How to find overshoot and undershoot in an RLC circuit?

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Discussion Overview

The discussion revolves around finding the overshoot and undershoot in an RLC circuit when subjected to a pulse input. Participants explore mathematical approaches to derive the voltage across the capacitor, particularly focusing on the effects of rise and fall times on the circuit's response.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks to determine the voltage at the capacitor in an RLC circuit with a specific pulse input, noting observed overshoot and undershoot in simulations.
  • Another participant suggests forming a second-order differential equation to analyze the circuit, mentioning the importance of damping and questioning the capacitor value used.
  • Some participants express skepticism about the equivalent circuit model and emphasize the need to include source resistance and capacitance in simulations.
  • There is a discussion about the nature of the input signal, with differing views on whether it should be classified as a pulse or a step input, and how this affects the circuit's behavior.
  • Resources related to Laplace Transforms are recommended for analyzing the system response to different inputs, including Dirac's delta function.
  • One participant notes that increasing the rise time of the step input leads to greater overshoot, prompting questions about how to account for this effect mathematically.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best approach to derive the overshoot and undershoot mathematically. There are competing views on the classification of the input signal and its implications for the analysis.

Contextual Notes

Some participants highlight limitations in the current understanding of the circuit's behavior, particularly regarding the assumptions made about the input signal and the need for accurate modeling of the circuit components.

likephysics
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Homework Statement


RLC circuit as shown in the attachment. Input is a pulse, of frequency 1MHz, 5v. Rise/fall time 1ns.
How to find the voltage at the capacitor.
In simulation, I see overshoot and undershoot. But how do I find the overshoot/undershoot amplitude mathematically?
Ringing frequency is f = 1/2*pi*sqrt(LC)


Homework Equations




The Attempt at a Solution



No idea. I tried VL = L di/dt
But not sure how to get dt.
 

Attachments

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The general approach is to form the second-order differential equation, and solve it. You have a series circuit, with a current i(t). You know the equations for voltage across a resistor, across an inductor, and across a capacitor, all in terms of the current through each, so sum those voltages. This sum equals the applied voltage at all times.

The topic is treated well in most textbooks, and at wiki http://en.wikipedia.org/wiki/RLC_circuit. Possibly your examiner requires nothing more of you than just using the equation the text derives for the overshoot, after plugging in the values for your circuit to determine the damping, ζ.

That 1pF capacitor is very tiny, though not totally unrealistic. Are you sure the value is correct?

Good luck! :smile:
 
NascentOxygen said:
The general approach is to form the second-order differential equation, and solve it. You have a series circuit, with a current i(t). You know the equations for voltage across a resistor, across an inductor, and across a capacitor, all in terms of the current through each, so sum those voltages. This sum equals the applied voltage at all times.

The topic is treated well in most textbooks, and at wiki http://en.wikipedia.org/wiki/RLC_circuit. Possibly your examiner requires nothing more of you than just using the equation the text derives for the overshoot, after plugging in the values for your circuit to determine the damping, ζ.

That 1pF capacitor is very tiny, though not totally unrealistic. Are you sure the value is correct?

Good luck! :smile:

It's not an assignment problem. I made it up.
The RLC ckt is the equivalent of a scope probe. I am trying to mathematically derive the overshoot amplitude.
Since the input is a pulse, I can't use the standard textbook approach.
I have attached a plot of the voltage across capacitor for rise/fall time of 0.5ns.
 

Attachments

Probes are usually carefully designed. I'm skeptical about your equivalent circuit, have you included the resistance of the source in your simulation? Also include the source capacitance. Try 50Ω and 10 pF if you are just making up values. :smile:

I wouldn't call that a pulse, your input is a step, repetitively, and that's exactly what the textbooks deal with. If a system rings with a step, it will ring with a delta.
 
NascentOxygen said:
Probes are usually carefully designed. I'm skeptical about your equivalent circuit, have you included the resistance of the source in your simulation? Also include the source capacitance. Try 50Ω and 10 pF if you are just making up values. :smile:
The values you mentioned are for passive probes.
I'm trying to play with approximate model of an active probe.
The L and C values are correct. I added the R to dampen the ringing caused from ideal L and C in simulation.
I wouldn't call that a pulse, your input is a step, repetitively, and that's exactly what the textbooks deal with. If a system rings with a step, it will ring with a delta.

Can you point me to resources which will help me find the delta?
 
likephysics said:
Can you point me to resources which will help me find the delta?
Laplace Transforms give you the system response for any input, including Dirac's delta. Look for an electronics textbook introducing Laplace Transforms. Many textbooks will have worked examples. Or search online.

Good luck!
 
NascentOxygen said:
Laplace Transforms give you the system response for any input, including Dirac's delta. Look for an electronics textbook introducing Laplace Transforms. Many textbooks will have worked examples. Or search online.

Good luck!

Found this - http://csserver.evansville.edu/~blandfor/EE210/MatLab/MLEx5.pdf
Plugged in values for time and got voltage close to the one in the plot (page3) for underdamped case.

But in my circuit, the overshoot increases as I make the step input rise time fast.
How do I take this into account?
 
likephysics said:
Found this - http://csserver.evansville.edu/~blandfor/EE210/MatLab/MLEx5.pdf
Plugged in values for time and got voltage close to the one in the plot (page3) for underdamped case.

But in my circuit, the overshoot increases as I make the step input rise time fast.
How do I take this into account?
Have you learned about Laplace Transforms in your studies?
 
NascentOxygen said:
Have you learned about Laplace Transforms in your studies?

Yes, I did learn LT back when I was in school.
 
  • #10
In the time domain, to generate a step input with a finite rise-time:
at t=t₀ apply a steep ramp of slope g volts/sec, i.e., v(t)=g·t
at t=t₁ add to this input a ramp of equal but opposite slope, viz., -g volts/sec,

With your system being represented by a linear second order DE, you can use the superposition of responses to more than one input to find the composite output. (I can't help with the mathematics, have forgotten those details.)

Your best hope lies in using Laplace Transforms. Maybe here's your opportunity to revise that topic? I only use LT for sinusoidal responses, but maybe someone else can help you with your piece-wise LT. Good luck!
 

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