Nonlinearity of frequency response of capacitors.

[J. Payne]

For a physics project I set up the following circuit:
_________
| < R1(=1Meg)
~Vs >
| |
| =C1(=22pF)
|_________|

I was just running a test run with a real capacitor before what I
intended to do, which was to measure the capacitance between two
parrallell wires.

Anyway, I varied the frequency of Vs (which I kept at a constant
voltage) and measured the voltage across C1. If my calculations are
correct (and I checked them a lot), then this voltage should equal:
Vs(1/(2*pi*R1*f*C1+1))
I also plotted the recipricol of this as a graph. What I was expecting
was a straight line passing through 1/Vs on the y axis with a gradient
of (2*pi*R*C)/Vs. What I got however, was not straight, but had a
decreasing gradient like this:

|V
|
| _______
| /
| /
|/_________________f

well, not quite that extreme.

What explanation would there be for this, as I know wish to maybe
study this phenomenon instead (rather than the cap between wires).

--JP

(PS I tried modelling this in spice but instead of a straight line or
line like I got, I got a line with increasing gradient - unless I used
the magnitude of the complex number I was given)

 

[Walter Harley]

"J. Payne" <jdapayne@hotmail.com> wrote...

For a physics project I set up the following circuit:
_________
| < R1(=1Meg)
~Vs
| |
| =C1(=22pF)
|_________|

I was just running a test run with a real capacitor before what I
intended to do, which was to measure the capacitance between two
parallel wires.
[...]

This might be a better question for sci.electronics.basics. But anyway:

What frequencies were you using?

Real capacitors have some series inductance, and also some series
resistance. Usually the effect of this inductance starts becoming
noticeable somewhere in the MHz range - depends a lot on the type of
capacitor.

In fact, all electrical components, including wires, have some resistance,
some capacitance, some inductance... there's no such thing as a "pure"
component. At low frequencies you can ignore that fact; at higher
frequencies you can't.

 

[Tim Shoppa]

jdapayne@hotmail.com (J. Payne) wrote in message news:<a09f4a2f.0310231236.6db8c82f@posting.google.com>...

For a physics project I set up the following circuit:
_________
| < R1(=1Meg)
~Vs
| |
| =C1(=22pF)
|_________|

I was just running a test run with a real capacitor before what I
intended to do, which was to measure the capacitance between two
parrallell wires.

Anyway, I varied the frequency of Vs (which I kept at a constant
voltage) and measured the voltage across C1. If my calculations are
correct (and I checked them a lot), then this voltage should equal:
Vs(1/(2*pi*R1*f*C1+1))
I also plotted the recipricol of this as a graph. What I was expecting
was a straight line passing through 1/Vs on the y axis with a gradient
of (2*pi*R*C)/Vs. What I got however, was not straight, but had a
decreasing gradient like this:

|V
|
| _______
| /
| /
|/_________________f

well, not quite that extreme.

What explanation would there be for this, as I know wish to maybe
study this phenomenon instead (rather than the cap between wires).

The 1 M resistor is acting like a capacitor above a certain frequency.

The model of the resistor in this case is a resistor with a parallel
capacitance. Some of this capacitance is in the resistor itself, but
the leads to the resistor are important at the pF level too.

The effective parallel capacitance is probably 5 pF, so
the impedance of the capacitor will be less than the impedance of the
resistor (and thus the resistor will be behaving more like a capacitor
than like a resistor) when

1/(2 Pi f C) < 1M

1/(31.4E-12 f) < 1E6

1/f < 31.4E-6

f > 32 kHz or so.

Is this the region where you see the transition away from your expected
curve?

At other frequencies the parasitic inductance of the resistor will become
relevant, and at other frequencies the parasitic inductance of the
capacitor will make the capacitor resonant, but I don't think you're
anywhere near that region.

Tim.

 

[Frank Miles]

In article <a09f4a2f.0310231236.6db8c82f@posting.google.com>,
J. Payne <jdapayne@hotmail.com> wrote:

For a physics project I set up the following circuit:
_________
| < R1(=1Meg)
~Vs
| |
| =C1(=22pF)
|_________|

I was just running a test run with a real capacitor before what I
intended to do, which was to measure the capacitance between two
parrallell wires.

Anyway, I varied the frequency of Vs (which I kept at a constant
voltage) and measured the voltage across C1. If my calculations are
correct (and I checked them a lot), then this voltage should equal:
Vs(1/(2*pi*R1*f*C1+1))
I also plotted the recipricol of this as a graph. What I was expecting
was a straight line passing through 1/Vs on the y axis with a gradient
of (2*pi*R*C)/Vs. What I got however, was not straight, but had a
decreasing gradient like this:

|V
|
| _______
| /
| /
|/_________________f

well, not quite that extreme.

What explanation would there be for this, as I know wish to maybe
study this phenomenon instead (rather than the cap between wires).

--JP

(PS I tried modelling this in spice but instead of a straight line or
line like I got, I got a line with increasing gradient - unless I used
the magnitude of the complex number I was given)

How did you measure the voltage on C1? 22pF is small enough that even
a 10x 'scope probe would substantially load the result. Not only that,
the impedance looking into the probe is not really a fixed R || C.
Tek scope probes (at least sometimes) come with information on this
variation.

You may want to consider using a different method for measuring small
capacitances.

-frank
--