Electrical – RC voltage divider

capacitorcircuit analysisresistors

You have a circuit like this, with two caps in parallel voltage divider style, and you send a single square pulse into Vn, so it goes from 0v to 10V for a few ms then back to 0v.

In this case, is it correct to model the caps as a voltage divider?
So I would get something like this:
\$\frac{1}{C_1jw}\$ and \$\frac{1}{C_2jw}\$
Which would give
$$\frac{\frac{1}{C_2jw}}{\frac{1}{C_1jw} + \frac{1}{C_2jw}}$$
Which simplifies to just $$V_o = \frac{C_1 +C_2}{C_2} (V_n)$$

schematic

simulate this circuit – Schematic created using CircuitLab

Assuming all this is correct I now have my real question. What happens if I add a resistor in parallel with C2?

schematic

simulate this circuit

I'm thinking I now get an RC style response curve at Vo. It will start at 0v. Spike to \$\frac{C_1 +C_2}{C_2} (V_n)\$, then fade back to zero with a time constant of (C1+C2) * R.
When Vn drops back to zero, I think I'll get a negative spike at Vo, but I'm not really sure to what anymore, since \$V_o = \frac{C_1 +C_2}{C_2} (V_n)\$ when Vn is zero gives me zero at vo.

Am I on the right track here or am I doing this totally the wrong way?
Thanks!

Best Answer

It appears that with a square wave in, the output (OUT1, below) is:

$$V_o = \frac{C_2}{C_1 +C_2} (V_n)$$

The spikes From OUT2 do have a decay time, and if you want to find out what it is, the LTspice circuit list follows:

enter image description here

Version 4
SHEET 1 880 680
WIRE 144 -192 64 -192
WIRE 272 -192 208 -192
WIRE 352 -192 272 -192
WIRE 272 -160 272 -192
WIRE 272 -64 272 -96
WIRE 64 80 64 -192
WIRE 144 80 64 80
WIRE 272 80 208 80
WIRE 384 80 272 80
WIRE 464 80 384 80
WIRE 384 96 384 80
WIRE 64 112 64 80
WIRE 272 112 272 80
WIRE 64 208 64 192
WIRE 272 208 272 176
WIRE 272 208 64 208
WIRE 384 208 384 176
WIRE 384 208 272 208
WIRE 64 256 64 208
FLAG 64 256 0
FLAG 272 -64 0
FLAG 352 -192 OUT1
FLAG 464 80 OUT2
SYMBOL cap 256 112 R0
SYMATTR InstName C1
SYMATTR Value 1µ
SYMBOL cap 208 64 R90
WINDOW 0 0 32 VBottom 2
WINDOW 3 32 32 VTop 2
SYMATTR InstName C2
SYMATTR Value 1µ
SYMBOL voltage 64 96 R0
WINDOW 0 36 94 Left 2
WINDOW 3 24 96 Invisible 2
WINDOW 123 0 0 Left 2
WINDOW 39 0 0 Left 2
SYMATTR InstName V1
SYMATTR Value PULSE(0 10 .1 1u 1u .1 .2)
SYMBOL res 368 80 R0
SYMATTR InstName R1
SYMATTR Value 10
SYMBOL cap 256 -160 R0
SYMATTR InstName C3
SYMATTR Value 1µ
SYMBOL cap 208 -208 R90
WINDOW 0 0 32 VBottom 2
WINDOW 3 32 32 VTop 2
SYMATTR InstName C4
SYMATTR Value 1µ
TEXT 30 280 Left 2 !.tran 1
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