Need Help... RC ciruit analysis

[kingmakerbull]

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

 

[LvW]

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.

 

[flyingsky]

It is just like to the time 0 to Tt .

 

[A_U_J]

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

 

[sophia8]

It makes me confused too

 

[LvW]

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

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.

 

[electronspin]

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!

 

[LvW]

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.

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

 

[electronspin]

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.

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

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

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!