# Capacitor actual value with DC bias

I did find this answer which explained why the capacitor is affected by the DC bias, however, my question is more on the application.

Let's say I have a capacitor for which I have the DC bias characteristic (Cap Charge [%] in function of DC Bias [VDC]) such as follow:

Now, let's say I set the capacitor voltage to a certain value, i.e. 5V and I try to maintain it through a feedback loop. What is the DC Bias induce? Is it 5V? What is VDC?

It may sounds like a stupid question, but I kinda struggle with the notations...

• A schematic to show context would help considerably. – Peter Smith Sep 3 '18 at 14:15
• Are you asking: I make a feedback loop to set V(cap) = 5 V DC, will there then be 5 V Dc across the capacitor? If the loop is working: then yes because the loop sets it to 5 V DC. – Bimpelrekkie Sep 3 '18 at 14:18
• @Bimpelrekkie Assuming it works, and the value is kept within a window of +/- 10%. i.e. The voltage accross the capacitor is not constant but varying randomly (noise) between 4.5 and 5.5V. The mean value can be computed, and it is the DC Bias, correct? Thus, to figure out the True capacity, I can simply look to the corresponding value for the mean voltage? – Mathieu Sep 3 '18 at 14:23
• Sure then you can use the mean value. Ideally your circuit should not be that sensitive to the capacitor's value, if it is then the tolerance of the capacitor will give you issues as well. There are always component variations, a proper design should be able to cope with that (be stable, function etc.). For high accuracy you would generally rely on trimming and/or calibration. – Bimpelrekkie Sep 3 '18 at 14:31
• The left axis of your graph is "cap change %", not "cap charge %" like you wrote in your text. – The Photon Sep 3 '18 at 15:14

### What is a DC bias

DC bias is a measurement of the average voltage on a wire on which can "ride" a signal, should this wire transmit data, and noise.
Its unit is DC Volts, or VDC. You can remember it because it is the direct voltage on the conductor.

### Variation of stored charge as a function of DC bias

Onto the phenomenon you describe in your question : as the signal varies, the capacitance "seen" by it will vary, introducing nonlinearities. But, the DC bias being most of the time large compared to the signal (or noise) voltage, they will be small.

Thus, you can use the DC bias as an effective voltage with which to consider the effective capacitance of your component, if and only if the voltage across the capacitor does not vary too much.

For example, if a $5$ to $-5$ volts audio signal had a $7$ volts DC bias and one end of the capacitor was grounded, the overall voltage would range from $2$ volts to $12$, which is a huge variation. You should not rely on a time constant or a precise capacitance then. If it was a $\pm 200 \text{ mV}$ signal on the other hand, you most likely could.

If you are using the capacitor at the output of a buck or a boost converter, than you are fine using the output voltage as a reference to use in the posted graph. Also if you use a capacitor with more than twice the rated than applied voltage this change should be negligible.