how to teach the analysis of electrical circuits at technical universities dalibor biolek university...

How to Teach the Analysis

of Electrical Circuits at Technical Universities

Dalibor Biolek

University of Defence Brno

and

Brno University of Technology

Czech Republic

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 Conclusions

Lecture Outline

Cultivating the "Engineering touch" inside student's mind

Basics of EE “The very first things for the very beginners" Network theorems

Prerequisities of teaching the analysis

Understanding the analyzed circuit Understanding before analysis Understanding during analysis Understanding after analysis

Heuristic methods of analysis

Heuristic versus algorithmic methods

Teacher:You need only the K.L. I and II and '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..

Algorithmic methods of analysis

Heuristic versus algorithmic methods

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

What is the NODE What is serial and parallel connection Do you really understand the Ohm's Law? Orientation of voltages and currents Understanding the Kirchhoff's Laws

Cultivating the “Engineering Touch" inside student's mind, i.e. knowledge that electrical circuit operates in such a way that its behavior at any time instance cannot be in contradiction with three simple laws of EE.

Two phases of cultivating the “Engineering Touch":

1] Really deep understanding of 's Law and Kirchhoff's Laws plus basic network theorems and methods.

2] Solving many examples, how to use the knowledge from item 1 for the solution of concrete circuit by creative, "detective" procedures.


What is the NODE


What is serial and parallel connection


Do you really understand the Ohm's Law?

1V

1k I=1V/1k


Orientation of voltages and currents

V I V I V VI I


Understanding the Kirchhoff's Laws

15VV1

15V

V2

R11k

R21k

V3

Ix=?

342A

10.29mA

0

0Ix= 10.29mA-342A=9.948mA

K.L. I


Understanding the Kirchhoff's Laws

K.L. II

5V 3V

Vx=?

5V

3V

Vx=8V

5V 3V

0V

5V-3V

5-(-3)=8V

Method of potentials

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

OpAmp as 5-outlet device + supply sources DC I/O behavior + important parameters Golden rules + when they are true Theory of the DWARF

Prerequisities of the analysis

1R

2R

5k

5k

+15V

-15V

Vd

1V

OpAmp AnalysisTheory of the DWARF

I must set Vd = 0

-1V

0V

0V

OpAmp AnalysisThe 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 AnalysisMethods 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 AnalysisMethods of analysis based on The Golden Rules

“Single-Stroke” solution Indirect solution

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 +’s L.

Sequential computing of voltages and currents cannot be executed without side-computing.

Method of Potentials

Wye-Delta Transfiguration

Method of the Key Quantity == Method of One Attempt and One Mistake

the Extra Element Theorem

1k

1k

1k

1k-15V

+15V

1V

OpAmp Analysis“Single-Stroke” solution

Negative feedback

0A

0V

0A

1]

1V

1V

2]

1V

3]

1V 4]1mA

5]

6]

1V

7]

2V

8]

1V9]

1mA

10]

11]

2mA

12]2V

13]

4V

14]

OpAmp AnalysisIndirect solution

Negative feedback

10k

1k

10k

10k

1k

+15V

-15V

0.5V

0A

0V

0A

1]

0.5V

2]

0.5V3]

?

OpAmp AnalysisIndirect solution - Method of the Key Quantity (1 Attempt+1Mistake)

10k

1k

10k

10k

1k

+15V

-15V

0.5V

0A

0V

0A

0.5V

0.5V

0.1mA

1.1V

0.11mA

1V

0.21mA0.21V

0.21mA

2.1V

0.31V

0.1V0.5V0.31V

0.5V=(50/31)*0.31V3.41V

multiplication

10k

1k

10k

10k

1k

+15V

-15V

0.5V

0A

0V

0A

0.5V

0.5V

0.1mA

1.1V

0.11mA

1V

0.21mA0.21V

0.21mA

2.1V

0.31V

0.1V

3.41V

OpAmp AnalysisIndirect solution - Method of the Key Quantity (1 Attempt+1Mistake)

10k

1k

10k

10k

1k

0.1613mA

1.774V

0.1774mA

1.613V

0.3387mA0.3387V

0.3387mA

3.387V

0.5V

0.1613V

5.5V

*50/31

0.5V

OpAmp AnalysisIndirect solution - Extra Element Theorem (EET)

Z

i

o

S

SK oS iS

dZ

oS 0iS

2nZ

nI

nU

iS 00S

3

d

nk

d

n

Z

ZZ

Z

K

Z

ZZ

Z

KK

1

1

1

1

0

or

i

kok S

SK ,

i

o

S

SK 0,

0

iS iS0,oS koS ,

1

driving point impedance

double injectionnull


d

nk

d

n

Z

ZZ

Z

K

Z

ZZ

Z

KK

1

1

1

1

0

8V

1k 1k

1k

1k

+15V

-15V

1k 1k

1k

+15V

-15V


d

nk

d

n

Z

ZZ

Z

K

Z

ZZ

Z

KK

1

1

1

1

0

Z = 1k

8V

K0= -1 Kk = 0

Zn = 0Zd = ?

1mA

1mA

1V

0V

1V

1mA

2mA

2V

3V

Zd = 3k

-2V

8*(-0.25)K = -1/(1+3/1)=-0.25

1k

1k

1k

-15V

+15V

3V


d

nk

d

n

Z

ZZ

Z

K

Z

ZZ

Z

KK

1

1

1

1

0

1kZ=1k K0

0A

0V

0A

3V

3V

Kk=1

Zd

Zn=?

0V

3V

1V

1V

2V

1mA Zn=3k Zn=3k

4V

3*4/3

K=1(1+1k/3k)=4/3


Ko Kk

0

∞

nZ

d

k

Z

ZK

K

1

0nZ

Z

ZK

Kd

1

0

dZ )1(n

k Z

ZKK 0dZ )1(0 Z

ZKK n

OTA Analysis

OTA as 5 (or more) -outlet device + supply sources

DC I/O behavior + important parameters Golden rules + when they are true

Prerequisites of the analysis

OTA AnalysisThe 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 AnalysisMethods of analysis based on The Golden Rules

“Single-Stroke” solution Indirect solution

Sequential computing of voltages and currents of individual circuit components without side-computing, utilizing only K’s L’s +’s L.

Sequential computing of voltages and currents cannot be executed without side-computing.

Method of Potentials

Wye-Delta Transfiguration

Method of the Key Quantity == Method of One Attempt and One Mistake

the Extra Element Theorem

gm2gm11mS

0.5mS

1k 5k

OTA AnalysisIndirect solution - Method of the Key Quantity (1 Attempt+1Mistake)

0.6mA1V

0A

0A

1mA

1mA

1V

-1V

1V

0.2mA

2V

1mA

1mA

1.2mA

gm2gm11mS

0.5mS

1k 5k

0.6mA

*(-0.6/1.2)

0.5mA

0.5mA 1V

0.5V

0.5V

Solving circuits on PCThe 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

how to teach the analysis of electrical circuits at technical universities dalibor biolek university...

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