Need Help... RC ciruit analysis

I am using a simple RC series circuit for a project. The excitation is a trapezoid with a period T.


For the figure shown below, I have calculated the voltage of the capacitor when the input is rising ramp. I am in trouble when i try for the falling ramp. Can anyone help me in deriving the capacitor voltage for the time Tt+Tf to 2Tt+Tf.



Thanks in advance

Can anyone help me in deriving the capacitor voltage for the time Tt+Tf to 2Tt+Tf.

If you wuld like to get some answers concerning the voltage across a capacitor it is absolutely necessary to see the circuit diagram which contains this cap.

It is just like to the time 0 to Tt .

The voltage across a capacitor is given by, Vc=Vfinal + (Vintial - Vfinal)*(exp -t/tau ),where tau is the time constant of your RC circuit.(You need to be careful in considering the series and parallel resistors/capacitors)

(Cross check : Initially t=0 ==>exp -t/tau = 1 ==>Vc=Vfinal + Vintial -Vfinal=Vintial. At t=infinity==> exp -t/tau = 0 ==> Vc=Vfinal + 0 =Vfinal)

Now at the falling edge, say the capacitor voltage is Vc(Tt+tf).Then using above formula, Vc(t)=0 + (Vc(Tt+tf)-0)*exp - t/tau.
Next, Vc(2Tt+tf) = (Vc(Tt+tf)-0)*exp - (2Tt+tf)/tau.

Hope this helps

It makes me confused too

A_U_J said:

The voltage across a capacitor is given by, Vc=Vfinal + (Vintial - Vfinal)*(exp -t/tau ),where tau is the time constant of your RC circuit.(You need to be careful in considering the series and parallel resistors/capacitor

Click to expand...

I suppose, you did not read the original question exactly:
The trapezoid signal as shown is the INPUT to the RC path. That means it is not created by the cap.

I admit to being confused at the confusion.

The only simple r/c circuit that demonstrates what is shown in the picture is the following:

input -----R----|------- output
......................|
.....................C
......................|
......................|
...................GND

where R = resistor, and C = capacitor.

The trapezoid is the input and the exponential rise and fall are the output. They follow the input at a slight delay and delightful roundedness associated with RC circuits.

The normal calculations associated with these circuits are the step response. The trapezoid, unfortunately, is not a step (either up or down). If you approximate it as a step then the problem simplifies greatly, if not, it becomes a pain. You would have to look up the response to a ramp, or a sloped step response to actually get it correct. Hopefully if this is for a class, they aren't really asking you for that.

Oh, maybe that is what LvW meant. Good luck!

electronspin said:

The trapezoid is the input and the exponential rise and fall are the output. They follow the input at a slight delay and delightful roundedness associated with RC circuits.

Click to expand...

An exponential rise and fall response is developed only in the case that the input is an ideal step.

LvW said:

electronspin said:

The trapezoid is the input and the exponential rise and fall are the output. They follow the input at a slight delay and delightful roundedness associated with RC circuits.

Click to expand...

An exponential rise and fall response is developed only in the case that the input is an ideal step.

Click to expand...

I believe I responded to the specifics of that in here:

electronspin said:

The normal calculations associated with these circuits are the step response. The trapezoid, unfortunately, is not a step (either up or down). If you approximate it as a step then the problem simplifies greatly, if not, it becomes a pain. You would have to look up the response to a ramp, or a sloped step response to actually get it correct. Hopefully if this is for a class, they aren't really asking you for that.

Oh, maybe that is what LvW meant. Good luck!

Click to expand...