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Passive components and circuits - CCP
Lecture 2
Introduction
1 /44
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 [kWh].
 For additional information:
http://scienceworld.wolfram.com/
http://www.megaconverter.com/Mega2/
4 /44
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 A
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 A
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.
element
de circuit
Circuit element
B
vAB
elementelement
de circuit
Circuit
B
i
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Conventional directions
Rule of receptor
circuits
i
A
elementelement
de circuit
Circuit
B
vAB
i
Rule of source
circuits
A
element element
de circuit
Circuit
B
vAB
7 /44
Generators and loads
 If the current and voltage arrows point into the
opposite direction (corresponding to the real situationthe 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.
p(t )  v(t )  i (t )
Pmed
1
  v(t )  i (t )dt
TT
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
symbol of the generated waveform
V1
V
I
I1
Ideal voltage source symbol
Symbols for generated
waveforms
V2
I2
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.
RO
A
A
V
B
Model of real voltage
source
I
B
RO
Model of real
current source
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Electrical voltage generators
Laboratory sources
Battery
Photovoltaic cells
9V
1.5 V
Few volts
Electrical plant
13,500 V
Some milivolts
Nerves
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Laboratory voltage source
Voltage up to 10 V
Voltage regulation
Red (+) and
Black (-)
Are equivalent with a battery
terminals
Important:
Earth-protection
The voltage is measured between two points
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Voltage measurement
The voltages are measured with a multimeter
 The voltage range will be set
 The red terminal is
connected to V
+2.62
volts
 The black terminal is connected
to COM (common)
 Read the voltage
I COM V
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Exercise
We set the voltage
source at 3.2 V.
What will be displayed
on the multimeter?
–3.2
V
Answer: –3.2 V
I COM 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/
21 /44
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 values
vO
1
VO    vO (t )dt
T T
vo  vO  VO
1 2
Vo 
vo (t )dt

TT
An output voltage
Its medium value in a period T
Instantaneous value of
variable component
The rms (root mean square)
value (effective value) of variable
component
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Example
VO  1,5 [V]
vo  A  sin t  A  sin 2πft  A sin
2π
t  1 sin 2000πt [V]
T
vO  vo  VO  1,5  sin 2000πt [V]
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Typical signals for electronics systems
Rectangular signal
B; t  [ pT ; pT  kT ]
v(t )  
 A; t  [ pT  kT; ( p  1)T ]
Vmed  kB  (1  k ) A
v
A
0
pZ
kT
T
t
B
25 /44
Other signal shapes
v
A
B
t
Trapezoidal signal
t
Triangular signal
0
v
A
0
B
v
A
0
Saw-tooth signal
t
B
26 /44
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
RBAT
Switch
v
BAT
R
L
LL
Lamp
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.
28 /44
Correspondence between electrical
diagram-equivalent circuit
Components
interconnected by
wires
branch
Multiple node
Simple node
nodes
Circuit elements
Multiple 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.

30 /44
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
?
31 /44
What is “earth ground”?

Connections of equipment to
the earth serve for protection.
R1
V

Theoretically, the current
through the earth conductor is
not zero only in a fault case.

The earth connection doesn’t
affect the circuit operation.
I
R2
32 /44
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.
e1
i1
v1
vs
es
i2
e2
i3
v2
e3
33 /44
Uniport, diport, multiport
 Terminals -The access
points of a circuit;
Supply Port
 Port (gate) – a pair of
terminals (the input
current must be equal
with the output current);
Input port
 Uniport – a circuit with a
single port;
 Diport, triport, multiport ....
Terminal
i
v
I
i
I
i
I
Electronic circuit
i
O
v
O
O
Otput Port
Test Port
34 /44
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.
35 /44
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
36 /44
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!
37 /44
Ohm’s law

The voltage across a resistor
is equal with resistance
multiplied with the value of a
current through resistor.
v
AB
A
B
i
R
vAB  R  iR
R
38 /44
Ohm’s law – equivalent forms
 From the mathematical point of view, the Ohm’s law
can be written under other two forms.
v
AB
A
B
i
R
R
v AB
v AB
v AB
 R  iR  iR 
R
R
iR
39 /44
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.
A
R1
R2
B
A
Rech
B
Rech  R1  R 2
Rech  R1; Rech  R 2
40 /44
Voltage divider
 By connecting two resistances in series, the voltage across
each one is a part of voltage between AB terminals:
V
AB
A
R1
V
R1
R2
V
B
R2
R1
R2
VR1 
VAB ; VR2 
VAB ;
R1  R 2
R1  R 2
41 /44
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:
R1
B
A
R2
Rech
Rech
A
Rech
B
R1 R 2
 R1 R 2 
R1  R 2
 R1; Rech  R 2
42 /44
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:
I
AB
I
R1
R1
B
A
R2
I
R2
R2
R1
I R1 
 I AB ; I R 2 
 I AB ;
R1  R 2
R1  R 2
43 /44
Homework
e2
 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.
e6
e1
e5
e4
R2
e7
V1
R1
C1
R3
C2
e3
e2
e1
e2
e4
e3
e5
e6
e5
e1
e3
e6
e4
C2
V1
C1
R1
R3
C2
V1
C1
R1
R2
R3
R1
C1
V1
R1
C2
C3
R2
C3
R2
R2
C1
C3
C2
C4
C5
V1
R3
R4
44 /44