How to Teach the
Analysis
of Electrical Circuits
at Technical Universities
Dalibor Biolek
University of Defence Brno
and
Brno University of Technology
Czech Republic
Lecture Outline
Prerequisities of teaching the analysis
 Heuristic versus algorithmic methods
 The very first things for the very beginners
 The truly basic circuits
 Networks theorems,..
 Special techniques for OpAmp analysis
 Special techniques for OTA analysis
 Solving
more complicated
circuits
on PC
Cultivating
the "Engineering
touch" inside
student's
mind
 Conclusions

Prerequisities of
teaching the analysis

Basics of EE
“The very first things for the very beginners"
Network theorems

Understanding the analyzed circuit





Understanding before analysis
Understanding during analysis
Understanding after analysis
Heuristic versus
algorithmic methods
Heuristic methods of analysis
Teacher:
You need only the K.L. I and II and W's law plus
basic circuit theorems. Analyze the circuit as
you want. No method is prescribed!
Student:
I am confused. It is really more complicated
than if you prescribe me a concrete method.
Teacher:
That's life. Nobody will give you directions how
to solve concrete problems..
Heuristic versus
algorithmic methods
Algorithmic methods of analysis
Teacher:
Here you have an algorithm. It enables the
analysis of various circuits via unified way.
Student:
Great! Now I can correctly solve circuits which I
never understood!
Teacher:
You study them not as your tool but as a tool of
SPICE-like programs.
Summary




Before you teach the analysis: proper
practicing of "very first things for very
beginners" + truly basic circuits (voltage and
current dividers) + network theorems
First heuristic methods, then algorithmic
First linear resistive circuits, then the other
Utilize the knowledge about the circuit for its
proper analysis, and the analysis for better
understanding of circuit behavior
The very first things
for the very beginners
Cultivating the “Engineering Touch" inside student's mind, i.e.
knowledge that electrical circuit operates in such a way that its
behavior
at any
 What
is time
the instance
NODEcannot be in contradiction with
three simple laws of EE.
 What is serial and parallel connection
 phases
Do you
really understand
Ohm's
Two
of cultivating
the “Engineering the
Touch":
Law?
 Orientation of voltages and currents
1] Really deep understanding of W's Law and Kirchhoff's Laws plus
basic
network theorems andthe
methods.
 Understanding
Kirchhoff's Laws
2] Solving many examples, how to use the knowledge from item 1 for
the solution of concrete circuit by creative, "detective" procedures.
The very first things
for the very beginners

What is the NODE
The very first things
for the very beginners

What is serial and parallel connection
The very first things
for the very beginners

Do you really understand the Ohm's Law?
1kW
1V
I=1V/1kW
The very first things
for the very beginners

V
Orientation of voltages and currents
I
V
I
V
I
V
I
The very first things
for the very beginners

Understanding the Kirchhoff's Laws
342mA
V1
15V
Ix=?
0
V3
0
10.29mA
R1
1k
K.L. I
V2
15V
R2
1k
Ix= 10.29mA-342mA=9.948mA
The very first things
for the very beginners

Understanding the Kirchhoff's Laws
K.L. II
Method of potentials
Vx=?
5-(-3)=8V
Vx=8V

5V

-3V
3V
5V
5V
3V
5V
3V

0V
The truly basic circuits



Voltage divider
Current divider
Loaded dividers
Network theorems, ...







The superposition theorem
The substitution theorem
Thévenin and Norton theorems
Equivalence of R-circuits
Equivalence of V and I sources
Wye-delta transfiguration
Extra element theorem
OpAmp Analysis
Prerequisities of the analysis




OpAmp as 5-outlet device + supply sources
DC I/O behavior + important parameters
Golden rules + when they are true
Theory of the DWARF
OpAmp Analysis
Theory of the DWARF
0V

R1 5k
R2
5k
+15V

Vd
0V

1V
I must set Vd = 0
-15V
-1V
OpAmp Analysis
The Golden Rules


The OpAmp input currents are zero
When

OpAmp operates in linear regime
then Vd=0
else
such circuit I cannot analyze so far
OpAmp Analysis
Methods of analysis based on The Golden Rules

Check the negative feedback in the circuit.
If yes, then:


Mark Vd=0 and Iinput=0 directly to the circuit
schematics
Solve the rest of the circuit as you want…
..with the utilization of K.L’s, Ohm’s L., plus creative approach..
OpAmp Analysis
Methods of analysis based on The Golden Rules
All the circuits containing OpAmps can be from one of two groups:
Sequential computing of voltages and currents of individual circuit
components without side-computing, utilizing only K’s L’s +W’s L.


“Single-Stroke” solution
Indirect solution
Method of Potentials
Wye-Delta Transfiguration
Method of the Key Quantity =
= Method of One Attempt and One Mistake
the Extra Element Theorem
Sequential computing of voltages and currents cannot be executed
without side-computing.
OpAmp Analysis
“Single-Stroke” solution
Negative feedback
1]
2]
8] 3]

1V
0A
+15V

6]
10]
0V
1k 2V 1k 1V
1V 1mA


-15V
0A
11]
1V
1V
1k
9]
1V
4]
1V
7] 1mA
12]

2mA
1k
5]
2V
13]
4V
14]

OpAmp Analysis
Indirect solution
1]
2]
0.5V

0A
Negative feedback
+15V
0V
0A
0.5V
3]
-15V
10k
0.5V

?
10k
10k
1k
1k

OpAmp Analysis
Indirect solution - Method of the Key Quantity (1 Attempt+1Mistake)
0.5V

0A
+15V
0V
2.1V
0.5V
-15V
10k
0.1mA
0A
0.5V

1V
0.21mA
1.1V
10k
0.11mA
0.5V0.31V
0.1V1k
0.5V=(50/31)*0.31V
10k
0.21V
1k
0.21mA
3.41V
multiplication
0.31V
OpAmp Analysis
Indirect solution - Method of the Key Quantity (1 Attempt+1Mistake)
0.5V

0A
+15V
0V
2.1V
0.5V
0A
-15V
10k
0.1mA
0.5V

1V
3.387V
10k
10k
10k
0.1613mA
0.21mA
1.1V
10k
*50/31
0.5V

1.613V
0.11mA
0.1V1k
0.21V
1.774V
10k
0.1774mA
1k
1k
0.21mA
3.41V
0.31V
0.3387mA
0.1613V
0.3387V
0.5V
1k
0.3387mA
5.5V
OpAmp Analysis
Indirect solution - Extra Element Theorem (EET)
Si
S
K= o
Si
So
Si
K0 =
S o ,0
S o, 0
Si
Kk =
Si
or
So
S o ,k
Si
1
Z
Si = 0
S o,k
S0 = 0
Si
Z
Zn
1+
Zn
Z =K
K = K0
k
Zd
Z
+
1+
1
Zd
Z
1+
Un
Zd
driving point impedance 2
In
Zn
3
null double injection
OpAmp Analysis
Indirect solution - Extra Element Theorem (EET)
1k
Z
Zn
1+
Zn
Z =K
K = K0
k
Zd
Z
+
1+
1
Zd
Z
1+
1k
1k
8V
1k
-15V
+15V
OpAmp Analysis
Indirect solution - Extra Element Theorem (EET)
1k
Z
Zn
1+
Zn
Z =K
K = K0
k
Zd
Z
+
1+
1
Zd
Z
1+
2V
1mA
Z = 1k
2mA
1k 1mA
1mA 1k
3V
Zd = ?

0V
K0= -1
-15V
Zd = 3kW

1V
8V
1V
+15V
8*(-0.25)
Kk = 0
Zn = 0
-2V
K = -1/(1+3/1)=-0.25
OpAmp Analysis
Indirect solution - Extra Element Theorem (EET)
3V

0A
+15V
3*4/3
4V

0V
3V
-15V
0A
1V
1k
1V
2V
3V

1k
0V

1k
Z=1k
3V
Z
Zn
1+
Zn
Z =K
K = K0
k
Zd
Z
+
1+
1
Zd
Z
1+
K0
Kk=1
Zd
1mA Z =3kW
=?
n
Zn=3kW
1k
K=1(1+1k/3k)=4/3
OpAmp Analysis
Indirect solution - Extra Element Theorem (EET)
Ko
0
Zn  
Kk
K=
Z
1+
Zd
Z
∞ Z d   K = K k (1 + )
Zn
Kk
Zn = 0
K0
K=
Zd
1+
Z
Zd = 0
Zn
K = K 0 (1 + )
Z
OTA Analysis
Prerequisites of the analysis



OTA as 5 (or more) -outlet device + supply
sources
DC I/O behavior + important parameters
Golden rules + when they are true
OTA Analysis
The Golden Rules


The OTA input currents are zero
When

OTA operates in linear regime
then Iout=gmVin
else
such circuit I cannot analyze so far
OTA Analysis
Methods of analysis based on The Golden Rules
Sequential computing of voltages and currents of individual circuit
components without side-computing, utilizing only K’s L’s +W’s L.


“Single-Stroke” solution
Indirect solution
Method of Potentials
Wye-Delta Transfiguration
Method of the Key Quantity =
= Method of One Attempt and One Mistake
the Extra Element Theorem
Sequential computing of voltages and currents cannot be executed
without side-computing.
OTA Analysis
Indirect solution - Method of the Key Quantity (1 Attempt+1Mistake)
-1V

1V
0A
gm1
1mS
1mA
0.5mA
1mA
gm2
0.5mS
gm1
1mA 1mS
gm2
0.5mS
0A 0.2mA
1V
0.5mA
0.5V 0.6mA
2V 1V
1V
0.6mA
1.2mA 0.5V 1k 5k
1mA 1k 5k
*(-0.6/1.2)
Solving circuits on PC
The recommended series of steps




Symbolic analysis via SNAP
PSpice on the level of input files
PSpice on the level of CAPTURE (briefly)
PSpice via Micro-Cap v.9 or higher
Conclusions





From heuristic to algorithmic methods
From resistive to RCL, passive to active,
linear to nonlinear circuits
From DC to other types of analyses
Solving the contradiction: student needs
the analysis for understanding the circuit
and he needs to understand the circuit
prior its analysis  well sophisticated
system of education based on heuristic
approach
Break the established system of teaching
the analysis via OrCad PSpice