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CH2 CIRCUIT ELEMENTS
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CHAPTER 2 CIRCUIT ELEMENTS
IDEAL ELEMENTS
IDEAL ELEMENTS
Ideal elements: Theoretical elements which are represented by a mathematical expression called "Definition relation"
components (market available) are described by these ideal elements which are the mathematical models.
Independent/dependent Sources
Resistors
Open/short circuit elements
SOURCES
DEPENDENT SOURCES
SOURCES
INDEPENDENT SOURCES
INDEPENDENT SOURCES:
- Could be a power source to run a device
- for example mains connected to a TV set
- Could be information included input signal of a device
- for example antenna input signal of a TV set
Independent voltage source
Theory
Independent voltage
source
Definition relation: Element of which voltage is a known function of (t).
Wherever this element is connected, its voltage do not change.
Although the voltage of an independent voltage source is known,
its current is not known and depends on the circuit it is connected to.
Examples:
DC (Direct-current voltage source) Vs=10 V battery, power;
AC (Alternate-current voltage source) Vs=100 sin (10t+50) V; Mains,
Practice
Mains are independent voltage sources (AC) in our houses. Vs=311 sin (314t+50) V;
Batteries are independent voltage sources (DC) in our lives. Vs=1,5 V battery, power;
Independent current source
Wherever this element is connected, its current do not change.
Examples:
- DC (Direct-current current source):
Is=1,5 A ;
- AC (Alternate-current current source)
Is=5sin (3t+50) A;
This is not a common element (like independent voltage source) at home.
Although the current of an independent current source is known,
- its voltage is not known and
- depends on the circuit it is connected to.
Independent current
source
"Dependent sources" are used in modeling transistor element (component) which is the most common element of electronic engineering.
Model of a component being used in practice is a circuit which composed of ideal elements. This model is used to analyze transistor-included circuits.
Transistor is available in the market and can be bought.
Ideal elements (like dependent sources) are not available in the market and can not be bought but used in mathematical analysis of transistor-circuits.
Dependent sources
Dependent voltage sources
CCVS
VCVS
Dependent voltage sources separated from dependent current sources by the voltage references on them.
There are two types of dependent voltage sources:
Current controlled voltage source Vccvs;
Voltage controlled voltage source Vvcvs.
"ro" and "mu" in the definition relations are element parameters. These parameters depend on chemical and physical structure of the element. Mathematically they are positive real numbers.
Dependent voltage sources
CCVS: Dependent voltage source of which voltage is controlled by another element's current (Ix) within the circuit.
Definition relation is given left side.
Normally Vccvs is not written!
.The current seen in definition relation is not Iccvs !.
VCVS: Dependent voltage source of which voltage is controlled by another element's voltage (Vx) within the circuit.
Definition relation is given left side
Normally Vccvs is not written!.
The voltage seen in definition relation is not Vccvs !.
Dependent current sources
vccs
Dependent current sources separated from dependent voltage sources by the current flow references on them. There are two types of dependent current sources:
CCCS: Current controlled current source
VCCS:Voltage controlled voltage source
Dependent current sources
CCCS: Dependent current source of which current is controlled by another element's current (Ix) within the circuit.
Definition relation is given below left.
Normally Icccs is not written!.
The current seen in definition relation is not Icccs !.
VCCS: Dependent current source of which current is controlled by another element's voltage (Vx) within the circuit.
Definition relation is given below right.
Normally Ivccs is not written!.
The voltage seen in definition relation is not Vccvs !.
RESISTORS
Common element used in electronics
Resistors
IDEAL RESISTOR ELEMENT
Definition relation, V-I relation:
Under the condition that voltage and current references are chosen according to PSC (Passive sign convention):
V(t)=R*İ(t)
R: resistance, element parameter
unit: ohm, [(1/R) conductance, Siemens]
R parameter's value depends on physical dimensions and chemical substance of the element.
Therefore R is a positive reel number.
R=r*l/s
r=specific resistance
l=length
S=cross section
IDEAL RESISTOR ELEMENT
If an element's current and voltage are both seen in its definition relation then this element has a V-I characteristic.
RESISTOR IN PRACTICE
V(t)=R*i(t)
- Third color code shows number of zeros to put to right.
- Last color code on right represents the tolerance percentage.
RESISTORS IN PRACTICE
Black 0
Brown 1
Red 2
Orange 3
Yellow 4
Green 5
Blue 6
Violet 7
Gray 8
White 9
Resistance:R=26 Ohm
26*%2=0.52 tolerance
26-0.52=25.48< R <26+0.52=26.52
OPEN AND SHORT CIRCUIT ELEMENTS
IDEAL ELEMENTS IN THEORY
Short circuit element, definition relation: Vab=0
Current changes depending on the circuit it is connected to.
No relation between its current and voltage. No V-I relation.
Open circuit element, definition relation: İ=0
Voltage changes depending on the circuit it is connected to.
No relation between its current and voltage. No V-I relation.
When a resistor is short-circuited, both its current and voltage becomes (0). That means resistor is removed from the circuit.
When control variable of a dependent voltage source is (0), that means it is short circuited.
When control variable of a dependent current source is (0), that means it is open circuited.
Open and
short
circuit elements
ON/OFF SWITCH THAT WE SEE IN ALL ELECTRICAL DEVICES IN PRACTICE
It is dangerous to short circuit mains in houses (connect a wire between an independent source terminals)
This causes electric shock!
WHY NEED ELEMENT CLASSIFICATION?
Element classification
- see common properties of elements
- grouping circuits according to the elements included in
- Circuit classification determines which mathematical model required to represent the circuit such as
- resistive circuits are mathematically modeled by linear algebraic equations
- linear circuits are mathematically modeled by ordinary differential equations
LINEAR/NONLINEAR ELEMENTS
IF AN ELEMENT DEFINITION RELATION IS LINEAR WITH RESPECT TO CIRCUIT VARIABLES THAN THIS ELEMENT CALLED LINEAR, OTHERWISE ITS CALLED NONLINEAR
Resistor is a linear element
Diode is a nonlinear element
Linear
Nonlinear
Linear elements: Resistors, dependent sources
Derivative and integral operations are linear. Why?
ACTIVE PASSIVE ELEMENTS
IF AN ELEMENT ENERGY IS ALWAYS POSITIVE FOR ANY (t) VALUE THAN THIS ELEMENT IS CALLED PASSIVE,
OTHERWISE IT IS CALLED ACTIVE.
IN OTHER WORDS, AREA UNDER THE POWER FUNCTION Of A PASSIVE ELEMENT SHOULD ALWAYS BE POSITIVE
RESISTOR ELEMENT IS PASSIVE ELEMENT
Active
Passive
INDEPENDENT SOURCES ARE ACTIVE OR PASSIVE? WHY?