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Passive components and circuits - CCP

Lecture 2

Introduction

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Index

Electrical quantities Ideal and real sources Electrical signals Electrical circuits topology Transmittances Ohm’s law

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Electrical quantities Electrical voltage is equal with the differences between

electrical potential of two points. Is measured in Volts [V]. It is denoted with u or v. The voltage appears between component terminals.

The electrical current represents an electrical charge flow. It is measured in Amps [A]. A current equal with 1A represents the flow of a 1 Coulomb charge through a conductor on a 1s period. The current is denoted with i.

The electrical current appears only in conductors.

The current appears in a circuit only if we have a conductive loop.

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Electrical quantities The multiplying of voltage and current represents

the electrical power. It is measured in Watts [W]. The power distributed or absorbed by a circuit in

time unit is called electrical energy. It is measured in Joules [J]. In measuring of energy distributed by power grid we use [kWh].

For additional information:

http://scienceworld.wolfram.com/

http://www.megaconverter.com/Mega2/

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Conventional directions for voltages and currents The conventional direction for electrical

voltage between two points is from higher to lower potential.

The conventional (positive) direction of the electrical current is the direction of positive-charged particles flow, producing the same effect as a flow of negatively charged particles (electrons), representing the actual current flow.

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Conventional directions for voltages and currents

Prior to the analysis of an electric circuit, the conventional directions of the currents in the circuit are not known.

So, before writing the equations (Kirchhoff’s laws) for each loop, a positive arbitrary direction is selected for each branch of the circuit.

After performing the analysis of the circuit, if the value of the current is positive, the arbitrary and conventional directions of the current flow are identical. If the value of the current is negative, the conventional direction is opposite to the arbitrary selected direction.

elem ent de circuitA B

vAB

elem ent de circuitA B

i

Circuit element

Circuit element

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Conventional directions

Rule of receptor circuits

Rule of source circuits

elem ent de circuitA B

vAB

i

elem ent de circuitA B

vAB

i

Circuit element

Circuit element

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Generators and loads

If the current and voltage arrows point into the opposite direction (corresponding to the real situation-the calculated power is positive) the power is generated (delivered). For example, it is obvious that in the case of resistors the power is only consumed.

)()()( titvtp

T

med dttitvT

P )()(1

Instantaneous power

Average power

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Ideal sources Applying some electrical quantities in the circuit can

be symbolized using some circuit elements called voltage or current sources. An ideal voltage source will always maintain the

voltage across its terminals at the voltage indicated, regardless of the value of the current at its terminals.

An ideal current source will always pass the indicated current out of the positive terminal and this current will return to the source at the negative terminal, regardless of the value of the voltage across its terminals.

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Symbols for ideal sources

Sometimes, next to the source symbol can be found the Sometimes, next to the source symbol can be found the symbol of the generated waveformsymbol of the generated waveform

Symbols for generated waveforms

I2

V1

I1

V2

V I

Ideal voltage source symbol Ideal current source symbol

Others standardized symbols

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Important remarks! It is forbidden to connect in parallel ideal voltage sources. It is forbidden to connect in series ideal current sources. It is forbidden to connect in short-circuit an ideal voltage

source. The term short-circuit means that the impedance between the terminals is zero. If we connect in short-circuit an ideal voltage source, the current flowing would be infinite.

It is forbidden to let the ideal current source in open circuit. The term open circuit means that the impedance between the terminals is infinite. If the terminals of an ideal current source are in open circuit, the voltage across its terminals would be infinite.

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Real sources model A real (practical) voltage source has an internal resistance,

Ro, in series, desirable to be very small (aiming to zero). A real (practical) current source has an internal resistance,

Ro, in parallel, desirable to be very high (aiming to infinite). AB port is output port and Ro is internal resistance.

V

Model of real voltage source

I

Model of real current source

AA

BB

RO

RO

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Electrical voltage generators

Battery

Electrical plant

Laboratory sources

Nerves

1.5 V

9 V

13,500 V13,500 V

Few volts

Photovoltaic cells

Some milivolts

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Laboratory voltage source

Important: The voltage is measured between two points

Voltage up to 10 V

Red (+) andBlack (-) Are equivalent with a batteryterminals

Voltage regulation

Earth-protection

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Voltage measurementThe voltages are measured with a multimeter

I COM V

volts

The red terminal is connected to V

The black terminal is connected to COM (common)

Read the voltage

The voltage range will be set

+2.62

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Exercise

We set the voltage source at 3.2 V. What will be displayed on the multimeter?

I COM V

–3.2 V

Answer: –3.2 V

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Electrical signal

A variable quantity, that carries information is called signal.

If the variable physical quantity does not carry information it is called noise.

In electric circuits, two types of electrical signals are presented: voltage current

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Symbols for electrical signals Any signal is denoted by letter symbol and one or

more indices. Letters and indices have a double significance:

By name of the letter By letter character (capital or low case letter)

vo .... ? Vo .... ?

vO .... ? VO ... ?

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Significance of letter name The signals are symbolized with the corresponding

letters: i or I for the intensity of the current and v or V for voltages

The letters are accompanied by indices (subscript letters) suggesting the measuring conditions or position in the circuit for those measurements (average value, maximum etc).

Example: I or i indices means input, and o or O means output.

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Significance of letter type

Capital letter symbols, such as I, U, P indicate a constant value in time (direct current regime) or a characteristic value of the variable signal (maximum, medium, effective).

Low case letters used as symbols u, i, p denote an instantaneous value of an electrical magnitude, variable in time.

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Significance of indices letter type Capital letter at indices means a total value. Low case letter at indices means a value of a

variable component of signals.

In case of editing text, italic, bold, roman have standardized signification. For more information visit:

http://physics.nist.gov/cuu/Units/

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Examples

vO – Total instantaneous value: combination of low case

letter and capital indices is generic for any type of signal

VO – Total constant value (also called static value or

average value);

vo – instantaneous value of variable components of output

voltage; is equal with difference between total instantaneous value and static value.

Vo – effective value (root mean square value ) of variable

components of output voltage

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Medium, instantaneous and rms Medium, instantaneous and rms valuesvalues

Ov

dttvT

VT )(

1OO

OOo Vvv

T

dttvT

V )(1 2

oo

Its medium value in a period T

An output voltage

Instantaneous value of variable component

The rms (root mean square) value (effective value) of variable component

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Example

]V[π2000sin5,1

]V[π2000sin1π2

sinπ2sinsin

]V[5,1

OoO

o

O

tVvv

ttT

AftAtAv

V

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Typical signals for electronics systems

ZpTpkTpTtA

kTpTpTtBtv

])1(;[;

];[;)(

t

v

0

A

B

TkT

AkkBVmed )1(

Rectangular signal

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Other signal shapes

Trapezoidal signal

Triangular signal

Saw-tooth signal

t

v

0

A

B

t0

v

A

B

t0

v

A

B

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Topology of electrical circuits The interconnection of a set of electrical/electronics components is called

network or an electrical/electronics diagram. By replacing of components with circuit elements (that describe the electrical

properties of components) we obtain the equivalent electrical/electronic circuit. Each element type is characterized by its function between voltage and current.

Battery

Lamp

SwitchR R

L

B AT L

LvB AT

Electrical diagram Equivalent electrical circuit

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Topology of electrical circuits In practice, the electrical components are interconnected with

wires, conductors, tracks on PCB etc.

The circuit elements from equivalent circuits are interconnected with nodes. Nodes can be simple (when only 2 elements are interconnected) or multiple (when more than 2 elements are interconnected).

The route of current between 2 nodes is called circuit branch.

If each component has a single circuit element as model, then the electrical diagram and the equivalent circuit are identical.

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Components interconnected by wires

Correspondence between electrical diagram-equivalent circuit

branch

nodes

Circuit elements

Multiple node

Multiple node

Simple node

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What is “ground”? The ground of any circuit is a

common reference point, from which all the circuit voltages are measured.

Theoretically, the choosing of the ground point is relative. The position of the ground point doesn’t influence the circuit operation.

The ground point is chosen in the node where the greatest number of branches are convergent.

Practically, it is important where the ground point is positioned.

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Circuit ground

In a circuit, there can be defined a number of ground points: analog ground, digital ground, power ground etc.

The different ground points can be galvanic isolated or not.

Symbols for ground ?

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What is “earth ground”?

Connections of equipment to the earth serve for protection.

Theoretically, the current through the earth conductor is not zero only in a fault case.

The earth connection doesn’t affect the circuit operation.

R1

R2VI

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Series and parallel connections Two or more circuit elements are connected in

series if the same current flows through them. Two or more circuit elements are connected in

parallel if they have the same voltage across them.

i1

i2 i3

v1

vs

v2es

e1

e2 e3

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Uniport, diport, multiport Terminals -The access

points of a circuit; Port (gate) – a pair of

terminals (the input current must be equal with the output current);

Uniport – a circuit with a single port;

Diport, triport, multiport - ....

Electronic circuit

T erm in a l

In p u t p o r t O tp u t P o rt

T es t P o rt

S u p p ly P o rt

iI

iI

iO

iO

vI

vO

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Limit operating situations for a gate (port) Open circuit - the impedance between the terminals

is infinite, the current is zero and the voltage reaches the maximum value;

Short-circuit - the impedance between the terminals is zero, the voltage is zero and the current reaches the maximum value.

The two extreme situations are dual.

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Transmittances Transmittance – the ratio between two electrical

signals Non-dimensional – the signals are the same type; Dimensional (immittance) – one signal is voltage and

other signal is current Impedance – voltage/current (are denoted with R and

are measured in ohms – ) Admitance – current/tvoltage (are denoted with G and

are measured in siemens – S) Immittances defined in DC are called:

impedance resistance admittance conductance

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Transfer transmittances Are transmittances defined between signals from different

gates.

If these two gates are one input and the second one output, then: Direct transmittance output signal/input signal Reverse transmittance input signal/output signal

Important: Reverse transmittance does not represent the mathematical inverse function of direct transmittance!

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Ohm’s law

The voltage across a resistor is equal with resistance multiplied with the value of a current through resistor.

RAB iRv R

A B

vAB

iR

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Ohm’s law – equivalent forms

From the mathematical point of view, the Ohm’s law can be written under other two forms.

R

ABABRRAB i

vR

R

viiRv

R

A B

vAB

iR

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Series connection of resistances By a series connection of two resistances it is

obtained an equivalent resistance equal with the sum of those two resistances.

R 1 R 2 R echA AB B

2;1

21

RRRR

RRR

echech

ech

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Voltage divider

By connecting two resistances in series, the voltage across each one is a part of voltage between AB terminals:

R 1 R 2A B

VAB

VR1

VR2

;21

2;

21

1ABR2ABR1 V

RR

RVV

RR

RV

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Parallel connection of resistances By parallel connection of two conductance, the value of

equivalent conductance is equal with the sum of those two conductances. For resistances:

2;121

2121

RRRRRR

RRRRR

echech

ech

R echA B

R 1

R 2A B

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Current divider By connecting two resistances in parallel between AB

terminals, the current through each resistance is a part of current that flows between AB terminals:

;21

1;

21

221 ABRABR I

RR

RII

RR

RI

R 1

R 2A B

IAB

IR1

IR2

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Homework

Write the mathematical form of signals presented in slide 26.

For each signal, determine the average value on a period.

For the following circuit, determine the elements connected in series and elements connected in parallel.

e2

e1

e3

e4

e6

e7e5

R1

R2

R3C2C1V1

R1

C2

C1V1

R3

R1 R3C2C1V1

R2

R2C3

e1 e6e4e2 e5e3 e1 e6e4

e2 e5

e3

C2C1

V1

R1 R2

C3 C5V1

R3 R4

R1 R2

C1

C2

C3

C4