EI1120, Electric Circuit Analysis

This will be the main website for course-material in EI1120 — Elkretsanalys, KTH Energi och Miljö, Year-2, in VT 2021.

Here you can find an activity plan, lecture notes, homework tasks and solutions, past exams and solutions, etc.

Here are quick links to the topic-files that are lower down this page:
01 (basics),    02 (simplify),    03 (nodal),    04 (theorems),    05 (opamps),
06 (C,L),    07 (equilib),    08 (timefunc),
09 (acintro),    10 (filter),    11 (acpower),    12 (transf),    13 (3ph-bal),    14 (3ph-unbal),    task (3ph-practical).

Subpages

(html) Past Exams (ex-tentor) for practice.

(html) Books for anyone who wants more course literature: here you can also get the pdf file of exercises and solutions from the KTH compendium!



Files and Week-plan (VT 2021)


Week 3

Topic 01 Subject Introduction, Course Information, Circuit Basics
The fascinating world of electric power, and the role of Circuit Analysis.
Administrative details (see also Course Admin page).
Fundamentals: circuit quantities, component definitions, Kirchoff's laws.

The following files are the course-material for this topic. The grey text is used for files that are not considered the core material but just for interest or alternative/additional information.

Focus on the core, that is: the notes, exercises and tutorial questions. It's important to get confident and competent at applying Kirchhoff's and Ohm's laws and calculating power: much of this is about being careful with directions and signs.

Most of the content of this Topic is considered repetition of school subjects, so quite a lot of content has been included (as most of it is not expected to need lots of work). For most later topics there will be rather fewer pages of notes, with less text.

(pdf) repetition-ellära elkretsrepetitionshäfte from ancient course-rounds, including concepts from our Topic 01 and Topic 02: so if you read it, remember some of the content is for the next topic! It's provided partly for Swedish words and partly in case its style suits you better than the other material.

(pdf) intro (18/Jan)   background about 'circuits' as a simplification of 'fields'; see also dimensional analysis on the final two pages!

(pdf) notes (18/Jan)   main content of topic-1, handwritten.

(pdf) exercises (18/Jan)   exercises for self-study / group-study.

(pdf) tutorial-q (19/Jan)   questions for tutorial (övning).
(pdf) tutorial-s (19/Jan)   solutions to tutorial questions.

(pdf) chapter course-material in book-format, which some students considered to have too much text in previous years ... the 'notes' (above) are intended as this year's material, but the old version might be liked by some students as an alternative or complement.

Topic 02 Solving by Successive Simplifications
Simplifying diagrams by re-drawing.
Components that are irrelevant to our solution.
Series and parallel resistors: equivalents, voltage/current division.
Other pairs of components in series or parallel (UU, UI, II, UR, etc).
Source transformation (swap Thevenin/Norton sources).

(pdf) notes (20/Jan)   main content of topic-1, handwritten.

(pdf) exercises (20/Jan)   exercises for self-study / group-study.

(pdf) tutorial-q (21/Jan)   questions for tutorial (övning).
(pdf) tutorial-s (21/Jan)   solutions for tutorial.



(pdf) chapter course-material (old form of notes) used a few years ago

Lab 1 (22-25/Jan 2021) Dividers and Multimeters



Week 4

Topic 03 Systematic methods: nodal analysis
Systematic methods versus simplifications.
Rules for handling nodal-analysis in the general case (good for computer).
Ways to use fewer equations: branches, supernodes.
Combination of simplifications and systematic methods.
The notes are split into two parts: general approach, and special cases of simplifying the work.

(pdf) notes(pt1)   (pdf) notes(pt2)   (25/Jan)

(pdf) exercises for own study (25/Jan)

(pdf) tutorial-q (26/Jan)   questions for tutorial (övning)
(pdf) tutorial-s (26/Jan)   solutions for tutorial



(pdf) chapter course-material (old form of notes) used a few years ago

Topic 04 Circuit theorems: Superposition and Equivalents
The principle of superposition, with multiple sources.
Two-terminal equivalents: Thevenin and Norton.
Maximum power transfer.
The notes are split into their three main parts: superposition, equivalents, maximum-power.

(pdf) notes(pt1)   (pdf) notes(pt2)   (pdf) notes(pt3)   (27/Jan)

(pdf) exercises   (27/Jan)

(pdf) tutorial-q(pt1)   (pdf) tutorial-q(pt2)   (28/Jan)
(pdf) tutorial-s   (pdf) tutorial-s   (28/Jan)



(pdf) chapter course-material (old form of notes) used a few years ago


Week 5

Topic 05 Opamps (operational amplifiers)
Overview and simple model of opamp.
Connection as comparator, or positive or negative feedback.
Simple analysis methods with negative feedback.
Inclusion of opamps within nodal analysis.

(pdf) notes   (1/Feb)
Suggestion/Warning: in this topic, I feel the computer-notes (see 'chapter' below) are better than the handwritten notes. See which you prefer.

(pdf) exercises   (1/Feb)

(pdf) tutorial-q   (2/Feb)
(pdf) tutorial-s   (2/Feb)

For this year we have no homework for Topic 05, as it's not such a core part in Electric Power, and it's good to have time for catch-up and revision.


(pdf) chapter course-material (old form of notes) used a few years ago

KS1 Topics 1--5: direct current

See (pdf) Exams page for former KS1 as examples.

(pdf) KS1 Q+Soln

This KS is not obligatory, but it can replace Section-A (dc) of the exam.
It's also a useful hint about how much you're keeping up with the course.

Topic 06 Capacitor & Inductor, Time-dependence
Capacitor and Inductor: another two fundamental components.
Closing or opening switch, and "unit-step" function.
Simple time-functions with capacitor or inductor.
Combining components, calculating stored energy.

(pdf) notes   (5/Feb)

(pdf) exercises   (5/Feb)

For the tutorial (8/Feb), use some of the Exercises (above).
I suggest Q1{c,g}, Q8, Q11, and perhaps Q9 and Q10.



(pdf) chapter course-material (old form of notes) used a few years ago


Week 6

(See previous week for Monday's tutorial ... it fitted better there.)

Topic 07 Equilibrium and Continuity with Capacitors and Inductors
Equilibrium state with constant sources (if it exists).
Continuous variables, and using continuity in solutions.
Systematic treatment of equilibrium/continuity calculations.

(pdf) notes(pt1) equilibrium   (pdf) notes(pt2) continuity   (8/Feb)

(pdf) exercises   (8/Feb)

(pdf) tutorial-q(pt1)   (pdf) tutorial-q(pt2)   (9/Feb)
(pdf) tutorial-s(pt1) (pdf) tutorial-s(pt2)



(pdf) chapter course-material (old form of notes) used a few years ago

Topic 08 Time-response of first-order circuits
Aim: find a time-function to describe a circuit quantity over some time-period.
We consider circuits with just one independent C or L component, and constant sources.
Use circuit equations to get a differential-equation that we can then solve.
Make use of equivalents (Thevenin/Norton) to simplify calculation.

These notes and tutorial questions are split into two parts: time-functions by solving an ODE; then shortcuts of equivalent circuits and `curve fitting'.
(pdf) notes(pt1)   (pdf) notes(pt2)   (11/Feb)

(pdf) exercises   (11/Feb)

(pdf) tutorial-q   (12/Feb)
(pdf) tutorial-s



(pdf) chapter course-material (old form of notes) used a few years ago


Week 7

Lab 2 Capacitors, Signal-Generators and Oscilloscopes


KS2 Topics 6--8: transient

See (pdf) Exams page for former KS2.

(pdf) KS2 Q+Soln

This KS is not obligatory, but it can replace Section-B (transients) of the exam.
It's also a useful hint about how much you're keeping up with the course.

Topic 09 Introduction to ac (alternating currrent) analysis
Relation to transients and dc; comparison of sinusoidal and other waveforms.
Complex numbers for ac analysis: phasors and impedance.
Solutions with translation between "time-domain" and "frequency-domain".

(pdf) notes   (17/Feb)

(pdf) exercises (17/Feb)

For the tutorial (18/Feb) the following are suggested from the exercises collection and from the exams linked on its first page; other choices can be made. There is no need to try to do all of these: it's probably better with a moderate number, giving time for clear explanation and for participants to do some of the steps. Questions: Q2b | 2014-01 IT tenta Q6a | Q8 | 2013-06 EM omtenta Q6a | 2013-03 EM tenta Q6.



(pdf) chapter course-material (old form of notes) used a few years ago


Week 8

Topic 10 Frequency-response and filters
Frequency-dependence of circuits.
Network functions – an ac form of gain: gain and phase.
Filters made of first-order sections: canonical form of network function.
Second order filters: resonance.
Bode plots, particularly for amplitude.

(pdf) notes   (22/Feb)

(pdf) exercises (22/Feb)

For the tutorial (22/Feb) the suggested exercises are:
  2016-10_IT_omtenta(Q4), 2016-03_IT_omtenta(Q5), 2015-03_EM_tenta(Q7).

There is no homework for Topic 10 this year, in order to give more time to get into 'AC' and to do homework 11.



(pdf) chapter course-material (old form of notes) used a few years ago

Topic 11 Power in ac circuits: nature and definitions
Time-functions of power in ac circuits.
Effective and rms values of phasors or waveforms.
Definitions: complex power, real and reactive power, power factor.
Maximum-power theorem in ac circuits
Power superposition

(pdf) notes   (23/Feb)

(pdf) exercises (23/Feb)

For the tutorial (24/Feb) the suggested exercises are:
  2016-03_IT_omtenta Q6; 2014-08_IT_omtenta Q5, Q6; 2015-03_EM_tenta Q6{b,c}.



(pdf) chapter course-material (old form of notes) used a few years ago

Topic 12 Coupled coils: mutual inductance
Coupled coils, coupling factor, mutual inductance.
The ideal transformer, as a special case of mutual inductance.
Analysis of circuits containing the above components.

(pdf) notes   (26/Feb)  

(pdf) exercises (26/Feb)

For the tutorial (26/Feb) the suggested exercises are:
  2015-03_EM_tenta Q8; 2013-06_E_omtenta Q3; 2015-06_EM_omtenta Q8; 2015-03_E_tenta2 Q6.



(pdf) chapter course-material (old form of notes) used a few years ago


Week 9

Topic 13 Three-phase ac (balanced systems)
Basic concept, advantages, comparison with other numbers than 3.
Some terminology, and common angles and diagrams.
Simplifications by symmetry: 1-phase equivalent of balanced system.

(pdf) notes   (1/Mar)

(pdf) exercises (1/Mar)

For the tutorial (2/Mar) the suggested exercises are:
  2014-05_EM_omtenta Q8,   2016-03_EM_tenta Q9-ab,   Exc.6,   Exc.9 (subset).



(pdf) chapter course-material (old form of notes) used a few years ago

Topic 14 Three-phase power (unbalanced cases)
Unbalanced cases.
Direct calculation by general AC principles.
Calculation taking advantage of partial symmetries.

(pdf) notes   (4/Mar)

(pdf) exercises (4/Mar)

For the tutorial (5/Mar) the suggested exercises are:
  2013-06_E_omtenta Q5;   Exc.3;   Exc.5;   Exc.9;   2016-06_EM_omtenta Q9-bc.
It's thoroughly expected that only the first three or so might be done in the time.

There is no homework in #14, but there is the project-task - see below.

See again topic 13 for the 'Chapter' used in previous years: it includes unbalanced three-phase systems.

Final Project Practical 3-phase calculations by computer
Examples of some three-phase systems in physical form (not just circuit diagram).
Solutions by Octave/Matlab: tips, examples, framework.


Week 10

Project help

A help session for the project task will be available on this Monday (8/Mar): 15:15 in the usual zoom room.

Week 11

TEN1 (Exam)           All topics

See (pdf) Exams page for examples.

(pdf) EXAM:_Q+Soln

Remember that KS1 can replace section A, and KS2 can replace section B, if the KS results are better than the results from those sections in this exam. So if you're happy with what you got in a KS, you can skip the respective section entirely in the exam: potentially you can answer just section C if you did well in both KS.

Good luck!


Week 2x

[OM]TEN1 (Re-exam) All topics

(pdf) RE-EXAM:_Q+Soln

See the section for the main exam, above: the re-exam is intended to have the same rules, level, coverage, available points, etc, as the main exam. The same conditions apply: KS grades from this year can replace the re-exam sections A or B.

Good luck!


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Last change: 2024-01-15