cours d'éléctronique pour les débutants 7
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Voltage DividersVoltage Dividersand Current Dividersand Current Dividers
Topics Covered in Chapter 77-1: Series Voltage Dividers
7-2: Current Dividers with Two Parallel Resistances7-3: Current Division by Parallel Conductances
7-4: Series Voltage Divider with Parallel Load Current7-5: Design of a Loaded Voltage Divider
Chapter Chapter 77
2007 The McGraw-Hill Companies, Inc. All rights reserved.
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77--1: Series Voltage Dividers1: Series Voltage Dividers
V T is divided into IR voltage drops that are proportionalto the series resistance values.Each resistance provides an IR voltage drop equal to its
proportional part of the applied voltage:V R = (R/R T ) V T
This formula can be used for any number of seriesresistances because of the direct proportion between
each voltage drop V and its resistance R .The largest series R has the largest IR voltage drop.
McGraw-Hill 2007 The McGraw-Hill Companies, Inc. All rights reserved.
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77--1: Series Voltage Dividers1: Series Voltage Dividers
The Largest Series R Has the Most V .
V 2 =R 2
R T V T
999 k ;
1000 k ;= 1000 V = 999 V
V 1 = R 1
R T V T
=1 k ;
1000 k ; 1000 V = 1 V
KVL check: 1 V + 999 V = 1000 VFig. 7-2a: Example of a very small R 1 inseries with a large R 2 ; V 2 is almostequal to the whole V T .
Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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77--1: Series Voltage Dividers1: Series Voltage Dividers
Voltage Taps in a SeriesVoltage Divider
Different voltages are
available at voltage taps A , B, and C.The voltage at each tappoint is measured withrespect to ground.Ground is the referencepoint.
Fig. 7-2b: Series voltage divider with voltage taps.Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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77--1: Series Voltage Dividers1: Series Voltage Dividers
N ote: V A G is the sum of thevoltage across R 2, R 3, and R 4.V A G is one-half of the appliedvoltage V T, because R 2+R 3+R 4 = 50% of R T.
VCG =1 k ;
20 k ; 24 V = 1. 2 V
VBG =
2.5 k ;
20 k ; 24 V = 3 V
VAG = 1 2 V
Voltage Taps in a Series Voltage Divider
Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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77--2: Current Dividers with2: Current Dividers withTwo Parallel ResistancesTwo Parallel Resistances
I T is divided into individual branch currents.Each branch current is inversely proportional to thebranch resistance value.
For two resistors,R 1 and R 2, in parallel:
N ote that this formula can only be used for two branchresistances.The largest current flows in the branch that has thesmallest R .
I !1
IR
R R I
T12
1 2
! v
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77--2: Current Dividers with2: Current Dividers withTwo Parallel ResistancesTwo Parallel Resistances
Current Divider
Fig. 7-3: Current divider with two branchresistances. Each branch I is inverselyproportional to its R . The smaller R hasmore I .
Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
I 1 = 4 /(2 + 4 ) 30 A = 2 0 A
I2= 2 /(2 + 4 ) 30
A= 10
A
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77--33 :: Current Division byCurrent Division byParallel ConductancesParallel Conductances
Fig. 7-5: Current divider with branch conductances G 1, G 2 , and G 3 , each equal to 1/ R . N ote thatS is the siemens unit for conductance. With conductance values, each branch I is directlyproportional to the branch G .Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
G 1 = 1/R 1 = 1/10 = 0.1 S
G 2 = 1/R 2 = 1/2 = 0.5 S
G 3 = 1/R 3 = 1/5 = 0.2 S
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77--3: Current Division by3: Current Division byParallel ConductancesParallel Conductances
K CL check: 5 m A + 25 m A + 10 m A = 40 m A = IT
The Siemens (S ) unit is the reciprocal of the ohm ( )
G T = G 1 + G 2 + G 3= 0.1 + 0.5 + 0.2
G T = 0.8 S
I1 = 0.1/0.8 x 40 m A = 5 m AI2 = 0.5/0.8 x 40 m A = 25 m AI3 = 0.2/0.8 x 40 m A = 10 m A
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77--4: Series Voltage Divider with4: Series Voltage Divider withParallel Load CurrentParallel Load Current
Voltage dividers are often used to tap off part of theapplied voltage for a load that needs less than the totalvoltage.
Fig. 7-6: Effect of a parallel load in part of a series voltage divider. (a ) R 1 and R 2 in series withoutany branch current. (b ) Reduced voltage across R 2 and its parallel load R L. (c ) Equivalent circuitof the loaded voltage divider.Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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77--4: Series Voltage Divider with4: Series Voltage Divider withParallel Load CurrentParallel Load Current
V1 = 40/60 x 60 V = 40 V
V2 = 20/60 x 60 V = 20 V
V1 + V2 = VT = 60 V( A pplied Voltage )
Fig 7-6
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77--5: Design of a5: Design of aLoaded Voltage Divider Loaded Voltage Divider
Fig. 7-7: Voltage divider for different voltages and currents from the source V T .Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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77--5: Design of a5: Design of aLoaded Voltage Divider Loaded Voltage Divider
R 1 = V1/I1 = 18 V/30 m A = 0.6 k = 600
R 2 = V2/I2 = 22 V/66 m A = 0.333 k = 333
R 3 = V3/I3 = 60 V/120 m A = 0.5 k = 500
NO TE: When these values are used for R 1, R 2, and R 3 andconnected in a voltage divider across a source of 100 V,each load will have the specified voltage at its rated current.