btec hnc - electrical and electronic principles - investigate transients in rlc circuits

Investigate Transients in R-L-C CircuitsElectrical and Electronic Principles

By Brendan Burr

Brendan Burr BTEC Higher National Certificate in ElectronicsInvestigate Transients in R-L-C Circuits

Table of Contents

TABLE OF CONTENTS - 2 -

TASK 1 - 5 -

1.1 Assuming initial conditions are zero in the following series R-C circuit, the switch is closed at t = 0 secs. - 5 -

(a) Draw a well labelled diagram of the circuit and the applied signal transformed into the S domain after the switch is closed. - 5 -

Solution:- - 5 -

(b) Derive an expression for the voltage across the capacitor (s) in the S domain. - 6 -

(c) Using Inverse Laplace Transforms derive an expression for the voltage across the capacitor in the time domain . - 7 -

(d) Using Graphmatica draw the waveform of and identify the transient part. - 8 -

1.2 Assuming initial conditions are zero in the following series R-L circuit , the switch is closed at t = 0 secs. - 9 -

(a) Draw a well labelled diagram of the circuit and the applied signal transformed into the S domain after the switch is closed. - 9 -

(b) Derive an expression for the voltage across the inductor . - 10 -

(c) Using Inverse Laplace Transforms derive an expression for the voltage across the inductor in the time domain. - 11 -

(d) Using Graphmatica draw the waveform of and identify the transient part. - 12 -

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TASK 2 - 13 -

2.1 In the following circuit the initial voltage on the capacitor is 0 V. - 13 -

The switch is closed at t = 0 sec - 13 -

(a) Draw a well-labelled diagram of the circuit transformed into the S-domain after the switch is closed. - 13 -

(b) Derive an expression for the current I(s). - 14 -

(c) Derive an expression for the voltage across the resistor - 15 -

2.2 Determine the conditional values of R for which the output response will be:-- 16 -

(a) Critically Damped - 16 -

(b) Over Damped - 16 -

(c) Under Damped - 16 -

(d) Undamped - 16 -

2.3 Simulate the circuit in Task 1 Q 1.1 using Croc Clips or Multisim and obtain a printout of the waveforms for the following voltages :- - 17 -

(a) Voltage across the resistor - 17 -

(b) Voltage across the capacitor - 17 -

2.4 Simulate the circuit in Task 1 Q 1.2 using Croc Clips or Multisim and obtain a printout of the waveforms for the following voltages :- - 18 -

(a) Voltage across the resistor - 18 -

(b) Voltage across the inductor - 18 -

3


2.5 Simulate the circuit in Task 2 Q 2.1 using Croc Clips or Multisim for the condition R = 20 - 19 -

(a) Obtain a printout of the voltage waveform in the time domain across the resistor. - 19 -

(b) Comment upon the type of waveform. - 19 -

EVALUATION - 20 -

CONCLUSION - 20 -

Books - 21 -

Catalogues - 21 -

Websites - 21 -

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TASK 1

1.1 Assuming initial conditions are zero in the following series R-C circuit, the switch is closed at t = 0 secs.

V = 10 Volts

R = 1k C = 1 F

(a) Draw a well labelled diagram of the circuit and the applied signal transformed into the S domain after the switch is closed.

Solution:-

5


(b) Derive an expression for the voltage across the capacitor (s) in the S domain.

Using Ohms Law:

Volts

6


(c) Using Inverse Laplace Transforms derive an expression for the voltage across the capacitor in the time domain .

Using tables of Inverse Laplace Transforms we get:

Multiplying both sides by , gives:

Volts

7


(d) Using Graphmatica draw the waveform of and identify the transient part.

The red coloured shaded area is known as the Transient State, everything to the right of it is known as the Steady State.

8


1.2 Assuming initial conditions are zero in the following series R-L circuit , the switch is closed at t = 0 secs.

V = 10 v DC

R = 10 L = 10 mH

(a) Draw a well labelled diagram of the circuit and the applied signal transformed into the S domain after the switch is closed.

9


(b) Derive an expression for the voltage across the inductor .

Using Ohms Law:

Divide both sides by , giving:

Entering values, gives:

Volts

10


(c) Using Inverse Laplace Transforms derive an expression for the voltage across the inductor in the time domain.

Using tables of Inverse Laplace Transforms we get:

Volts

11


(d) Using Graphmatica draw the waveform of and identify the transient part.

The red coloured shaded area is known as the Transient State, everything to the right of it is known as the Steady State.

12


TASK 2

2.1 In the following circuit the initial voltage on the capacitor is 0 V.

The switch is closed at t = 0 sec

L = 1 mHC = 10 F

V = 1 volt

(a) Draw a well-labelled diagram of the circuit transformed into the S-domain after the switch is closed.

13


(b) Derive an expression for the current I(s).

Using Ohms Law:

Multiplying both sides by , gives:

Entering values, gives:

Amps

14


(c) Derive an expression for the voltage across the resistor

Volts

15


2.2 Determine the conditional values of R for which the output response will be:-

(a) Critically Damped

(b) Over Damped

When or when .

(c) Under Damped

When or when .

(d) Undamped

When .

16


2.3 Simulate the circuit in Task 1 Q 1.1 using Croc Clips or Multisim and obtain a printout of the waveforms for the following voltages :-

(a) Voltage across the resistor

See Task 2.3b Graph (Pink Waveform)

(b) Voltage across the capacitor

See Graph (Red Waveform)

17


2.4 Simulate the circuit in Task 1 Q 1.2 using Croc Clips or Multisim and obtain a printout of the waveforms for the following voltages :-

(a) Voltage across the resistor

See Task 2.4b Graph (Pink Waveform)

(b) Voltage across the inductor

See Graph (Red Waveform)

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2.5 Simulate the circuit in Task 2 Q 2.1 using Croc Clips or Multisim for the condition R = 20

(a) Obtain a printout of the voltage waveform in the time domain across the resistor.

(b) Comment upon the type of waveform.

This waveform is Critical Damping heading towards 0 Volts. This confirms my calculation of 20 Ohms in Task 2.2a to be correct, as the conditional value of R for my Vout response was 20 Ohms.

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EvaluationI managed to get this assignment completed within a day, which was very useful as it enabled me to concentrate on other assignments.For Task 1, I was asked to use Laplace Transforms to analyse the transients in networks. Firstly I had to make a circuit diagram which represented the components at 0Volts, i.e. at the point when the switch was closed. This was made easy from the explanation given to us in class, and the use of existing knowledge from RLC related assignments in the past. Deriving an expression for Vout across the Capacitor and Inductor was simple a case of transposition and using Ohms Law.For Task 1.1 and 1.2 c, I could put the equation I worked out for Vout in the S domain and easily convert it to Vout in the Time Domain.Using Graphmatica to illustrate the waveform was straightforward, and this actually proved as a general check for Tasks 2.3 and 2.4. The Transient Part is the part that is moving, i.e. in transit, the Steady State is the bit that is in the operating voltage, which is the usual working condition of the circuit.I had to do a similar thing for Task 2.1, where I created a circuit diagram of the circuit in the S Domain, derived and expression for current through and voltage across the resistor.Task 2.2 was a simple calculation of the conditional values of the resistor. I was able to understand this from the work I had done in second Science assignment, with regards to mechanical damping as it is a very similar principle in the electrical damping.Task 2.3 and 2.4 were simulation checks of Task 1.1 and 1.2. These showed that the equations I worked out and entered into Graphmatica were correct as the waveform produced from them was identical to those in the simulation.I then also had to simulate Task 2.1 with a known value for the resistor. This value happened to be the same value as I received for Task 2.2a, so I knew that if I was right the waveform produced would be Critically Damped. What I was looking for on the waveform was something that didn’t overshoot 0Volts, but reached the peak voltage and then began an exponential decay down to 0Volts.

ConclusionI felt I managed to complete this assignment quickly but also accurately. I received a result immediately which is different to the start of this course when I used to have to play around with the circuit a lot to get the results required.This shows a definite progress in my understanding of the general working out stages and the application of it to simulation software.This unit as a whole has gone very well for me, and I have enjoyed working on it throughout the year.

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Bibliography

Through guidance from my lecturer, the following text books, catalogues and websites I was able to complete this assignment:

Books

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Catalogues

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Websites

N/A

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btec hnc - electrical and electronic principles - investigate transients in rlc circuits

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