Electric Circuits II

Course Objectives: To continue work in Electric Circuits I including the use of the Laplace Transform to determine the time and frequency domain responses of electric circuits.

1.0 Matrix Methods in Network Analysis: (4 Hours)
1.1 Mesh Analysis
1.2 Nodal analysis

2.0 Review of Classical Solution if Ordinary Differential Equations With Constant Coefficients: (5 hours)
2.1 First order differential equations, RL and RC circuits
2.2 General and particular solution
2.3 Initial conditions on L's and C's
2.4 Natural unforced response of LR and CR circuits from initial conditions, time
constant
2.5 Complete transient and steady state response of first order system including
initial conditions and applied forcing functions.

3.0 Complete Time Domain Response of Second and Higher Order System: (5 hours)
3.1 Initial conditions
3.2 Transient and steady state components of response including initial conditions
3.3 RLC resonance, damping factors, high and low Q circuits

4.0 Review of Laplace Transform: (4 hours)
4.1 Definitions and properties valuable for network analysis
4.2 Laplace transform of common forcing functions
4.2.1 Step and shifted step functions
4.2.2 Ramp and impulse functions
4.2.3 Sinusoidal functions
4.3 Real translation and complex translation theorem
4.4 Partial fraction expansion

5.0 Use of Laplace Transform Techniques for Solution of Ordinary Differential Equations with Constant Coefficients: (4 hours)
5.1 Transient and steady-state responses of networks to step, ramp, impulse and
sinusoidal forcing functions with and without initial conditions on L's and C's
5.1.1 First order systems
5.1.2 Second and higher order systems

6.0 Transfer Functions, Poles and Zeros of Networks: (4 hours)
6.1 Concept of complex frequency
6.2 Transfer functions for two part networks
6.3 Poles and zeros of network functions
6.4 Relationship between pole/zero and system time response

7.0 Frequency Response of Networks: (4 Hours)
7.1 Magnitude and phase response
7.2 Bode diagrams
7.3 Band width, high-Q and low-Q circuits
7.4 Basic concept of filters, high-pass, band stop, low and band-pass filters

8.0 Fourier Series and transform: (5 hours)
8.1 Basic concept of Fourier series and analysis
8.2 Evaluation of Fourier coefficients for periodic non-sinusoidal waveforms in electric networks
8.3 Introduction of Fourier transforms

9.0 Two-port Parameters of Networks: (6 hours)
9.1 Definition of two-port networks
9.2 Short circuit admittance parameters
9.3 Open circuit impedance parameters
9.4 Transmission Short circuit admittance parameters
9.5 Hybrid parameters
9.6 Relationship and transformations between sets of parameters
9.7 Applications to filters
9.8 Applications to transmission lines

10.0 State Space Analysis: (4 hours)
10.1 Concept of state and state variables
10.2 State space representation of network equations

Laboratory:
1.0 Transient Response in first Order System Passive Circuits
- measure step and impulse of RC and RL circuits using oscilloscope
- relate time responses to analytical transfer function) calculations
2.0 Transform Response in Second Order System Passive Circuits
- measure step and impulse response of RLC series and parallel circuits using oscilloscope
- relate time responses to transfer functions and pole-zero configuration
3.0 Frequency Response of first and Second Order Passive Circuits
- measure amplitude and phase response and plot Bode diagrams for RL, RC and RLC circuits
- relate body diagrams to transfer functions and pole-zero configuration circuits.
4.0 Electric circuits Simulation Study
- Use SPICE program to simulate circuit and tests carried out in lab 1-3 and compare result from measurement with those from SPICE
5.0 Measurement of Harmonic Content of a Voltage
- Calculate Fourier coefficients for a square wave and variety this by harmonic measurements of a signal form a square wave generator using harmonic analyser.
- Repeat for a half wave rectified wave form using a diode and a resistor

Reference Books:
a) M.E. Van Valkenburg, "Network Analysis", third Edition, Prentice hall, 1995
b) William H. Hayt. Jr. & Jack E. Kemmerly, “Engineering Circuits Analysis", Forth edition, McGraw Hill International, Editions, Electrical Engineering Series, 1987.
c) Michel D. Cilletti, "Introduction to Circuits Analysis and Design", Holt, Hot Rinehart and Winston International Edition, New York, 1988.