Electric Circuit and Electron Device–Unit 1 - Version 2 Lectures

Anna University

Electric Circuit and Electron Device

UNIT-I – Version 2

CIRCUIT ANALYSIS TECHNIQUES


INTRODUCTION

Circuit Definitions

• Node – any point where 2 or more circuit elements are connected together

– Wires usually have negligible resistance

– Each node has one voltage (w.r.t. ground)

• Branch – a circuit element between two nodes

• Loop – a collection of branches that form a closed path returning to the same node without going through any other nodes or branches twice

• Voltage-current characteristic of ideal resistor:

clip_image002_thumb_thumb v(t) = R × i(t)

• A Node is a point of connection between two or more circuit elements

• Nodes can be “spread out” by perfect conductors

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Ki rcho ff’s Current Law (KCL)

• The algebraic sum of all currents entering (or leaving) a node is zero

• Equivalently: The sum of the currents entering a node equals the sum of the currents leaving a node

• Mathematically: 1_thumb_thumb

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• When applying KCL, the current directions (entering or leaving a node) are based on the assumed directions of the currents

• Also need to decide whether currents entering the node are positive or negative;

this dictates the sign of the currents leaving the node

• As long all assumptions are consistent, the final result will reflect the actual current directions in the circuit

Kirchoff’s Voltage Law (KVL)

· The algebraic sum of all voltage differences around any closed loop is zero

· Equivalently: The sum of the voltage rises around a closed loop is equal to the sum of the voltage drops around the loop

· Mathematically:

2_thumb_thumb

· Voltage polarities are based on assumed polarities

· If assumptions are consistent, the final results will reflect the actual polarities

· The algebraic sum of voltages around each loop is zero

· Beginning with one node, add voltages across each branch in the loop (if you encounter a

+ sign first) and subtract voltages (if you encounter a – sign first)

· Σ voltage drops - Σ voltage rises = 0

· Or Σ voltage drops = Σ voltage rises

NETWORK THEOREMS

• This chapter introduces important fundamental theorems of network analysis. They are the

• Superposition theorem

• Thevenin‟s theorem

• Norton‟s theorem

• Maximum power transfer theorem

Superposition Theorem

_ Used to find the solution to networks with two or more sources that are not in series or parallel.

_ The current through, or voltage across, an element in a network is equal to the algebraic sum of the currents or voltages produced independently by each source.

_ Since the effect of each source will be determined independently, the number of networks to be analyzed will equal the number of sources.

_ The total power delivered to a resistive element must be determined using the total current through or the total voltage across the element and cannot be determined by a simple sum of the power levels established by each source.

Théven in ’s Th eorem

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_ Any two-terminal dc network can be replaced by an equivalent circuit consisting of a voltage source and a series resistor.

Thevenin’s Theorem can be used to:

_ Analyze networks with sources that are not in series or parallel.

_ Reduce the number of components required to establish the same characteristics at the output terminals.

_ Investigate the effect of changing a particular component on the behavior of a network without having to analyze the entire network after each change.

Procedure to determine the proper values of RTh and ETh

Preliminary

_ Remove that portion of the network across which the Thévenin equation circuit is to be found. In the figure below, this requires that the load resistor RL be temporarily removed from the network.

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_ Mark the terminals of the remaining two-terminal network. (The importance of this step will become obvious as we progress through some complex networks.)

RTh:

_ Calculate RTh by first setting all sources to zero (voltage sources are replaced by short circuits, and current sources by open circuits) and then finding the resultant resistance between the two marked terminals. (If the internal resistance of the voltage and/or current sources is included in the original network, it must remain when the sources are set to zero.)

ETh:

_ Calculate ETh by first returning all sources to their original position and finding the open- circuit voltage between the marked terminals. (This step is invariably the one that will lead to the most confusion and errors. In all cases, keep in mind that it is the open-circuit potential between the two terminals marked in step 2.)

_ Draw the Thévenin equivalent circuit with the portion of the circuit previously removed replaced between the terminals of the equivalent circuit. This step is indicated by the placement of the resistor RL between the terminals of the Thévenin equivalent circuit.

Norton’s Th eore m

Norton‟s theorem states the following:

_ Any two-terminal linear bilateral dc network can be replaced by an equivalent circuit consisting of a current and a parallel resistor.

The steps leading to the proper values of IN and RN.

Preliminary steps:

_ Remove that portion of the network across which the Norton equivalent circuit is found.

_ Mark the terminals of the remaining two-terminal network.

Finding RN:

_ Calculate RN by first setting all sources to zero (voltage sources are replaced with short circuits, and current sources with open circuits) and then finding the resultant resistance between the two marked terminals. (If the internal resistance of the voltage and/or current sources is included in the original network, it must remain when the sources are set to zero.) Since RN = RTh the procedure and value obtained using the approach described for Thévenin‟s theorem will determine the proper value of RN.

Finding IN :

_ Calculate IN by first returning all the sources to their original position and then finding

the short-circuit current between the marked terminals. It is the same current that would be measured by an ammeter placed between the marked terminals.

Conclusion:

_ Draw the Norton equivalent circuit with the portion of the circuit previously removed replaced between the terminals of the equivalent circuit.

Maximum Power Transfer Theorem

_ For loads connected directly to a dc voltage supply, maximum power will be delivered to the load when the load resistance is equal to the internal resistance of the source; that is, when: RL = Rint

The maximum power transfer theorem states the following:

A load will receive maximum power from a network when its total resistive value is exactly equal to the Thévenin resistance of the network applied to the load. That is,

RL = RTh

Series resistors & voltage division

Series: Two or more elements are in series if they are cascaded or connected sequentially and consequently carry the same current.

The equivalent resistance of any number of resistors connected in a series is the sum of the individual resistances N

Req = R1 + R2 + × × × + RN = 3_thumb_thumb

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4_thumb_thumb

Parallel resistors & current division

Parallel: Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them.

The equivalent resistance of a circuit with N resistors in parallel is:

5_thumb_thumb

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Delta -> Star transformation

 

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8th_thumb[3]_thumb

Star -> Delta transformation

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