homework (circuit theory)

Circuit Theory (EEEN30020)Homework 1
Due by: 11:00AM, Thursday 07 November 2019
Electrical and Electronic Engineering School Office
Engineering and Materials Science Centre, Room 226
Name:_________________________________________
Student number:
2
Corresponding symbols, to be used throughout
this homework set in the places indicated:
For examiner’s use only
Q1 (/10)
Q2 (/5)

Q3(/10)
0
5
6
0
8





Q4(/25)
Total (/50)
Read the following carefully before proceeding:
This cover sheet is to be attached to the front of your submission.
This homework set accounts for 10% of the marks for this module.
Late submissions will be penalised by having marks deducted. No submissions will be accepted after 11:00 am
on Thursday 14 November.
The last six digits of your student number are used to define certain circuit elements in this homework set.
They are indicated by      and , and the correspondence is as given above. Be sure that you enter
these correctly in the appropriate places.
Note that in all questions you must document your method: writing down the right answer with no method
documented will gain you no marks.
When submitting your homework, an individual label containing a unique barcode for this coursework
component will be available in the School office. This label should be attached to the report. The report
should then be scanned using the automated submission system and the homework placed in the box
provided. An email will simultaneously be sent to your UCD account confirming the date and time of your
submission.
Plagiarism and copying are offences under the terms of the Student Code, and you should be aware of the
possible consequences.
Declaration of Authorship
I declare that all material in this assessment is my own work.
Signed____________________________________________ Date___________________
Question 1 (10 marks)
(i)
Find the transmission (ABCD) matrix at frequency  of the two-port in Figure 1(a).
(ii)
Using your answer from (i), or otherwise, find the input impedance at port 1 of the two-port if port 2
is terminated in a (1+)  resistance, again at frequency . By replacing the capacitors and inductor
by their dc steady state equivalents, check your answer at  = 0.
Question 2 (5 marks)
Using your answer from Q1(ii), or otherwise, find the magnitude of the voltage gain |Vo/Vs| as a function of
frequency for the circuit in Figure 1(b).
(2 + 2) H
1
(1 + ) F
(1 + ) F
vs
(a)
(1 + ) F
(2 + 2) H
(1 + ) F
1
vo
(b)
Figure 1
Question 3 (10 marks)
Write the MNA equations that a circuit simulator such as SPICE would produce for the circuit in Figure 3.
Show how the stamps for the (1 + ) S conductance and the CCCS contribute to your equations. Label the
additional node(s), if required, as nodes 5, 6, etc.
Figure 2
Question 4 (25 marks)
A circuit consists of a series combination of a (1+) H inductor, a (1/(1+)) pF capacitor, a 1 kΩ resistor,
and a 5V DC voltage source. The initial inductor current is 0A and the initial capacitor voltage is 0 V.
Derive expressions for the capacitor voltage and inductor current as functions of time.
Use LTspice to plot the capacitor voltage and inductor current for time periods of 10 ns and 100 ns in turn.
Attach copies of your plots with a brief discussion, comparing the simulated behaviour with your analytical
predictions.
LTspice
I