Capacitors and phase question

[jimboyogi]

I have a couple of questions on basic theory, which I should know, but don't!

There are 2 parts to this question.

1 - When 2 capacitors are in series, then the total capacitance becomes 1/C total = 1/C1 + 1/C2.

Now say I insert a series resistor in between the 2 capacitors. Does this resistance then prevent the capacitance of the 2 caps interacting?


2 - When an AC signal (let's say an audio signal) travels through a capacitor, it's phase is shifted from the original. If 2 capacitors are connected in series, is the total phase shift twice that of one capacitor? Does inserting a series resistor between the 2 caps modify the phase shift in any way?


Thanks!

[Jazz P Bass]

Adding the resistor in the capacitor series circuit causes the circuit values to become an impedance.

The higher the resistor value, I think will have less of an effect on the phase shift of the next capacitor.

My 2 cents.

The equations can get pretty involved.
Got Math?

Series Resistor-Capacitor Circuits : Reactance And Impedance -- Capacitive - Electronics Textbook

RC circuit - Wikipedia, the free encyclopedia

[Chuck H]

Probably a question for someone who's actually studies this stuff, but as I understand it...

A series resistor won't change the relationship between the caps. That is, if you arrange a circuit as cap/cap/resistor it will be the same as if you arrange it cap/resistor/cap. There should be no additional phase shift than if you had used only one capacitor.

It's different with a load, rather than a series resistor. If you arrange a circuit as cap/cap/load the caps keep to the uncomplicated series cap formula. If you arrange the circuit cap/load/cap there will be an additional phase shift. In my non tech way I imagine this has to do with the load offering a point of reference from which to shift.

[R.G.]

Resistors are measured in how much current they let flow through them for a voltage across them; R = V/I. We could just as well call them "conductors", measured in conductance, or Mhos.

Conductances in parallel add. Resistances in series add. In many cases, solving for a set of parallel resistances is best done on a calculator by adding and subtracting conductances, then taking 1/X.

Caps? Oh, yeah. Coming to that.

Capacitance is a conductance at a specific frequency. Parallel capacitors add. You can do the resistor trick in reverse with series caps. Take 1/C1, add it to 1/C2, then take 1/x of that sum and you get the equivalent capacitance.

As for capacitors in series with resistors: the order of parts in a series string makes no difference at all at the end points as long as you don't put in or take out current in the middle, and don't rely on any intermediate voltages. So, if you had a string of R1 - C1 - C2 - R2 - R3 - C3 -R4 - C4- C5, the current through it and the voltage across it are the same if you do R1 - R2 - R3 -R4 - R5 - C1 - C2 - C3 - C4 - C5. And in fact this is the same as one resistor equal to the sum of the whole lot of resistors and one capacitor equal to the series sum of the capacitors. No difference whatsoever.

So putting a resistor between two caps is the same as putting it on either end of the two caps in series *** as long as you don't look at or use the voltages and currents in the middle of the string***.

[Dave H]

"When an AC signal (let's say an audio signal) travels through a capacitor, it's phase is shifted from the original. If 2 capacitors are connected in series, is the total phase shift twice that of one capacitor?"

If the circuit is just two capacitors in series across a generator the phase shift between voltage and current will still be 90deg.

"Does inserting a series resistor between the 2 caps modify the phase shift in any way?"

Yes it will reduce it. For zero resistance the phase shift is 90deg. For a resistor equal to the reactance of the cap at frequency f the phase shift will be 45deg at f. For a resistor much larger than the reactance of the cap at f the phase shift at f will be close to zero.

Hope I got that right

[Malcolm Irving]

The equation for a capacitor is I(t) = C dV(t)/dt. (In English: the current at any time equals C multiplied by the rate of change of voltage at that time.) When the voltage is a sine wave its rate of change is cosine (which is the same as sine but shifted by 90 degrees).
In amps the 'signal' is (nearly always) a voltage which varies with time. Putting a resistor in series with a cap turns the current coming through into a voltage - so a voltage signal across a cap and resistor in series gives us a new voltage signal across the resistor. (The current through the cap and series resistor are identical at every moment in time.)
Sorry it's maths, but I hope it might just help someone to fit the pieces of the jig-saw together.

[jimboyogi]

Thanks to all above for all of the explanations!

I wish I had the maths (or the brain) to understand the more involved explanations, but there is plenty of plain english above to answer my questions I think.

So the answers to my questions so far, I think, are -

1 - For a series string of capacitors and resistors, it makes no difference the order of the components, as long as nothing is added or subtracted within the series string.

2 - Different answers here. Two caps in series behave as one cap WRT phase shift. Putting a series resistor between the 2 caps may change the phase shift in a frequency dependent way, or it may have no effect on the phase shift. Putting a load between the caps does cause the phase shifts in the 2 caps to become additive (like in a tremolo oscillator .

[Dave H]

2 - Different answers here. Two caps in series behave as one cap WRT phase shift. Putting a series resistor between the 2 caps may change the phase shift in a frequency dependent way, or it may have no effect on the phase shift. Putting a load between the caps does cause the phase shifts in the 2 caps to become additive (like in a tremolo oscillator .

Sorry, my post was confusing because I didn't quote enough of your first post. We are all saying the same thing.

"If 2 capacitors are connected in series, is the total phase shift twice that of one capacitor? Does inserting a series resistor between the 2 caps modify the phase shift in any way?"

I thought you were asking what happens when a resistor is added to two caps in series. i.e going from a CC series string to a CRC string which does change the phase but the order doesn't matter. It could be CRC, CCR or RCC and it would be the same. It's the act of adding the resistor that changes it.

Yes, putting a 'load' (resistor to ground) between the two caps will cause extra phase shift, up to 180deg total (90+90) if there is also a load after the second cap.

[jimboyogi]

Thanks for clarifying Dave H