Overdamped Series RLC Circuit Transient Response

In summary, an overdamped series RLC circuit is an electrical circuit consisting of a resistor, inductor, and capacitor connected in series. Its response to a sudden change in input voltage does not exhibit any oscillations and eventually returns to its equilibrium state. The transient response of this circuit refers to its behavior and how long it takes to reach equilibrium after a sudden change in input voltage. It can be calculated using the circuit's time constant, which is determined by the values of the components. Factors affecting the transient response include the component values and initial conditions. An overdamped circuit differs from underdamped and critically damped circuits in its lack of oscillations and response time.
  • #1
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Homework Statement


Find the voltage across each component is an overdamped RLC circuit. The circuit is powered by a square wave of peak voltage 2 V. The square wave is used to model a DC source.

Homework Equations



Vs(0)=-2 (Everywhere else in the transient response, Vs=2)
i(t)=Ae^(s1t)+Be^(s2t)
i(0)=0
Vr(t)=i*R
Vr(0)=0
Vl(t)=L*(di/dt)=L*(As1e^(s1t)+Bs2e^(s2t))
Vl(0)=0
Vc(0)=1/C *∫i dt =1/C *(A/s1 e^(s1t)+B/s2 e^(s2t))
Vc(0)=-2



The Attempt at a Solution



Using the above equations, A=-B and B=(-2*C*s1*s2)/(s1-s2)


As part of my assignment, I created a simulation of the circuit in MultiSim. For some reason that I cannot figure out, at every point in time, Vr and Vl calculated using the above equations are half the voltage that I found in the simulation! Meanwhile the calulated and simulations value for Vc are off by varying amounts at each time interval! Needless to say, I am very confused. A screen shot of the MultiSim circuit is attached for evalution. In the simulation, I used the oscilloscope to measure the voltages at different times. It would be very very helpful if someone could tell me whether my math is wrong or my circuit is wrong.
 

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  • #2


Thank you for your post. I understand your confusion and I will do my best to help you figure out the issue.

Firstly, I want to mention that it is always a good practice to double check your math and circuit simulations, as it is possible to make a mistake in either one. However, since you have already done that and have found a discrepancy, it is important to investigate further.

One possible explanation for the discrepancy could be due to the assumptions made in the equations. For example, the equations you have used assume ideal components, which may not be the case in a real circuit. In your simulation, have you considered the internal resistance of the components and the effects of stray capacitance and inductance? These factors can affect the actual voltage across each component and may explain the difference between your calculated and simulated values.

Additionally, it is important to ensure that the simulation settings are accurate and reflect the conditions in the real circuit. For example, make sure the time step and simulation duration are appropriate and that the power source is accurately modeled as a square wave.

I would also recommend checking the simulation results at different time intervals to see if the discrepancy is consistent or if it changes over time. This could provide more insight into the possible cause of the difference.

In summary, it is important to carefully consider the assumptions made in the equations and simulation, as well as any external factors that may affect the circuit. I hope this helps in identifying the issue and finding a solution. Good luck with your assignment!
 
  • #3


Dear student,

Thank you for sharing your work and asking for feedback. After reviewing your equations and circuit simulation, it appears that there may be some issues with your calculations. First, it seems that you may have made a mistake in your calculation for B, as it should be (-2*C*s1*s2)/(s1+s2). Additionally, it is important to note that the voltage across each component in an overdamped RLC circuit will not be a constant value, but rather a decaying exponential function. This means that at different points in time, the voltage across each component will be different.

It is also possible that there may be some discrepancies in your simulation setup or measurements. I recommend carefully checking all of your circuit parameters and simulation settings to ensure they match the given problem. Additionally, you can try running the simulation for longer periods of time to see if the voltages eventually match your calculated values.

Overall, it is important to carefully check your calculations and simulation setup to ensure accuracy. If you continue to have trouble, I recommend reaching out to your instructor or a TA for further assistance. Good luck with your assignment!
 

What is an overdamped series RLC circuit?

An overdamped series RLC circuit is an electrical circuit that consists of a resistor, inductor, and capacitor connected in series. It is called "overdamped" because the circuit's response to a sudden change in input voltage will eventually return to its equilibrium state without any oscillation.

What is the transient response of an overdamped series RLC circuit?

The transient response of an overdamped series RLC circuit refers to the behavior of the circuit's voltage and current when a sudden change in input voltage is applied. It describes how the circuit will respond to the change and how long it will take to reach its equilibrium state.

How is the transient response of an overdamped series RLC circuit calculated?

The transient response of an overdamped series RLC circuit can be calculated using the circuit's time constant, which is determined by the values of the resistor, inductor, and capacitor. The formula for the time constant is τ = L/R, where L is the inductance in henries and R is the resistance in ohms.

What factors affect the transient response of an overdamped series RLC circuit?

The factors that affect the transient response of an overdamped series RLC circuit include the values of the resistor, inductor, and capacitor, as well as the initial conditions of the circuit, such as the voltage and current at the time the input voltage changes. The time constant also plays a significant role in determining the transient response.

How does an overdamped series RLC circuit differ from an underdamped or critically damped circuit?

An overdamped series RLC circuit differs from an underdamped or critically damped circuit in that it does not exhibit any oscillations in its response to a sudden change in input voltage. In contrast, an underdamped circuit will exhibit oscillations, and a critically damped circuit will reach its equilibrium state in the shortest amount of time.

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