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Circuit Analysis using the Thevenin Equivalent and Norton Equivalent

One of the most important analytical tools used in circuit analysis is the Thevenin Equivalent.   The Thevenin equivalent reduces an network of resistors and independent sources into a single resistor and a single voltage sources.   The Thevenin equivalent can be transformed into a Norton equivalent consisting of a single resistor in parallel with a current source.

One simple application of the Thevenin equivalent is to maximize power transfer to a load by matching the load resistance with the Thevenin resistance.

Below is a collection of videos involving the Thevenin Equivalent.

[tubepress mode="tag" tagValue='Thevenin Equivalent drjctu']

Here is an article  that provides more information about electronics that briefly discusses the Thevenin Equivalent  (Reference:  http://www.articlealley.com/basic-electronics-2289057.html)

Basic Electronics

BASIC ELECTRONICS BY JITENDRA CHITNIS (B.E.- Electronics)
INTRODUCTION
As a child I was fond of electronic gadgets like Digital Wrist Watch cum stop watch, Colour Television, FM Radio, Walkman, Calculator and many more gadgets were on my want list. And I was lucky enough to get them for handling and after careful use for a year or two I used to open them for my study. All was possible due to my father, my maternal uncle and other family friends who knew about it. It was real fun to open and study though used to understand very little about the circuit inside.
Slowly when I completed my schooling I joined a Radio, Tape and Television Repairing classes and started understanding the real science and technology involved in these black boxes.
Here in this article I want to give a brief Introduction about the basics of the electronics and knowledge to help beginners or learners about what is the importance of this technology how we can use this knowledge to make a better life out of this.

Definition of Electronics
The branch of science which study the flow of electron through a semiconductors such as silicon or germanium is called electronics.
(Silicon and Germenium are the minerals from the Chart of Chemistry)
Conductors, Semiconductors and Insulators
Conductors
Conductors are nothing but the materials which allow the passage of current very easily. This is because they large number of free electrons available. Examples – Copper, Aluminium.
Insulators
These substances which do not allow the passage of electric current through them. In terms of energy band, the valance band is full while the conduction band is empty.
Semiconductors
Semiconductors are those substances which have conductivity inbetween the Conductors and Insulators. In terms of energy bands valence band is almost filled and conduction band is empty and gap between them is very thin.
Types of Semiconductors
1. P type and trivalent impurity to semiconductor
2. n type pentavalent impurity to semiconductor

pn Junction
When a p type semiconductor is joined to n type semiconductor it forms a pn junction.
Forward and Reverse bias of pn junction.
P type to positive and n type to negative is a forward bias condition of pn junction.
On the other hand if we connect p type to negative and n type to positive it becomes a reverse bias condition for pn junction.
Different semiconductor devices used in common electronic circuit
1. Diode- Use as Rectifier, Regulate current flow direction.

2. Transistors- pnp and npn type. Use as Aplifier, Switch

pnp npn
3. Field Effect Transistor- Use as Switch

4. Thyristor- High Voltage Switches for Power Circuits

5. Integrated Circuits- A composition of Different devices in small space to save space and electric consumption.(It consists thousands of diodes, transistors and resistors, capacitors in small size of 0.5 cm by 3 cm – many different combinations can be built as per requirement)
Other circuit devices
1. Resistor- To resist the current and drop voltage to the required level.

2. Capacitor- To maintain a electric charge at a point in circuit. Use Filteration of Voltage

3. Inductor- To oppose the fluctuating current. Use Filteration of current

BASIC LAWS and THEOROMS FOR LAYMAN
Ohm’s Law
When an applied voltage E causes a current I to flow through an impedance Z, the value of the impedance Z is equal to the voltage E divided by the current I
.
Impedance = Voltage / Current Z = E / I
Similarly, when a voltage E is applied across an impedance Z, the resulting current I through the impedance is equal to the voltage E divided by the impedance Z.
Current = Voltage / Impedance I = E / Z
Similarly, when a current I is passed through an impedance Z, the resulting voltage drop V across the impedance is equal to the current I multiplied by the impedance Z.
Voltage = Current * Impedance V = IZ
Alternatively, using admittance Y which is the reciprocal of impedance Z:
Voltage = Current / Admittance V = I / Y
Kirchhoff’s Laws
Kirchhoff’s Current Law At any instant the sum of all the currents flowing into any circuit node is equal to the sum of all the currents flowing out of that node: Iin = Iout Similarly, at any instant the algebraic sum of all the currents at any circuit node is zero: I = 0 Kirchhoff’s Voltage Law At any instant the sum of all the voltage sources in any closed circuit is equal to the sum of all the voltage drops in that circuit: E = IZ Similarly, at any instant the algebraic sum of all the voltages around any closed circuit is zero: E – IZ = 0
Thévenin’s Theorem
Any linear voltage network which may be viewed from two terminals can be replaced by a voltage-source equivalent circuit comprising a single voltage source E and a single series impedance Z. The voltage E is the open-circuit voltage between the two terminals and the impedance Z is the impedance of the network viewed from the terminals with all voltage sources replaced by their internal impedances.
Norton’s Theorem
Any linear current network which may be viewed from two terminals can be replaced by a current-source equivalent circuit comprising a single current source I and a single shunt admittance Y. The current I is the short-circuit current between the two terminals and the admittance Y is the admittance of the network viewed from the terminals with all current sources replaced by their internal admittances.
Thévenin and Norton Equivalence
The open circuit, short circuit and load conditions of the Thévenin model are: Voc = E Isc = E / Z Vload = E – IloadZ Iload = E / (Z + Zload) The open circuit, short circuit and load conditions of the Norton model are: Voc = I / Y Isc = I Vload = I / (Y + Yload) Iload = I – VloadY Thévenin model from Norton model
Voltage = Current / Admittance Impedance = 1 / Admittance E = I / Y Z = Y -1
Norton model from Thévenin model
Current = Voltage / Impedance Admittance = 1 / Impedance I = E / Z Y = Z -1
When performing network reduction for a Thévenin or Norton model, note that: – nodes with zero voltage difference may be short-circuited with no effect on the network current distribution, – branches carrying zero current may be open-circuited with no effect on the network voltage distribution.
Joule’s Law
When a current I is passed through a resistance R, the resulting power P dissipated in the resistance is equal to the square of the current I multiplied by the resistance R: P = I2R
By substitution using Ohm’s Law for the corresponding voltage drop V (= IR) across the resistance: P = V2 / R = VI = I2R

Electronic students should learn the following units and formulae:
Units
Current (amp)
Resistance (ohm)
Voltage (volt)
Capacitance (farad)

Resistors in Series Rtotal = R1 + R2 + R3 etc.
Resistors in Parallel Rtotal =
or
1/Rtotal =
Time Period Time period = Resistance x Capacitance (T = R x C)
Ohm’s Law Voltage = Current x Resistance
(V = I x R)
Resistance = Voltage / Current
Current = Voltage / Resistance


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