LRC Meter - Different readings at different frequencies - Why?

[pigtwo]

Hello everyone!

This question has been bothering me for a while.  I have an LCR meter that lets you choose between multiple frequencies and when I measure the capacitance at different frequencies, I get different values. 

For example, If I measure a 1 uf capacitor at 100 Hz, I get roughly 1 uf but If I read it at 100 kHz, I get roughly half that value.  The same seems to happen for inductors.

I don't understand why this happens.   As far as I knew capacitance/inductance isn't dependent on frequency.  I do notice that at higher frequencies it appears to be more precise.  Another example.  A 2 pf cap at 100 Hz is read as 2 pf but at 100 kHz it is 1.72 pf.  IE more sig figs.

I tried asking one of my TAs in one of my classes, but he was less than informative. 

So my question is 1) what is causing this and 2) what is the real value?

I realize that the second question is probably dumb, but I can't think of a better way to phrase it.

Thanks!

[Memphis]

It is simple, the world is not ideal  . Means every passive part is not just R or C or L. Every part is a linear combination of this elements.
Means if you have for example cap, it has a parasitic inductance and resistive leads. The real value of capacitance at low frequency will appear, but in higher frequency the inductance and resistive lead takes into account and thus the read value from the meter is different. At frequencies bigger than 1MHz you will got significantly bad values  .

So yes, you can imagine that capacitance, inductance and resistance in real world are frequency dependent, depends on the construction of the component.

Than next question should be, is your LCR meter well calibrated? Read the manual about self calibration before measuring. 

[Wytnucls]

The impedance of reactive components is proportional to frequency, which affects accuracy.
For example, measurement of a 1mF capacitor at 1 kHz would be within basic measurement
accuracy; the same measurement at 1MHz would have significantly more error due to the
decrease in the impedance of a capacitor at high frequencies.

That's the reason why the capacitor datasheet must be consulted to find out what test frequency was used to characterize the device. Usually, it is 120Hz for electrolytic capacitors.

[jpb]

Just to second the other replies.

At 100kHz the impedance of 1uF is only 1.6 ohms and you're trying to measure this in the presence of parasitic resistance, lead inductance and so on.
At 100Hz it is 1.6kohms which is much easier to measure.

For a 2pF capacitor at 100Hz its impedance is nearly 800Mohms so measuring it in the presence of leakage is going to be difficult.
(The applied voltage is typically only about 0.7V so your trying to measure a reactive current of less than a nA!)
At 100kHz it is a much more manageable 800kohms so it is reasonable to give more significant figures.

You just need to do some back-of-an-envelope calculations to get an idea at what sort of frequency you might be able to make reasonable measurements.

[kg4arn]

Also you may want to take a look at the Aglent Impedance Measurement Handbook.

http://cp.literature.agilent.com/litweb/pdf/5950-3000.pdf

[JackOfVA]

If the inductor being measured is not an air core type, the permeability of the core material may well change with frequency. And, for that matter, the permeability may change with the applied test signal level.  Ferrite material is perhaps the most well known for permeability change with frequency, but it's not the only material.

Second order effects also causes change in inductance with frequency - for example as the frequency increases, the current distribution on the wire an inductor is wound with changes. Skin effect drives the current to the outside of the conductor and proximity effect drives current away from the conductors surfaces that are adjacent. These effects are small in many cases but they alter the equivalent dimensions of the inductor and hence the physical flux linkages and therefore the inductance.

Finally, as has been mentioned, all practical inductors have self-capacitance. At some frequency, the inductor becomes self-resonant where the distributed capacitance and inductance form a parallel resonant circuit. As you measure an inductor with a variable frequency source, the closer you are to the SRF, the greater the indicated inductance. At the SRF, the indicated inductance is 0 and above the SRF, the sign inverts and the instrument indicates you are measuring a capacitor, not an inductor.

It is possible to "de-embed" these various parasitic effects and model a real inductor as a network of theoretically perfect parts, none of which change with frequency.  So in one sense, it is correct to say that the "inductance does not change with frequency" provided that you mean one part of the model of a real world inductor. However, if one conceptualizes the real world inductor as a black box it is just as accurate to say that the box contains an inductor with parameters that are a function of frequency (and applied test signal level, etc.)

[Rufus]

This question has been bothering me for a while.  I have an LCR meter that lets you choose between multiple frequencies and when I measure the capacitance at different frequencies, I get different values.

LCR meters don't measure L, C, or R.

They measure the complex impedance of the circuit placed between the terminals at a particular frequency.

They then display the values of perfect L or C and R components placed in series or parallel which would produce the same complex impedance at that frequency.

Real world capacitors have inductance, the higher the frequency the more the inductance is responsible for the impedance across its terminals and the smaller the value of perfect capacitor required to produce the same impedance. At the capacitor self resonant frequency the required perfect capacitor value is zero, above that frequency the required perfect capacitor value is negative. 

[JackOfVA]

As a practical example, plots below are for a 103A-21 100uH standard reference inductor as originally manufactured by Boonton Electronics. (The particular 103A-21 inductor I used for these measurements was made by a different company under government contract.) It's a stable shielded air-core inductor wound on a ceramic form and intended to be used with a Q-meter or other similar device for calibration and for component measurements.

The first plot shows the "apparent" inductance of the device over the range from a few Hz to 13 MHz. The plot shows the inductance varies considerable over this range - most all of this apparent change is due to the distributed capacitance of the 103A-21 inductor forming a parallel resonant circuit at about 6.1 MHz. See the second plot. At the SRF, the inductance is 0 (the capacitive and inductive reactance cancel and all that is left is the loss element, which is resistive.) Above the SRF, note that the instrument reports "negative inductance" or capacitance since the sign of the net impedance flips negative.

The final plot shows how to extract the "true" inductance - that is to say the inductance that would be measured at 0 Hz where distributed capacitance, skin effect, etc. all can be disregarded since those are AC effects only.

But, as has been said, whatever the measuring instrument is called, it can only measure the complex impedance of the device under test. It can display the results of the complex impedance in various forms, one being inductance and Q, or  R+jX, or G+jB, or whatever. It's up to the instrument operator to understand what those results mean.
 

[pigtwo]

Wow thanks for the awesome replies!

It makes much more sense now.  I had never thought about it resonating with itself.  I thought that was really interesting. 

I was messing around with an inductor and I think I can see this.  Around one frequency, the capacitance jumps up really high, then goes low again.  I'm glad a read this first because if I had seen this a few days ago I would have probably returned my meter. 

Especially thanks to JackOfVA for the graphs.   

[free_electron]

I got some cool plots a few days ago. I'll post some tomorrow. It show the exact behavior of some capacitors over frequency. I use a 4395 network analyser with the impedance mode installed.
This machie sweeps the capacitor from a few kilohertz all the way into the 500MHz range.

It show the impedance of the capacitor as well as the effective capacity over frequency.
The machine has a built in spice engine. It 'extracts' a spice model from the measured data nad plots the simulated model curve on the same screen. That way you can use an accurate model of the real component in a simulator.

I was optimizing a switchmode power supply for ripple. The switchers runs at 1.5 MHz so i wanted to find some good caps that have their lowest impedance point precisely there. I ran over a few different 10uf multlayer ceramics. I found a particular type from tdk that sat the closest to where i was operating. Swapped the caps on the board and my output ripple dropped by 15mV.. Perfect ( on a 1.2 volt output that is sunstantial .. )

The testhead i use allows the injection of DC into the capacitor so i can see how it behaves at different operating voltages well. ( effective capacitance collapses as dc voltage increases for multilayers, and depending on the dielectric used. X7r is pretty stable. Z5u or y5v , not so.. Also a 10u 10volt in 0805 brhaves differently than a 10u 10volt in 0402 body ...)

Here's another little known fact: when you solder a multilayer ceramic cap you create an effect in the dielectric that actually increase the capacitance by about 5%...
Over the next 5 years! It will lose 1% per year. After that it settles.

So, NEVER use ceramics in oscillator circuits where longterm stability is key ! That you just soldered it on the board kicks off a 5 year process.... The process happens at about 147 degree c for most barium titanate based dielectrics.

Another little known fact : foil capacitors have an orientation ! Some foil capacitors have a strip on their body. This marks the terminal attached to the outer electrode ( foil caps are rolled or stacked. For a stacked cap : there is one more odd plate thanthere are even plates). The odd plates are marked.

The reason for this indication is again so you can optimize your circuit.

Lets say you make a filter with an opamp. The input of the opamp ishi impedant. Thats where you want the inner foil. The output of the opamp is low impedant. Thats where you want the outer foil. The outer foil no acts as a shield for ambient noise. Anything picked up by the first turn of the outer foil sees the hard impedance of the opamp output.

These are things to take into account when designing precision analog stuff !

[jpb]

I used to work with microwave integrated circuits. The rule of thumb that everyone used was that gold bond wires had an inductance of one nH per mm.

At high frequency 1nH is quite a lot if it is in the source of a FET (62 ohms at 10GHz more than enough to kill any gain) and even 250 microns of bond wire was significant.

You had to use multiple bond wires or bond tape.

The point being that even something as simple as gold wire to connect your chip doesn't look like a simple lumped component at high frequency.

On the circuits themselves Ls where obtained using transmission lines but Cs were close to being what you expect, i.e. over-layed metal plates with dielectric between except for smaller values where they were interdigitated fingers of metal.