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7/28/2019 Resistor Network

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Chapter 7

Series-ParallelCircuits


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Objectives

Identify series-parallel relationships

Analyze series-parallel circuits

Analyze loaded voltage dividers

Determine the loading effect of a voltmeter on acircuit

Analyze ladder networks

Analyze a Wheatstone bridge


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Identifying Series-Parallel Relationships

A series-parallel circuit consists of combinations ofboth series and parallel current paths.

Series Parallel


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R1 & R4 are in series.

R1,R4 are is series with the parallel circuit R2,R3.


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GroupA: R1 in series with R4, in parallel with R6.Group B: R2 in series with R5, in parallel with R3.

GroupAis in series with Group B.

GroupA

Group B

See Ex. 7.1, 7.2, 7.3, 7.4 & 7.5


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Analysis ofSeries-Parallel Circuits

Objectives:

Analyze series-parallel circuits

Determine total resistance

Determine all currents Determine all voltage drops


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Total Resistance

Identify the parallel resistances, and calculate theequivalent resistance(s).

Identify the series resistances for the circuit.

Sum the series and series equivalent resistances for

RT.

See Ex. 7-6 & 7.7


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Total Current

Using the total resistance and the source

voltage, find the total current by applyingOhms law.

IT

= VS/R

T


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Branch Currents - Kirchoffs Current Law

Using the current-divider formula, Kirchhoffs current

law (KCL), Ohms law, or combinations of these, youcan find the current in any branch of a series-parallelcircuit.

See Ex. 7-8, 7-9.

Kirchoffs Current Law

The sum of the currents into a node (total currentin) is equal to the sum of the currents out of anode (total current out).

**


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Voltage Drops - Kirchoffs Voltage Law

Using the current-divider formula, Kirchhoffs current

law (KCL), Ohms law, or combinations of these, you

can find the current in any branch of a series-parallelcircuit.

See Ex. 7-10, 7-11, & 7-12.

Kirchoffs Voltage Law:

The sum of all the voltages around a single closedpath in a circuit is equal to the total source voltagein that loop.


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Unloaded Voltage Dividers

A voltage divider produces an output which depends

upon the values of the dividing resistors.

This voltage is the unloadedoutput voltage.

This voltage is the loadedoutput voltage.


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Loaded Voltage Dividers

When a load resistor RL is connected from the outputto ground, the output voltage is reduced by anamount that depends on the value of R

L.

See Ex. 7-13


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Load Current and Bleeder Current

Bleeder current is the current left (I3) after the totalload current (IRL1 and IRL2) is subtracted from thetotal current into the circuit.

See Ex. 7-14

I3


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Bipolar Voltage Dividers

Note the Vs is not connected to Gnd.


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Loading Effect of a Voltmeter

When measuring across a resistor, a voltmeter isconnected in parallel with the resistor.

Being in parallel, the internal resistance of thevoltmeter will have a loading effect on the circuit thatis being measured.

Modern digital voltmeters (DMM) have an internalresistance of 10M.

See Ex.7-15


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Ladder Networks

A resistive ladder network is a special type of series-parallel circuit.

One form of ladder network is commonly used toscale voltages to certain weighted values fordigital-to-analog conversion (D/A converter).


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Analysis of a Ladder Network

To find total resistance of a ladder network, start atthe point farthest from the source and reduce the

resistance in steps.Start


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Analysis of a Ladder Network

1. R5 + R6 // R4 R456

2. R456 + R3 // R2 R23456

3. R23456 + R1 = ReqStart

See Ex 7-16


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R/2R Ladder Network

The name comesfrom the relationship

of the resistorvalues.

This type of ladder

network is used indigital-to-analogconverters, were the

switches arecontrolledelectronically.


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R/2R Ladder Network

Analysis:1. SW4 is @ +V & SW1

SW3 @ Gnd


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parallelR1,2 in series w/ R3


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Wheatstone Bridge

A Wheatstone bridge is used to precisely measureresistance.


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Balanced Wheatstone Bridge

The Wheatstone bridge is in the balanced bridge

condition when the output voltage between terminalsA and B is equal to zero.


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Wheatstone Bridge

A Wheatstone bridge is also applied with transducermeasurements, to measure physical quantities suchas temperature, strain, and pressure, where smalltransducer resistance changes can be precisely

measured with the Wheatstone bridge. Tiny changes in transducer resistance will unbalance

the bridge, thereby providing a measurement

reading.


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Unbalanced Wheatstone Bridge

The unbalanced bridge is used to measure sometransducer quantities, such as strain, temperature, orpressure.

The bridge is balanced at a known point, then the

amount of deviation, as indicated by the outputvoltage, indicates the amount of change in theparameter being measured.


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Unbalanced Wheatstone Bridge

The value of the

parameter beingmeasured can bedetermined by the

amount that the bridgeis unbalanced.


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Open Circuits

May be caused by:

burnt out resistors,

broken wires,

bad solder connections,

poor contacts.

Troubleshooting


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Short Circuits

A short circuit is considered to be a zero resistancepath between two points.

May be caused by:

solder splashes,

broken insulation on wires.


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Summary

A series-parallel circuit is a combination of both seriespaths and parallel paths.

To determine total resistance in a series-parallelcircuit, identify the series and parallel relationships,

and then apply the formulas for series resistance andparallel resistance.

To find the total current, apply Ohms law and divide

the total voltage by the total resistance.


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Summary

To determine branch currents, apply the current-divider formula, KCL, or Ohms law.

To determine voltage drops across any portion of aseries-parallel circuit, use the voltage-divider formula,

KVL, or Ohms law.

When a load resistor is connected across a voltage-divider output, the output voltage decreases.


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Summary

A load resistor should be large compared to theresistance across which it is connected, in order thatthe loading effect may be minimized.

To find total resistance of a ladder network, start at

the point farthest from the source and reduce theresistance in steps.

A balanced Wheatstone bridge can be used to

measure an unknown resistance.


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Summary

A bridge is balanced when the output voltage is zero.The balanced condition produces zero currentthrough a load connected across the output terminalsof the bridge.

An unbalanced Wheatstone bridge can be used tomeasure physical quantities using transducers.

Open circuits and short circuits are typical circuit

faults.

Resistors normally open when they burn out.

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