-3db point on RC filter not @ -45deg

[kickit2]

So I'm messing with a 1st order, low pass RC filter, and the break freq is at 100Hz. Measure it with the scope - attenuation is perfect (or within 1% anyways), but the phase difference is only coming out at -39.2 degrees.

Now I know this happens with RL filters because of the DC resistance of the inductor, but with an RC filter, this shouldn't really happen (as far as I understand anyways). I tried multiple cap values, changing the R values as needed to maintain the break freq and no change. The only way that I can get the phase to agree (within reason) of -45 degrees is by moving from an electrolytic cap to a ceramic cap.

I'm assuming that this is an ESR related thing, but in order to get the phase to be close in my calculations / simulations, the ESR has so be 18-20ohms on a 10uF electrolytic cap. This is roughly 20x the documented average for this value. I've tried multiple values, voltage ratings, and mfgs, but it always has this odd ball phase shift.

What am I missing here? What is it about electrolytic caps that cause a goofy phase shift?

I attached a bode plot, and scope reading at 100Hz, of the physical circuit so you can see I'm not imagining this. In my use, the phase shift really doesn't affect anything, but it still peaked my interest. Any ideas?

 

[Laplace]

Does your SPICE model for an electrolytic capacitor include series inductance?

 

[kickit2]

By default - I'm assuming no. I've used NI's Multisim as well as Linear's LTSpice with both coming out at -45deg. I know with Multisim, if I want to model ESR, I have added a resistor in series with the capacitor. There may be a way to do this, but its beyond me.

My knowledge of ESL with caps is minimal - but from what I understand, its usually not a factor until higher freqs. Could that really be a sizable issue at 100Hz?

 

[Arouse1973]

I think it's all about component tolerances which is why simulating without tolerance taken into account will sometimes give a result that is different from real life. I have done this for you to show some differences. The top set of figures show 5% on the resistor value and 5,10,20% on the cap. The bottom set show -5% on the resistor and -5,-10,-20% on the capacitor. I believe what you are seeing is the large variation in capacitance of an electrolytic capacitor.

Thanks
Adam

 

[Laplace]

Component tolerance may shift the frequency of the 3dB point, but why would that affect the phase shift at the 3dB point?

 

[Arouse1973]

Yes agreed if he matched the input signal to the new 3dB point now shifted due to component tolerances. But if he keeps the input at 100Hz and then compares this to the output won't he see a phase different to what he is expecting?
Adam

 

[Arouse1973]

I have amended my chart to explain what I mean.
Thanks
Adam

 

[kickit2]

I get what you are saying - but all the caps used and resistors where measured with an LCR meter and the math taken into account. In any case, you can clearly see within the bode plot that the -3db point does NOT agree with -45 degrees. So as was already pointed out, its not that the -3db point isn't at a certain freq, but that the -3db point (where ever it lands) does not have a -45deg phase shift. Interestly, it also does not have the -20dB / decade roll-off that you would expect from a first-order filter either. The elctrolytic being swapped to a ceramic fixed this, and swapping to other electrolytics did not. Its something to do with the elctrolytic.

 

[Laplace]

Initially I thought LabVIEW provided the experimental results as a Spice simulation, not being familiar with that product. As for series inductance in the capacitor, the inductor would need to be well over a thousand times larger than is physically possible to produce the observed effect. Found the following article from Cornell-Dubilier which addresses the complexities of electrolytic capacitors. It may provide some useful information.

"Improved Spice Models of Aluminum Electrolytic Capacitors for Inverter Applications"

Abstract — Impedance modeling of aluminum electrolytic capacitors presents a challenge to design engineers, due to the complex nature of the capacitor construction. Unlike an electrostatic capacitor, an electrolytic capacitor behaves like a lossy coaxial distributed RC circuit element whose series and distributed resistances are strong functions of temperature and frequency. This behavior gives rise to values of capacitance, ESR (effective series resistance), and impedance that vary by several orders of magnitude over the typical frequency and temperature range of power inverter applications. Existing public-domain Spice models do not accurately account for this behavior. In this paper, a physics-based approach is used to develop an improved impedance model that is interpreted both in pure Spice circuit models and in math functions.

http://mexico.newark.com/pdfs/techarticles/cornell/impedance.pdf

 

[Arouse1973]

I get what you are saying - but all the caps used and resistors where measured with an LCR meter and the math taken into account. In any case, you can clearly see within the bode plot that the -3db point does NOT agree with -45 degrees. So as was already pointed out, its not that the -3db point isn't at a certain freq, but that the -3db point (where ever it lands) does not have a -45deg phase shift. Interestly, it also does not have the -20dB / decade roll-off that you would expect from a first-order filter either. The elctrolytic being swapped to a ceramic fixed this, and swapping to other electrolytics did not. Its something to do with the elctrolytic.

Can you give us the actual component values and the frequency you were using if different from 100Hz. I'll do a quick test later myself with a proper scope.

 

[Arouse1973]

I have done an experiment using a 1K and a 1uF electrolytic. At 159Hz gave a phase of -43.5, gave -45 degrees at 161Hz.
I swapped the cap for ceramic 100nF and resistor for 100K. At 159Hz gave a phase of -44.4 degrees, gave -45 degrees at 160Hz.

Oh one other thing that I didn’t mention is make sure your resistor value is miles away from the output impedance of your generator e.g 50-Ohms otherwise this will affect your RC and oh shift your phase. I guess this had already been thought of and I guess Laplace would have mentioned this also if it was relevant.
Example.
1000R+50R*1uF= 1.05ms
10R+50R*100uF= 6ms
Thanks
Adam

 

[kickit2]

Actual componant values where a 10uF, 50V rated, electrolytic cap which measured 11.3uF and a trimmer cap set to 138.2Ohm. I also tried this a physical 150 ohm resistor and the bode plot still didn't show -45 (wasn't worried about specific freq - just wanted to see the phase straightened out).

The idea of it being close to the output inpedance of the function generator is an idea, however I did try a 1uF electrolytic cap and a 1.3k Ohm and it still didn't resolve it, although it was closer.

I should mention I confirmed this on LabView's soft-scope (part of the NI ELVIS Suite), a Rigol DS1102E, and a Tektronix 2014C Scope. I've use'd NI ELVIS's fgen, a Siglent SDG1020, and a Tektronix AFG3101C. Results followed regardless of equipment - the softscope was just the easiest to post to the forum.

 

[Arouse1973]

I tried this with a 1u and 1K and got pretty close. So could it be your set up? What frequency did you get -45 phase shift at then? should be about 101Hz.. How are you measuring the values? Capacitors value can change with applied voltage and will depend on the type, electrolytics are quite stable though which is strange in what your seeing. The only thing I can think of that will do this is either a change in capacitance or resistance for a given input frequency. The phase angle is -tan^-1(RC*w) if w (2PI*F) stays the same then that only leave R and C. But I agree now that it still doesn't explain why when you actually measure the 3dB point and plot the phase that 3dB is not 45 degrees. I'll do some more digging.
Adam

 

[Arouse1973]

Ok, the only other way I can think of your circuit being effected is somehow loosing gain else where and not through the capacitor. This could happen if you have some parallel resistance. If you have a 1K and a 1uF then with 10K parallel resistance the phase at 3dB is about 39 degrees.

Adam

 

[Arouse1973]

Just done some calculations and this is what I have found. An example of capacitors parallel resistance is as follows. 100uF @ 159Hz ESR=0.01R

Rp= 1/GP=ESR*(1+Q^2)
Q=XC/ESR
Xc= 10
So 0.01*(1+(10/0.01)^2) = 10,000R
This could be what is causing the reduction of gain which is changing the 3dB point phase angle.
Just a thought
Thanks
Adam