# Capacitors, Loss angle, Tan something, how to use it.

Discussion in 'General Electronics Chat' started by #12, Nov 1, 2013.

1. ### #12 Thread Starter Expert

Nov 30, 2010
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Capacitors have a rating called Tan delta (if I looked it up correctly).
How do you use that number and what does it mean?
No calculus allowed.

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2. ### wayneh Expert

Sep 9, 2010
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I guess you've seen this already? I suppose it explains it, if I could understand it.

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3. ### #12 Thread Starter Expert

Nov 30, 2010
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That is serious, "Greek to me" stuff. At least now, I know it's about dielectric losses.
I understand that the dielectric can and does absorb some energy. It seems to increase with increasing frequency. I could use an example of how to use these numbers for a real circuit.

Here is a circuit. If I have made the sizes so that this circuit is useless, change them.
Try to use this to show me how the loss angle changes the output to, "not ideal".

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4. ### The Electrician AAC Fanatic!

Oct 9, 2007
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Consider what happens at a frequency of 10 kHz. The reactance of the 1 nF cap is about 15.9k ohms. If the cap has a tan delta of .01, then that is represented by a resistor of 15900*.01 = 159 ohms in series with the cap. That resistor in series with the cap will affect the circuit performance, and that effect can be calculated.

If tan delta is .4, then the resistor in series with the cap will be 6360 ohms. That will affect circuit performance more than a 159 ohm resistor in series with the cap. A larger tan delta means a larger effective resistor in series with the cap.

Using tan delta is just another way of expressing the fact that every cap has an ESR at a given freqency, and just how big the equivalent resistor in series with the cap is.

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5. ### #12 Thread Starter Expert

Nov 30, 2010
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Thanks. That gets me far enough to work some math.

6. ### Papabravo Expert

Feb 24, 2006
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It represents the deviation from ideality of a capacitor. The angle gives the real part or resistive component of the capacitor's impedance. It is also refered to in the literature as Equivalent Series Resistance (ESR). Using low ESR capacitors is recommended in SMPS design.

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7. ### bance Member

Aug 11, 2012
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I'm trying to repair some old scopes at the moment, and ESR is a common problem with the cap's in them.

So I thought I'd build an ESR meter to help with the diagnostics, anyway I found a design that I liked but being a relative noob, didn't (don't yet fully,) understand how it works.

The guy that designed the meter gives an overview of how the circuit works, it's different from conventional ESR meters, and he provides a link to some test and measurement experiments that he carried out whilst developing the meter.

I think it may be of help to you.... (NO CALCULUS)

I'm still trying to digest it, and understand how his circuit works. I'm sure I'll get there eventually!

HTH Steve.

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8. ### tindel Active Member

Sep 16, 2012
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I've got a good app-note at work from kemet that explains a lot of it... I don't fully grasp it, but it has to do with ESR. I use it to calculate my impedance at a given operating frequency. ESR is usually spec'd at one frequency... this will let you get a idea of your real impedance over frequency.

Here's a similar app note to the one I keep at work - I couldn't find the exact one. I think AVX has similar app notes.

9. ### wayneh Expert

Sep 9, 2010
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I had the same thought not long ago and actually built one that I wasn't thrilled with. I didn't pursue it because I found an article explaining why a DIY solution wasn't realistic, and I found the argument compelling. I'll find the link if you want.
 see here.

Last edited: Nov 1, 2013
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10. ### WBahn Moderator

Mar 31, 2012
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I'll try to avoid any calculus.

Imagine a capacitor C in series with a resistor R. What is the impedance?

Zc = R - j/(ωC)

If R is zero, then the angle of this impedance is -90° and it is a lossless, purely reactive element.

But if R is not zero, then there is some loss and this shows up in the impedance angle by being less than (i.e., closer to 0°) than -90°.

Now, if the R is constant and independent of frequency, the we can just take whatever value R has and call it Effective Series Resistance and be done with it. But because of dielectric losses, the R tends to depend on frequency.

So we define a "loss angle", δ, such that the angle of the real capacitor's impedance is

θ = -(90-δ)°

If you sketch that you will see that

δ = atan(ωRC)

Note that the tangent of the angle is R/X and not X/R because δ is measured with respect to the negative impedance axis, not the real resistance axis.

Taking the tangent of both sides, we have

tan(δ) = ωRC

R = tan(δ) * (1/(ωC)) = tan(δ) * |Xc|

11. ### bountyhunter Well-Known Member

Sep 7, 2009
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There is a formula relating Tan Theta back to ESR.ESR is critical for calculating internal heat on caps used for filtering ripple.

12. ### wayneh Expert

Sep 9, 2010
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Doesn't that mean that learning tan delta doesn't really give any more information than learning what ESR is at a specified frequency (I believe 100kHz is standard)?

13. ### #12 Thread Starter Expert

Nov 30, 2010
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The datasheet shows Tan delta at several frequencies. I guess interpolation should work pretty well.