Teaching linear circuit
analysis effectively
D. Biolek, V. Biolkova & K. Vrba
Brno University of Technology
Czech Republic
Introduction
Possible techniques of teaching the analysis of
linear circuits are discussed. Three pedagogic
aims are followed: student’s understanding of the
function of the circuit analyzed, ability to solve
moderate circuits algorithmically, and the basic
understanding of the function of professional
circuit simulators as an assumption of their later
effective utilization.
Teaching aims
To promote an engineering way of thinking while
solving electrical circuits, accentuating creative
solutions.
To master the effective tool - algorithm of “hand
and paper” solution of relatively simple circuits.
To understand the principle of modern methods
of circuit analysis used in computer simulators
(and to frame preconditions for mastering them
better).
Analysis methods
Methods of analysis:
heuristic
(creative analysis by using Ohm's and Kirchhoff's laws
(K.Ls) and the fundamental principles of theoretical EE )
algorithmic
with injected creative features
algorithmic (matrix or graph methods).
Analysis methods
Aim No 1 should be pursued by means of heuristic
methods, starting in the opening courses of EE.
However, we must simultaneously break new
ground for the teaching of algorithmic methods.
After understanding the algorithm, its application
always leads to a conclusion. However, utilizing the
algorithm can be "dangerous" because of the
solution being separated from the physical
background of problem solved.
Analysis methods
Algorithmic method with injected creative features:
In the course of analysis it is necessary to decide on
the next procedure. This decision is taken on the
basis of physical consideration.
Analysis methods
How to teach analysis methods:
Instead of clear-cut considerations whether to teach
by the first or the second group of methods, a more
advantageous variant appears: to combine them. In
this symbiosis, each method fulfills its function: the
heuristic method induces physical thinking, the
algorithmic one offers a useful tool of practical
solution.
Algorithmic matrix methods
Methods used in many schools:
Method of state equations.
Method of Kirchhoff’s and Ohm’s Laws.
Method of current loops.
Method of nodal voltages.
Modified nodal analysis (MNA).
Modified Nodal Analysis
Why to teach MNA:
It is implemented in most modern simulators of
analog networks.
It is thus well algorithmized.
It is also suitable for "hand and paper" analysis.
Modified Nodal Analysis
There are numerous MNA variants. Which one
should we concentrate on?
The answer depends again on the teaching aims.
Our choice represents a compromise between the
"transparency", i.e. simplicity, of the algorithm of
equation compilation, and the number of these
equations, i.e. the computation complexity.
Modified Nodal Analysis
Choice between two extremes:
The maximum number of circuit equations
and
a
Optimum for
primitive and "easy-to-remember"“hand-andalgorithm of
their compilation without the necessity
of using
paper” analysis
the creative approach.
The minimum number of circuit equations and a
more complicated algorithm of their compilation,
utilizing the creative approach.
Modified Nodal Analysis
for “hand-and-paper” computation
From the
thepedagogical
point of point
viewof of
view,computational
the optimal
complexity,should
method
the optimal
represent
method
a is
well-balanced
that which
leads to the
compromise
between
minimum
the number
number of circuit
circuit
equations. and the complexity of the algorithm of
equations
their compilation.
Opinions on how to realize this compromise differ
from one teacher to another.
Modified Nodal Analysis
for “hand-and-paper” computation
Number of equations of the standard nodal
analysis is equal to the number of independent
nodes.
Method maintaining the number of equations
(“dead row” method).
Method decreasing the number of equations
(modified two-graph method).
Modified Nodal Analysis
“dead row” method
Equations of the first K.L. will be compiled only
for those nodes to which no voltage source is
connected.
For the node where a voltage source is connected
we write so-called voltage coupling equation.
Modified Nodal Analysis
“dead row” method
Example:
C1
I
R2
R1
3
4
1
A=1
2
C2
V
dead row
V2
V3
V1
 G1
1 G11
 G22
2  G1 G1  G2  sC1
G2  sC 22
 G2
3
A
4
V44

 sC11
1

VV11
VI
VV22

VV33
VV44
dead row
Modified Nodal Analysis
modified two-graph method
Example:
Reduction of
equations due
to uncontrolled
voltage source
C1
I
R2
R1
3
1
4
A=1
2
C2
V
V2
V3
 G2
2 G1  G2  sC1
 G2
G2  sC 2
3
A
4
V4
 sC1
1
V2

V3  
V4
V1
 G1
V.
Modified Nodal Analysis
modified two-graph method
Example:
C1
I
Reduction of
equations due
to controlled
voltage source
R2
R1
3
1
4
A=1
2
C2
V
V2
2 G1  G2  sC1
 G2
3
V3  V4
 G2  sC1
V2
G2  sC 2
V3  V4

V1
 G1 V .
Modified Nodal Analysis
modified two-graph method
Example:
+ 2
1
Antonious
impedance
converter
3
Y1
Y4
4
5
Y2
- +
I
V1  V3  V5 V2
 Y1
1 Y1
3 Y2  Y3
5 Y4  Y5
Y3
 Y2
Y5
V4
V1  V3  V5
 Y3
 Y4
V2
V4
I

.
Conclusions
The choice of a proper type of the taught method
of analysis depends on the pedagogical aims.
In the second
first stage
stage,
of study,
the student
the methods
should acquire
should
helpeffective
an
the student
tool of the
to algorithmic
develop engineering
analysis of
mentality,
circuits
containing
emphasizing
activethe
elements.
creative approach.
We prefer two variants of MNA, in particular the
method of dead row.