RC analysis

[Sylvia Else]

I have the circuit whose LTSPICE text is given below. The voltage
sources and voltage controlled switches are only there to set the
initial voltages on the capacitors. Thus the circuit of interest
consists of two capacitors and two resistors.

I've been trying to determine an equation that describes the voltage on
C2 as it varies with time, but with my limited mathematical skill,
haven't been able to. I end up with differential equations that contain
the voltage on C1 as well, in a way that I can't substitute for.

Any thoughts?

Sylvia.


Version 4
SHEET 1 880 680
WIRE 624 16 256 16
WIRE 96 32 0 32
WIRE -48 128 -96 128
WIRE 0 128 0 112
WIRE 576 128 528 128
WIRE 624 128 624 96
WIRE -48 144 -48 128
WIRE 96 144 96 32
WIRE 144 144 96 144
WIRE 256 144 256 16
WIRE 256 144 224 144
WIRE 320 144 256 144
WIRE 576 144 576 128
WIRE 96 208 0 208
WIRE 256 208 96 208
WIRE 368 208 256 208
WIRE 400 208 400 144
WIRE 400 208 368 208
WIRE 544 208 528 208
WIRE 576 208 576 192
WIRE 576 208 544 208
WIRE -96 224 -96 208
WIRE -64 224 -96 224
WIRE -48 224 -48 192
WIRE -48 224 -64 224
WIRE 400 256 400 208
WIRE 624 256 624 208
WIRE 624 256 400 256
FLAG 368 208 0
FLAG -64 224 0
FLAG 544 208 0
SYMBOL cap 80 144 R0
SYMATTR InstName C1
SYMATTR Value 10
SYMBOL cap 240 144 R0
SYMATTR InstName C2
SYMATTR Value 300
SYMBOL res 240 128 R90
WINDOW 0 0 56 VBottom 2
WINDOW 3 32 56 VTop 2
SYMATTR InstName R1
SYMATTR Value 0.5
SYMBOL res 416 128 R90
WINDOW 0 0 56 VBottom 2
WINDOW 3 32 56 VTop 2
SYMATTR InstName R2
SYMATTR Value 1
SYMBOL sw 0 112 R0
SYMATTR InstName S1
SYMATTR Value SW1
SYMBOL voltage 0 16 R0
WINDOW 123 0 0 Left 2
WINDOW 39 0 0 Left 2
SYMATTR InstName V1
SYMATTR Value 50
SYMBOL voltage -96 224 R180
WINDOW 0 24 96 Left 2
WINDOW 3 24 16 Invisible 2
WINDOW 123 0 0 Left 2
WINDOW 39 0 0 Left 2
SYMATTR InstName V2
SYMATTR Value PULSE(-1 1 0 0 0 1 2 1)
SYMBOL sw 624 112 R0
SYMATTR InstName S2
SYMATTR Value SW1
SYMBOL voltage 528 224 R180
WINDOW 0 24 96 Left 2
WINDOW 3 24 16 Invisible 2
SYMATTR InstName V3
SYMATTR Value PULSE(-1 1 0 0 0 1 2 1)
SYMBOL voltage 624 0 R0
WINDOW 123 0 0 Left 2
WINDOW 39 0 0 Left 2
SYMATTR InstName V4
SYMATTR Value 1
TEXT -412 232 Left 2 !.tran 50
TEXT -368 328 Left 2 !.model SW1 SW(Ron=0.0001)

 

[Sylvia Else]

On 2/04/2014 3:40 PM, Sylvia Else wrote:

I have the circuit whose LTSPICE text is given below. The voltage
sources and voltage controlled switches are only there to set the
initial voltages on the capacitors. Thus the circuit of interest
consists of two capacitors and two resistors.

I've been trying to determine an equation that describes the voltage on
C2 as it varies with time, but with my limited mathematical skill,
haven't been able to. I end up with differential equations that contain
the voltage on C1 as well, in a way that I can't substitute for.

Any thoughts?

Sylvia.

Actually, never mind. It involves solving simultaneous differential
equations. I'll just have to read up on that.

Sylvia.

 

[Jim Thompson]

On Thu, 3 Apr 2014 00:11:04 +0000 (UTC), Geoff <public@email.com>
wrote:

Jim Thompson
To-Email-Use-The-Envelope-Icon@On-My-Web-Site.com> wrote in
news:aj3pj99b8pkkt9ghd71r8dsm5d5sptivuj@4ax.com:

On Wed, 2 Apr 2014 22:09:50 +0000 (UTC), Geoff
public@email.com> wrote:

Sylvia Else <sylvia@not.at.this.address> wrote in
news:bq1jg6F8cenU1@mid.individual.net:

On 2/04/2014 3:40 PM, Sylvia Else wrote:
I have the circuit whose LTSPICE text is given below.
The voltage sources and voltage controlled switches are
only there to set the initial voltages on the
capacitors. Thus the circuit of interest consists of two
capacitors and two resistors.

I've been trying to determine an equation that describes
the voltage on C2 as it varies with time, but with my
limited mathematical skill, haven't been able to. I end
up with differential equations that contain the voltage
on C1 as well, in a way that I can't substitute for.

Any thoughts?

Sylvia.

Actually, never mind. It involves solving simultaneous
differential equations. I'll just have to read up on
that.

Sylvia.



Or get into the S-domain and use Laplace maths, which
should get you some time domain equation at the end. Don't
ask me the details though, its been a long time

Yep, that's the correct way.

Replace C's with an impedance value 1/(Cs), where "s" is
the Laplace variable, then simply write a transfer
V(OUT)/V(IN)

You'll get a second order equation which must be
partial-fraction expanded, then you can write down the time
domain by observation.

I do it automatically... trying to explain it is hard :-(

I'll look for a write-up... must have it around here
somewhere.

The technique, BTW, is courtesy of Oliver Heaviside... not
Laplace.

...Jim Thompson

I remember Heaviside being mentioned occasionally in maths
class in college. I just looked him up in wiki. What a
character, and to think he coined words like impedance and
permeativity.

Yep. Neat fellow. Lots of engineering short-hand techniques from
him.

...Jim Thompson
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