# How to find the step and impulse response of a circuit with a diode

I have a circuit similar to the following:

simulate this circuit – Schematic created using CircuitLab

I am trying to find the impulse and step response mathematically. I know I can split the responses up from the time the left part of the circuit switches from positive to negative. Is that the proper way to do it? Also, I am wondering how to find the Laplace Transform of an if statement.

I have the formula from node voltage for the response when the diode is turned on (assuming the diode drops .7V). Problem is when the diode is turned off the stored voltage in C2 determines the output. If this was a function of time, this would be simple, but it is a function of when the diode turns off which is tied to the voltage of the input.

Diode turned on: $$V_o = -1.4V + 0.7(sC_1/(1/R+sC_2))+V_i$$

I'm not sure how to go about finding the response when the diode is turned off.

Update: The input would be a decaying sine wave.

• Depends if you want + or -ve step and impulse. Just assume ideal diode no need to get complicated. Positive is just C1 load , negative is C1 up to -0.6V then R1C2 // C1 up to -1V. But warning Ideal Caps do not exist with ESR=0 so this is a theoretical training exercise. ESR*C> 100us for general purpose and down to ~1us for ultra low ESR electrolytic Plastic and NPO ceramics are lower. No need for Laplace yet. – Sunnyskyguy EE75 Apr 5 '17 at 18:07
• Voltage or current response can define conditionally for e.g. 0 ~ -0.65V – Sunnyskyguy EE75 Apr 5 '17 at 18:08