Basic circuit theory

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ST07 – Basic circuit theory

Basic circuit theory

Lecturer:Smilen Dimitrov

Sensors Technology – MED4

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Introduction

• The model that we introduced for ST

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Introduction

• We have discussed

– The units of voltage, current and resistance, in terms of electric circuits

– The definition of an elementary electric circuit

– Ohm’s law

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Resistors

• Construction of resistors– Different sizes for different power ratings

• As far as construction of resistors goes, generally we can discern – Carbon Composition Resistors– Film Resistors

• Carbon Film Resistors• Metal Film Resistors• Metal Oxide Resistors

– Wire Wound Resistors

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Resistors – color code

• Ratings of resistors – written as color code

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• Electrical circuit is a mathematical model that approximates the behavior of an actual electrical system. Circuit theory [consists of] models and mathematical techniques

• Circuits (also known as 'networks') are collections of circuit elements and wires.

• Electric circuits will be considered as graphs of two types of elements: nodes and branches. The branches, which are electric components like resistors and voltage sources, connect the nodes, which can be viewed as representatives of voltage potentials.

• Circuit analysis is concerned with the computation of voltages and currents in a circuit for a certain excitation. There are various methods for equation formulation for a circuit. These are based on three types of equations found in circuit theory:– equations based on Kirchhoff's voltage law (KVL),– equations based on Kirchhoff's current law (KCL), and– branch constitutive equations.

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• Solving a set of equations that represents a circuit is straightforward, if not always easy. However, developing that set of equations is not so easy.

• The two commonly taught methods for forming a set of equations are the node voltage (or nodal) method and the loop-current (or mesh) method.

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• Conventions – schematics

• While analysing a state of a circuit, one also writes the direction of current and the polarity of voltage in a schematic

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• Marking voltage

• Technical and real direction of current

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• Active and passive convention: the elements within a circuit will either: control the flow of electric energy or respond to it.

• Open and Closed Circuits

• 'Shorting' an element

• Kirchhoff's laws are expressions of conservation laws: in physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. A partial listing of conservation laws that are said to be exact laws, or more precisely have never been shown to be violated.

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1st Kirchhoff (current) law - KCL

• Statement of the law of conservation of charge – “what goes in, must go out”

• Or in particular – the sum of currents going in and out of a given node, is always equal to zero.

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2nd Kirchhoff (current) law - KVL

• Statement of the law of conservation of energy

• The directed sum of the voltages (electrical potential differences) around a circuit (loop)must be zero.

• Sum of voltages around every closed loop in the circuit must equal zero. A closed loop has the obvious definition: Starting at a node, trace a path through the circuit that returns you to the origin node.

• An element's voltage enters with a plus sign if traversing the closed path, we go from the positive to the negative of the voltage's definition.

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Ohms law and equivalence principle (Thevenin)

• Ohms law here is the branch equation for a resistor:

• Equvalence principle - Thevenin theorem – for resistive circuits, it is possible that circuits are represented through an equivalent circuit – a ”black box”

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Measurement

• Voltmeter is connected ”across” two points, ampermeter is connected ”through” a point

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Elementary electric circuit

• Simplest to solve using circuit theory:

• Output voltage is simply equal to input voltage !

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Series connection – the voltage divider

• Our basic circuit in this course.

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Series connection – the voltage divider

• Our basic circuit in this course.

21 RR

EI

21

2

21222 RR

RE

RR

ERIRU

The output voltage U2

is the input voltage E,

divided by 2

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R

RR

The input voltage E

is divided in two output

voltages U1 and U2

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Equivalent resistance of series connection

• What does the power supply E ”see”?

• The equivalent resistance for resistors in series is, as a value, always dominated by the biggest resistor in the sum

eqR

E

RR

EI

2121 RRReq

N

iNeq RiRRRR

121 ...

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Parallel connection – current divider

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Parallel connection – current divider

111 IREU 222 IREU

->021 III 21 III

21

21

212

2

1

121

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RR

RRE

RRE

R

U

R

UIII

The input current I

is divided in two output

currents I1 and I2

The output voltage is the same as the input voltage !

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Equivalent resistance of parallel connection

• What does the power supply E ”see”?

• The equivalent resistance for resistors in parallel is, as a value, always dominated by the smallest resistor in the parallel combination.

eqR

E

RR

RR

EI

21

21 21

2121 || RR

RRRRReq

N

iNeq RiRRRR 121

11...

111

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Combined connection

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Combined connection

RIHRR

RIHR

RR

III

UU

UUE

21

2

21

RIHIHRIH

RR

RR

IRU

IRU

IRU

222

111

To solve the circuit (find all the currents and voltages, we must set a system of 6 equations, using Kirchoff Laws and brach equations (Ohms law).

IH

o

RRR

EV

111

21

The output voltage will be:

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Combined connection

Easier way to solve the circuit:

The output voltage will be:

IH

IHIHP RR

RRRRR

2

22 ||

Find equivalent parallel resistance

IH

IH

IH

IH

P

P

RR

RRR

RR

RR

ERR

REV

2

21

2

2

10

And solve a voltage divider....

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Combined connection

• Important – when Rih is almost infinite; simulates a connection of a voltage divider to the data acquisition (Arduino)!

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Analysis methods

• Just a mention of two analysis methods for solving complicated circuits:

– Node Voltage Method (Nodal analysis)

– Loop Current Method (Mesh current analysis)

Basic circuit theory

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