't the equivalent parallel resistance constant with frequency?  It's because that's the way complex arithmetic works.  This Application note explains it well; look at the discussion of Figure 1 and Figure 2:

http://www.low-esr.com/QT_LowESR.pdf

[The Electrician]

The same effect occurs in the other direction.  Here's the same capacitor in parallel with a 100 ohm resistor.  When swept in PARALLEL EQUIVALENT mode, the resistive part (yellow curve) appears to be constant with frequeny (there's a slight roll off at the highest frequency due to capacitor parasitics):



But now let's do a sweep in SERIES EQUIVALENT mode.  Now the resistive part (Rs; the ESR) is not constant with frequency.  In a real capacitor, the dielectric loss appears mainly as a parallel resistance, and that transforms into a series resistance which is NOT constant with frequency:



Since a real capacitor has losses from many causes, some behaving as a parallel resistance, some behaving as a series resistance, one would not expect the ESR, which is just the EQUIVALENT of all the losses in the capacitor converted into a SERIES resistance, to be constant with frquency.

This is why if an accurate measurement of the ESR is wanted, the waveshape of the applied voltage must be a sine wave.

High end professional instruments all use a sine wave (or equivalently with an FFT) to make the measurement, and they directly measure the real and imaginary parts, calculating other parameters like DF from those parts.

[The Electrician]

So how do the low cost ESR meters get such a good result?  Let's look at a series mode sweep of a typical aluminum electrolytic.  You can see that the cap is so lossy that the ESR (yellow) dominates the impedance (green) over a fairly wide range of frequencies, and that the ESR is nearly constant with frquency in the vicinity of 100 kHZ.  A lot of the modern aluminum electrolytics have this nearly constant ESR, but not all; I'll give more examples later:



Remember from above, if a resistance is constant with frequency, we can use any waveshape and get the same result as with a sine wave, so in a case like this where the ESR is nearly constant with frequency, a square wave stimulus is ok.

It has been a criticism of low cost and DIY ESR meters that they don't really measure ESR, but impedance.  When the sweep looks like this one, the ESR and impedance are coincident (and oftimes they're nearly coincident so the error is small) at 100 kHz and measuring impedance is the same as measuring ESR.

There are other situations where the criticism is valid, and I'll show some, but for a lot of electrolytics like the one swept here, it doesn't matter.

If resistance doesn't vary too much with frequency, even though using a square wave for the stimulus gives an error, the error won't be too much.  And, if the capacitor has failed, the ESR becomes very large, and totally dominates the impedance.  In this case, we're just looking for an indication that the cap has failed.  Suppose the true ESR of a failed cap is 200 ohms, and a simple ESR meter says it's 100 ohms; this error won't matter if what we're doing is repair work.

[The Electrician]

Jay_Diddy_B (hereafter known as JDB) sent me one of his ESR adapters, fully stuffed and tested.  I'll be using it for some further ESR tests and explanation.  Thanks, JDB!

Earlier in this thread, I explained how using a square wave stimulus gives an incorrect result if the ESR is not constant with frequency.  I have encountered some unusual caps, and I'll use some of them as examples.

Here's a sweep of a cap whose ESR decreases substantially past 100 kHz.  I've noticed that small, high voltage electrolytics often have this characteristic.  This can be used to show the effect I described whereby the harmonics of a square wave stimulus are effectively "sampling" the ESR at the harmonic frequencies.  If the ESR is lower at the higher frequencies, I would expect that to cause the measured ESR (as measured with square wave stimulus) to be lower than its true value.  By "true value", I mean the value read by a professional instrument using sine wave stimulation.  This cap is a 4 uF, 450 volt electrolytic:



The true value of the ESR is 9.1 ohms at 100 kHz.  JDB's adapter reads it as 8.9 ohms, and the Atlas ESR70 also reads it as 8.9 ohms.  Both readings are too low.

Both the JDB meter and the ESR70 consistently read high on everything else.  This is the only case where I get a too low measurement, and it's also the only capacitor where the ESR is decreasing with frequency above 100 kHz AND the ESR and impedance magnitude are coincident thereby avoiding the problem of the meter "reading" the impedance magnitude rather than the ESR.

[The Electrician]

Here's another cap where the ESR decreases substantially with frequency above 100 kHz, BUT the ESR is NOT coincident with the impedance magnitude AT 100 kHz.  This is a film cap so its losses are less than a typical electrolytic; this is why the ESR and impedance magnitude are not coincident over a wide frequency range:



The true ESR is .281 ohms at 100 kHz.  The JDB adapter reads .375 ohms, and the ESR70 reads .34 ohms.  Both meters are being fooled somewhat by the impedance magnitude of .9 ohms, which is quite a bit higher than the ESR.

Because the ESR decreases so much with frequency above 100 kHz, I would have expected the readings of meters with square wave stimulus to be lower than the true ESR as in the previous post, but apparently the phase sensitive rectifiers aren't rejecting the reactive part of the impedance (which is quite a bit larger than the ESR, the real part of the impedance) as well as would be desirable.

[KedasProbe]

Better to use 'v' (or u) instead of 'e' for voltage now.

[The Electrician]

Here's an example where the criticism that impedance, rather than ESR, is being measured, is valid.

This is a 4700 uF axial lead electrolytic.  The axial lead construction results in higher ESL (equivalent series inductance) than radial lead construction does, so the impedance at higher frequencies is high:



The true ESR at 100 kHz is .036 ohms and the impedance magnitude is .192 ohms.  The JDB adapter reads .100 ohms, the Atlas ESR70 reads .107 ohms, and the MESR-100 reads .216 ohms.

The MESR-100:

http://www.amazon.com/MESR100-AutoRanging-Circuit-Capacitor-Tester/dp/B00G7OPBP2

is a very low cost, but poor performing meter.  Version 2 of this meter improved the waveform applied to the DUT, but it still isn't a sine wave.  Furthermore, I believe it doesn't attempt to reject the reactive part of the measured impedance by using a phase sensitive rectifier as the JDB adapter does.  The measurement the MESR-100 got of .216 ohms is so close to the true impedance of .196 ohms that I consider it evidence that a phase sensitive circuit is not used.

Note however, that when the impedance and ESR curves are coincident (or nearly so), the MESR-100 will get a reading very close to the true ESR.  Also, when the capacitor is bad, even the MESR-100 can detect that fact.

In all the cases I've examined so far, the DE-5000 reads the true ESR (to within its accuracy specification) because it uses a sine wave and a good phase sensitive detector.  Its performance is outstanding for the price.

[dannyf]

For a resistor, E = I*R

If you allow E/I/R to be vectors (ie. complex numbers),

The relationship can be simplified to

E = I * R, and it applies to all resistive / reactive parts (= R, C and L).

A more common way to express that is:

Z = V / I, where Z is the impedance, V / I are the voltage / current, all are in vector format.

You are done then.

[dannyf]

Here's an example where the criticism that impedance, rather than ESR, is being measured, is valid.

The impedance approach is to basically reduce the ESC (the capacitive portion of the impedance) to a level that is substantially below ESR. To do that, you have to increase the frequency of the excitation signal. However, doing so will increase the ESL (the inductance portion of the impedance).

Another way to put it, the impedance approach is useful if the part's ESL is low (so you can afford to measure at higher frequency), or its ESR is large (so you can afford to measure at lower frequency that ESL isn't a major factor).

[dannyf]

Having said all that, you have to take any ESR measurement into consideration in that it is fundamentally a flawed approach.

Any ESR measurement is based on a highly simplistic and often static / independent view of the dut. We follow a parallel or serial model and we assume, without substantiation, that the parameters are "static" and mutually independent.

We don't consider, for example, the fact that the capacitance could change with frequency or excitation levels, or the "parasitic parameters" can impact each other, or we don't consider any "leakage" - ie the basic model constructs (parallel or serial) may not apply....

The point is that you should take any of the measurements and any of the measurement approaches to be a "ballpark" figure, to be indicative rather than precise. Once you have done that, you will see the value as well as limitations of the impedance approach.

[The Electrician]

Another way to put it, the impedance approach is useful if the part's ESL is low (so you can afford to measure at higher frequency), or its ESR is large (so you can afford to measure at lower frequency that ESL isn't a major factor).

What this is saying is that if the impedance curve is coincident with the ESR curve at the frequency of measurement (and the significant harmonic frequencies if a square wave stimulus is used), measuring the impedance gives the same result as measuring the ESR, which is true, or close enough to true, in many cases where ordinary aluminum electrolytics are being measured.  I gave examples where it's not true.

Here are sweeps of 7 ordinary aluminum electrolytics superimposed.  The capacitors range from 1 uF to 15000 uF.  We can see that the impedance and ESR curves are nearly coincident in all cases between 10 kHz and 100 kHz, so that measuring impedance gives a reasonable approximation to the true ESR:

[The Electrician]

Having said all that, you have to take any ESR measurement into consideration in that it is fundamentally a flawed approach.

Any ESR measurement is based on a highly simplistic and often static / independent view of the dut. We follow a parallel or serial model and we assume, without substantiation, that the parameters are "static" and mutually independent.

We don't consider, for example, the fact that the capacitance could change with frequency or excitation levels, or the "parasitic parameters" can impact each other, or we don't consider any "leakage" - ie the basic model constructs (parallel or serial) may not apply....

The point is that you should take any of the measurements and any of the measurement approaches to be a "ballpark" figure, to be indicative rather than precise. Once you have done that, you will see the value as well as limitations of the impedance approach.

I disagree that it is a flawed approach.  Measurement of the real part of a capacitor's impedance at a single frequency is not intended to be a complete model of the capacitor.  It serves a purpose.  For a repairman, it is a single measurement that helps detect a defective capacitor.

For the circuit designer, it give a good indication of the heating due to ripple current at the frequency of the ESR measurement.

If a professional designer wants a more complete model of the cap, then an impedance analyzer is used to make measurements over a wide range of frequencies and excitation levels, although aluminum electrolytics don't have the large variation of capacitance with excitation level that high K ceramic caps do.

Your objections:

 "We follow a parallel or serial model and we assume, without substantiation, that the parameters are "static" and mutually independent.

We don't consider, for example, the fact that the capacitance could change with frequency or excitation levels, or the "parasitic parameters" can impact each other, or we don't consider any "leakage" - ie the basic model constructs (parallel or serial) may not apply...."

are directed to something more than what a simple ESR measurement is intended to be.

Of course we don't consider whether the capacitance could change with frequency when we make an ESR measurement at a single frequency.  The ESR (real part of the impedance) can be measured and plotted over a range of frequencies as in the images I've posted, and the effect of capacitance variation with frequency, if any, is part of the impedance variation with frequency.

I explained early on that the effect of all the parallel and serles loss components are combined and transformed into a single equivalent series resistance called ESR.  An ESR measurement is not intended to be more than just that.

[dannyf]

What this is saying is that ...

Let me try it differently.

At low enough of a frequency, the impedance from the capacitor will dominate, resulting in the wrong measurement using the impedance approach;
At high enough of a frequency, the impedance from the inductance will dominate, resulting in the wrong measurement using the impedance approach;
At low enough of a ESR, the impendance measurement will fail as the impedance from the capacitor + inductor is substantial vs. the ESR.

In other conditions, the impedance approach will work.

That's just simple math.

Measurement of the real part of a capacitor's impedance at a single frequency is not intended to be a complete model of the capacitor.

That's the basic message. So don't let being perfect get in the way of being good enough.

[robrenz]

I have found that the DE-5000 in auto mode will indeed show the dominant behavior of a DUT for a given frequency. A capacitor can read as an inductor at certain frequencies yet correctly read as an capacitor at other frequencies.

[The Electrician]

Let me try it differently.

At low enough of a frequency, the impedance from the capacitor will dominate, resulting in the wrong measurement using the impedance approach;
At high enough of a frequency, the impedance from the inductance will dominate, resulting in the wrong measurement using the impedance approach;
At low enough of a ESR, the impendance measurement will fail as the impedance from the capacitor + inductor is substantial vs. the ESR.

In other conditions, the impedance approach will work.

That's just simple math.

Are you suggesting that I've said something that contradicts this?

[The Electrician]

I have found that the DE-5000 in auto mode will indeed show the dominant behavior of a DUT for a given frequency. A capacitor can read as an inductor at certain frequencies yet correctly read as an capacitor at other frequencies.

My DE-5000 behaves this way, and that's what I would expect.

Here's a sweep of a 470 uF cap.  The impedance (green) has a minimum at about 70 kHz; this is the self resonance frequency.  The impedance begins to rise above the ESR (yellow) at higher frequencies.  This rise is due to the equivalent series inductance (ESL).  The DE-5000, when measuring this cap in auto mode and 100 kHz, says it's an inductance of 12 nH:



Here's a sweep showing the phase angle of the impedance as a green curve.  For this sweep the vertical axis for the green curve is linear with 100 degrees at the top and -100 degrees at the bottom.  Zero degrees is at the very middle.  The angle is negative (capacitive) in the left side of the sweep, crossing the middle at 70 kHz.  To the right of 70 kHz, the angle is positive (inductive) as we would expect.

[The Electrician]

LCR meters are good for other things than measuring capacitor ESR.  In fact, I don't I've ever measured so many capacitors as for this blog.

Usually I'm concerned with inductive components.

Here's an example.  A very low loss inductor was needed for a switcher operating from 200 kHz to 500 kHz.  A prototype was designed using litz wire on a gapped ferrite core.  Here's a sweep of the real part of the impedance--the lossy part, in other words:



As we continued the project, an outside vendor was selected.  This vendor was located in a certain large far east country.  They sent us a sample and its low frequency inductance and DC resistance checked on a simple hand instrument (not a DE-5000) looked ok.  But when used in the working switcher it overheated.  Here's a sweep of the sample AC resistance:



At first glance, it doesn't look too different, but if the sweep of the original prototype and the outside vendor's sample are superimposed, we can see the problem:



The outside vendor's sample has about the same AC resistance at low frequencies, and, surprisingly, also at 2 MHz!  But in the critical zone around several hundred kHz, the sample's AC resistance is an order of magnitude higher than our in-house designed prototype!  Not good!

The DE-5000, with its ability to make measurements at 100 kHz can see this serious problem, but for a full appreciation of it, a sweep of the AC resistance on an impedance analyzer is necessary.

[dannyf]

A capacitor can read as an inductor at certain frequencies

Both are 90 degrees apart from the resistive load's phase angle. so the firmware may not be able to tell them apart.

One approach that we haven't talked about but is done by DDS-based network analyzers is to use the frequency sweep to find the point where the reactivity cancels out -> the "impedance" at that point degenerates into resistance (=ESR in this case).

There are quite a few designs that utilize that approach, utilizing Analog impedance analyzer chips.

[dannyf]

Are you suggesting that I've said something that contradicts this?

Not at all. I was only suggesting that you seem to work too hard to disagree with yourself.

[The Electrician]

Are you suggesting that I've said something that contradicts this?

Not at all. I was only suggesting that you seem to work too hard to disagree with yourself.

If you think that I've disagreed with myself, then you've misconstrued what I said.

Give me an example, and I'll explain how I didn't disagree with myself.

[The Electrician]

A capacitor can read as an inductor at certain frequencies

Both are 90 degrees apart from the resistive load's phase angle. so the firmware may not be able to tell them apart.

That's not what's going on.  When the DE-5000 is indicating that a capacitor's impedance is inductive, it's because the measurement frequency is above the self resonance frequency.  The phase angle is not 90 degrees; it's more like a few degrees positive, a lossy inductor, and the meter has no problem measuring it.

See the sweeps in reply #19