Step and Impulse Responses in RC Circuits

[circuits83]

Hello very body
i got confused understanding how we can get the derivative of V(t) equal to Hv(t) :


V= (1/R) e^(-t/RC) U(t) its derivative V' = Hv(t) = -(1/R²C)e^(-T/RC) U(t) +(1/R)&(t)
where : U(t) is the unite step fonction and &(t) is the delta fonction
please some help
thanks for your time

 

[trambolin]

So here we are again with another instance of convention. The result is the application of the product rule. If this is enough for you don't read the rest. But the delta function is a tricky business.


You take the unit step function and it's derivative is the delta function. But the delta function is not even a function rather a distribution or a generalized function. You can memorize this shortcut but always keep in mind that there is a whole another story running behind.

 

[oswaler]

Hello,

Thank you for reaching out. I can understand how the concept of step and impulse responses in RC circuits can be confusing. Let me try to explain it in simpler terms.

In RC circuits, we have a resistor (R) and a capacitor (C) connected in series. When a voltage is applied to the circuit, the capacitor will charge up gradually, causing a current to flow through the circuit. This charging process can be described by the equation V= (1/R) e^(-t/RC) U(t), where V is the voltage, t is time, and U(t) is the unit step function (a function that is 0 for t<0 and 1 for t>0).

Now, when we take the derivative of this voltage equation, we get V' = Hv(t), where Hv(t) is the impulse response. This means that the impulse response is the derivative of the voltage equation. In your example, the impulse response is given by -(1/R²C)e^(-T/RC) U(t) +(1/R)&(t).

The impulse response is important because it tells us how the voltage changes in response to a sudden change in the input (such as a sudden increase or decrease in voltage). It is a measure of how the circuit responds to an impulse or sudden change.

I hope this helps clarify the concept for you. If you need any further assistance, please let me know. Thank you.