I'm trying to understand the maths behind the simple RC differntiator. I'm reading the sections in Horowidtx and Hill, which sort of make sense. But then the text uses a real world example and give a scope capture of the output. The text then challenges me to prove the results using the formula.


I've tried but I don't really know how to approach this. Can somebody please show me.





Thanks

Garry

 

The derivation is easy to find online. It is here for example:

What is RC Differentiator? Circuit Diagram, Working & Waveforms - ElectricalWorkbook

 

The derivation is easy to find online. It is here for example:

What is RC Differentiator? Circuit Diagram, Working & Waveforms - ElectricalWorkbook

Thanks

But I'm stuck trying to apply the math. I want to check that the results on the scope trace match the value predicted by the math.

 

I'm stuck trying to apply the math.

d/dt Vin(t) is the linear rise time of the input (here in V/ns).
So you multiply the differentiator RC time-constant value times that rise-time value to get the differentiated output voltage during that rise-time.
For example, the 1V/ns rise-time gives an output of 1pF*50Ω*1V/ns = 50mV (as observed).

Edit: Added simulation--
Below is an LTspice idealized simulation (no stray impedances):

 

It would be difficult to arrive at a mathematical model of the real signal.
A simple approach would be to model the input signal with a known ramp between a starting and ending voltage.

 

I thought the TS was asking for the derivation of the relation between the output voltage and the derivative of the input voltage.

 

I thought that the TS was asking for a comparison of the mathematical modelling with the results given by the oscilloscope.

 

I'm trying to understand the maths behind the simple RC differntiator. I'm reading the sections in Horowidtx and Hill, which sort of make sense. But then the text uses a real world example and give a scope capture of the output. The text then challenges me to prove the results using the formula.
View attachment 334090

I've tried but I don't really know how to approach this. Can somebody please show me.


View attachment 334088

Pick one of them. Use the most well-behaved on first, which is the slowest of the three. If the input voltage is ramping at 0.25 V/ns, what is dV(in)/dt?

What do you get if you multiply that by the product of R and C for that circuit?

How does that compare with the magnitude of the corresponding differentiator output signal in that plot?

 

d/dt Vin(t) is the linear rise time of the input (here in V/ns).
So you multiply the differentiator RC time-constant value times that rise-time value to get the differentiated output voltage during that rise-time.
For example, the 1V/ns rise-time gives an output of 1pF*50Ω*1V/ns = 50mV (as observed).

Edit: Added simulation--
Below is an LTspice idealized simulation (no stray impedances):

View attachment 334122

Thanks, I thought this would be more complex!