Does the step response from the Multisim measurement match the theoretical curve

Question

Does the step response from the Multisim measurement match the theoretical curve from MATLAB for R = 1 ?? Note the magnitude of the peak value of the step response produced by MATLAB and compare it to the peak value produced by the experimentally measured curve. Why is the MATLAB value much higher than the experimental value?

      2. What is the mathematical relationship between the impulse and step response of a system?

      3. How will the shape of the step response change as the value of resistance is increased?

      4. Why is it desirable to include an op-amp buffer to drive the RLC circuit rather than driving the circuit directly from the function generator?

      5. Why is it that we never see an oscillatory response in an RC circuit, whose response is always exponential regardless of resistance?

Explanation / Answer

1) MATLAB is just theoretical value. While Multisim is a simulator. Multisim actually uses an inbuilt circuit designing and testing tool to test your circuit like real time. It is almost always close to real circuits except for error testing. While MATLAB is just theoretical way of doing it so you wouldn't attain much insight by using MATLAB but it is easy to use and gives you a theoretical picture of how you are doing it.

2) Step response is a piecewise time response, while impulse is kind of limiting towards instantaneous time.

If u(t) is a step response then

Impulse response = Lt x->0+( u(t) - u(t-x) )/x

3) I am sorry but you should have given circuit first before asking this question. However in general sense I can say that as resistance increases. Voltage can't just abruptly change. It introduces a larger time constant for the capacitor to charge. So increasing resistance increases time constant value and curve changes acccordingly depending upon the circuit. In case RC, exponential curve becomes more prominent.

4)The input impedance of the opamp is very high so the distortion introduced in the voltage value due to impedance of the function generator is nullified and output impedance of opamp is very low so it doesn't offer any input impedance for the circuit you want to drive with this voltage. There by opamp buffer helps in idealizing the function generator into an ideal voltage source without any input impedance.

5) There should be atleast two varying voltage sources/storages inorder to exhibit oscillatory behaviour. Your RC circuit does exhibit oscillatory behaviour for AC voltage. But for DC case there is only one "memory/storage" and it has nothing else to transfer the stored energy. DC voltage bank doesnt absorb and reciprocate so it is always exponential behaviour as is the characteristic of charging of the capacitor goes. Resistance value just changes the time constant for charging. It can't change the behaviour of the circuit.

P.s. Feel free to ask any further doubts

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