Download ST07 – Basic circuit theory Basic circuit theory

Sensors Technology – MED4 ST07 – Basic circuit theory
Basic circuit theory
Lecturer:
Smilen Dimitrov
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ST07 – Basic circuit theory
Introduction
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The model that we introduced for ST
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ST07 – Basic circuit theory
Introduction
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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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ST07 – Basic circuit theory
Resistors
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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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ST07 – Basic circuit theory
Resistors – color code
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Ratings of resistors – written as color code
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ST07 – Basic circuit theory
Basic circuit theory
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•
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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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ST07 – Basic circuit theory
Basic circuit theory
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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.
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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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ST07 – Basic circuit theory
Basic circuit theory
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Conventions – schematics
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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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ST07 – Basic circuit theory
Basic circuit theory
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Marking voltage
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Technical and real direction of current
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ST07 – Basic circuit theory
Basic circuit theory
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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.
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Open and Closed Circuits
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'Shorting' an element
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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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ST07 – Basic circuit theory
1st Kirchhoff (current) law - KCL
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Statement of the law of conservation of charge – “what goes in, must go out”
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Or in particular – the sum of currents going in and out of a given node, is
always equal to zero.
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ST07 – Basic circuit theory
2nd Kirchhoff (current) law - KVL
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Statement of the law of conservation of energy
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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
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the obvious definition: Starting at a node, trace a path
through the circuit that returns you to the origin node.
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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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ST07 – Basic circuit theory
Ohms law and equivalence principle (Thevenin)
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Ohms law here is the branch equation for a resistor:
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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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ST07 – Basic circuit theory
Measurement
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Voltmeter is connected ”across” two points, ampermeter is connected
”through” a point
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ST07 – Basic circuit theory
Elementary electric circuit
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Simplest to solve using circuit theory:
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Output voltage is simply equal to input voltage !
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ST07 – Basic circuit theory
Series connection – the voltage divider
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Our basic circuit in this course.
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ST07 – Basic circuit theory
Series connection – the voltage divider
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Our basic circuit in this course.
I
The input voltage E
E
R1  R2 
is divided in two output
R2
E
U 2  R2  I  R2 
E
R1  R2 
R1  R2
voltages U1 and U2
The output voltage U2
is the input voltage E,
divided by
R1  R2
R2
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ST07 – Basic circuit theory
Equivalent resistance of series connection
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What does the power supply E ”see”?
E
E
I

R1  R2  Req
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Req  R1  R2
N
Req  R1  R2  ...  R N   Ri
i 1
The equivalent resistance for resistors in series is, as a value, always
dominated by the biggest resistor in the sum
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ST07 – Basic circuit theory
Parallel connection – current divider
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ST07 – Basic circuit theory
Parallel connection – current divider
U1  E  R1  I1
U 2  E  R2  I 2
I  I1  I 2  0 -> I  I1  I 2
 1
 R  R2 
U U
1 
  E 1

I  I1  I 2  1  2  E 
R1 R2
R
R
R
R
2 
 1
 1 2 
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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ST07 – Basic circuit theory
Equivalent resistance of parallel connection
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What does the power supply E ”see”?
E
E
I

 R1 R2  Req


R

R
2 
 1
•
RR
Req  R1 || R2  1 2
R1  R2
N
1
1
1
1
1


 ... 

Req R1 R2
RN i 1 Ri
The equivalent resistance for resistors in parallel is, as a value, always
dominated by the smallest resistor in the parallel combination.
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ST07 – Basic circuit theory
Combined connection
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ST07 – Basic circuit theory
Combined connection
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).
 E  U R1  U R 2

 U R 2  U RIH
I  I  I
R2
RIH
 R1
The output voltage will be:
Vo 
 U R1  R1  I R1

 U R 2  R2  I R 2
U
 RIH  RIH  I RIH
E
 1
1 

1  R1 

R
R
IH 
 2
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ST07 – Basic circuit theory
Combined connection
Easier way to solve the circuit:
Find equivalent parallel resistance
RP  R2 || RIH 
R2 RIH
R2  RIH
And solve a voltage divider....
The output voltage will be:
R2 RIH
RP
R2  RIH
V0  E 
 E
R R
R1  RP
R1  2 IH
R2  RIH
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ST07 – Basic circuit theory
Combined connection
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Important – when Rih is almost infinite; simulates a connection of a voltage
divider to the data acquisition (Arduino)!
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ST07 – Basic circuit theory
Analysis methods
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Just a mention of two analysis methods for solving complicated circuits:
– Node Voltage Method (Nodal analysis)
– Loop Current Method (Mesh current analysis)
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