ece65_w13-1-intro_theory

5/24/2018 ECE65_W13-1-Intro_theory

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1. Review of Circuit Theory

Concepts

ECE 65, Winter 2013, F. Najmabadi

Lecture notes: Section 1


2/15

Circuit Theory is an Approximation to

Maxwells Electromagnetic Equations

F. Najmabadi, ECE 65, Winter2013, Intro (2/15)

A circuit is made of a bunch of elements connected with ideal

(i.e., no resistance) wires.

Circuit Theory is an Approximation to Maxwells Electromagnetic

Equations by assuming

o Speed of light is infinite (or dimension of the circuit is much smaller

than wave-length of voltage/current waveforms).

o Electric and magnetic fields are confined within each element:

1) Internal of an element manifests itself as an ivcharacteristic eq.

2) Elements communicates with each other only through the wires!

Since the rest of the circuit only sees the ivcharacteristics of an

element, different physical elements with similar iv

characteristics are identical!


3/15

Linear circuits have

many desirable properties


A linear circuit element has a linear ivcharacteristic equation,Av + B i + C= 0(either in time or frequency domain)

If all elements in a circuit are linear, the circuit would be linear and

has many desirable properties (e.g., proportionality and

superposition) which are essential for many functional circuits.

Circuit theory has symbols for ideal linear elements:

o Five two-terminal elements: resistors, capacitors, inductors,

independent voltage and independent current sources

o Four four-terminal elements: controlled voltage and current sources.

It is essential to remember that the above ideal elements are NOT

representative of physical devices. Rather they are representative

of elements with a certain ivcharacteristic equation.


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Practical elements are only approximated by

ideal circuit theory elements


i

v

i

v

At high enough current, the

resistor burns up

As the current increases,

resistor heats up and its

resistance increases

A Lab resistor can be approximated as an ideal

circuit theory resistor for a range of current or

voltage (identified by its rated maximum power)

Real resistor


5/15

Ideal circuit theory elements are NOT

representatives of physical devices!


Is a symbol for

IsNOT representative

of this


6/15

Ideal circuit theory elements are representative of

elements with a certain ivcharacteristic equation.


Can be approximated

with this

Can be approximated

with this (for small signals)

In fact, in integrated circuit we usually configure transistors

to act as resistors (to save space among other benefits).


7/15

Currents and voltages are circuit variables


Equations governing the circuits are:o Internal of each element:

ivcharacteristic equation of each element: v = f(i)

o How the elements are connected:

KCL: (conservation of charge), and KVL: (topology)

A circuit with N two-terminal element has 2N variables and need

2N equations:

o N ivcharacteristic equation

o N KCL/KVL

Node-voltage (or mesh current) method reduces the number of

equations to be solved by automatically satisfying all KVLs (or

KCLs).

oUse node-voltage methods unless circuit is very simple!


8/15

We will analyze many functional circuits


Two-terminal Networks

Function is defined by the iv

equation

Two-port Networks

Function is defined by the

transfer function (e.g., vointerms of v

i)

If the network only contains linear elements, its function can be characterized

by several parameters (or numbers) instead of an algebraic function


9/15

A linear two-terminal network can be

represented by its Thevenin Equivalent


Thevenin Theorem: If all elements inside a two-terminal network are

linear, the ivequation of the two-terminal network would be linear:

Av + B i + C= 0

o A linear two-terminal network can be modeled with two ideal circuit

theory elements (vT

= C/A, RT

= B/A)

o If the two-terminal network does NOT contain an independent source,

vT= 0and it reduces to a resistor.

o See Lecture note for examples of computing/measuring Thevenin

equivalent circuit

iRvvTT

=


10/15

A Functional circuit contains several two-

terminal and two-port networks


Two-terminal network

containing an

independent source

Two-terminal network

containing NO

independent source

We divide the circuit into building blocks to

simplify analysis and design


11/15

Source only sees a load resistor


A two-terminal network containing NO

independent source

We only need to analyze the response of

a source ONCE with RLas a parameter.

For a linear source, we only find the

Thevenin parameters of the source.


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Two-port network


A two-terminal network containing

NO independent source

Transfer function of a two-port network can

be found by solving the above circuit once.

A two-terminal network

containing AN independent source


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Accuracy

Mathematical precision is neither possible

nor required in practical systems!


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Accuracy (or tolerance) in practical systems


Measurement Accuracy:

o Measuring instruments have a finite accuracy.

o When a scope with an 2% read a voltage of 1.352 V, it means that the real

voltage is in the range of 1.352 0.02 1.352 (or between 1.325 and 1.379 V).

Component Accuracy:

o Components are manufactured with a finite accuracy (tolerance).

o A 1k resistor with 5% accuracy has a resistance between 0.950 and 1.050k.

Modeling Accuracy

o We approximate practical circuit elements with ideal circuit theoryelements. (we will see this throughout the course for non-linear elements)

Analysis Accuracy:

o We make approximation in the analysis by ignoring terms. (next Slide)


15/15

How accuracy affect analysis:

F Najmabadi ECE 65 Winter2013 Intro (15/15)

When a number has,A, has a relative accuracy of , it means thatits value is betweenA(1 ) andA(1 + ).

Alternatively, we are saying that all numbers in that range are

approximately equal to each other.

When we assume a

ece65_w13-1-intro_theory

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linear circuit element

ideal elements

integrated circuit

circuit variablesf

terminal elements

ideal linear elements

representativeof elements

practical elements