# E1.1 Analysis of Circuits

Mike Brookes
18 lectures in the Autumn Term

## Aims

To give students an understanding of the laws governing the quiescent, frequency domain and small-signal behaviour of electrical circuits, and the ability to apply this understanding to the analysis and design of circuit behaviour To give students an understanding of the analysis and design of common circuits such as those involving operational amplifiers.

## Learning Outcomes

By the end of the course, a student should understand, and be able to apply to both analysis and design: - the overall process of design, including modelling - component description (resistors and controlled sources) - Kirchoff's Laws - equivalence: Thevenin and Norton models - superposition - nodal analysis - the handling of controlled sources - component description - capacitors and inductors - significance of phase relationships - concept of complex voltages and currents - extension of Kirchoff's Laws to complex voltages and currents - the relevance of linear circuits theorems to frequency-domain behaviour - asymptotic behaviour The Operational Amplifier (opamp) - the characteristics of the opamp - the mathematical operations that can be achieved with opamps - feedback and stability; gain-bandwidth limitations. First-order transients: - passive CR and LR circuits - transients in active circuits. Transmission lines: - forward and backward waves, reflections, standing waves.

## Syllabus

Circuit variables; voltage, current, charge and power Circuit elements Kirchoff's current and voltage laws Nodal analysis for resistor circuits Transient analysis of 1st order RC and RL circuits Superposition Thevenin and Norton theorems Controlled sources Phasors and phasor analysis Transfer functions and Filters Operational amplifier circuits, systematic nodal analysis, Power in AC circuits, Transmission lines.

## Textbook

There are two recommended textbook which both cover broadly similar material:

(1) "Engineering Circuit Analysis" by Irwin, Nelms & Patnaik, Wiley, 11th Ed. 2015. ISBN 9781118960639, £39 [Wiley, Amazon].

(2) "Engineering Circuit Analysis" by Hayt, Kemmerly & Durbin, McGraw Hill, 8th Ed. 2011. ISBN 9780073529578, £48 [McGraw Hill, Amazon]. Out of print but still available.

## Lecture List

1. Introduction and basic concepts [slides, handouts]
2. Resistor Circuits [slides, handouts]
3. Nodal Analysis [slides, handouts]
4. Linearity and Superposition [slides, handouts]
5. Norton/Thevenin Equivalent [slides, handouts]
6. Ideal Op Amps [slides, handouts]
7. Negative Feedback [slides, handouts]
8. Nonlinear Components [slides, handouts]
9. Reactive Components [slides, handouts]
10. Phasors [slides, handouts]
11. Frequency Responses [slides, handouts]
12. Resonance [slides, handouts]
13. Filter Circuits [slides, handouts]
14. Power in AC circuits [slides, handouts]
15. 1st order Transients (Part 1) [slides, handouts]
16. 1st order Transients (Part 2) [slides, handouts]
17. Transmission Lines [slides, handouts]
18. Phasors and Transmission Lines [slides, handouts]

Complete set of handouts (4.6 MB)

## Tutorial Questions

There are four tutorial problems for discussion in tutorials that take place in weeks 4/5, 6/7, 8/9 and 10/11 respectively.

## Problem Sheets

1. Resistor Circuits [probs, solutions]
2. Nodal Analysis, Linearity, Superposition  [probs, solutions]
3. Norton/Thevenin, OpAmps, Diodes  [probs, solutions]
4. Reactive Components and Phasors  [probs, solutions]
5. Filters and Resonance  [probs, solutions]
6. Transformers and Transients  [probs, solutions]
7. Transmission Lines  [probs, solutions]

Complete Set of Problems + Solutions

## Revisions Lectures

1. Nodal Analysis and Frequency Responses [slides, handouts]
2. Transients & Transmission Lines [slides, handouts]

Complete set of Revision Lecture handouts

## Past Exam Papers

Exam format: The exam has three compulsory questions. Question 1 is worth 40% and contains eight parts covering the whole course. Questions 2 and 3 are on a single topic and are worth 30% each.

Note that exams prior to 2009 were based on a slightly different syllabus. In particular, the following topics are no longer included: Two-port parameters (2008:1j), Gaussian elimination (2007:2c), Application areas (2008:3d), Nullators and Norators (2008:4c), Small-signal component models (2008:4e), Gain-bandwidth product (2006:4c), Zener Diodes (2008/9 syllabus).

"Feedback" and "Transmission Lines" were added to the syllabus in 2011; the latter topic was previously included in the Communications syllabus.