# 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. Apr 5 '17 at 18:07
• Voltage or current response can define conditionally for e.g. 0 ~ -0.65V Apr 5 '17 at 18:08

## 1 Answer

The step and impulse response are characteristical of linear systems.

Thus, those responses can't be calculated for systems containing non-linear devices acting as such.

Of course, if those non-linear devices are continuously operating within their linear region (as most transistors and diodes sometimes do), then they can be assimilated to linear devices and their "effect" can be computed into a step or impulse response.

But in no way a device that will be switching during normal continuous operation (rectifiers, etc) can be reduced to a linear model for the purpose of calculating the system response.

• Good answer. You should put some bits in shouty bold in case we're all too thick to know they're important :-) Apr 5 '17 at 21:00
• Nice suggestion... now I'm thinking of doing that for the word DIODE. And add "wink-wink, nudge-nudge" close to the word DIODE. :D Apr 5 '17 at 23:11
• "But in no way a device that will be switching during normal continuous operation (rectifiers, etc) can be reduced to a linear model for the purpose of calculating the system response. " Usually not, but state-space averaging does exactly that for switching power supply small-signal response. The PWM switch model does the same thing in a different way. Apr 6 '17 at 0:09