Cours d'éléctronique pour les débutants 7

8/8/2019 Cours d'lctronique pour les dbutants 7

1/16

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.


2/16

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.


3/16


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.


4/16


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.


5/16


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



6/16

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


7/16

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 .


I 1 = 4 /(2 + 4 ) 30 A = 2 0 A

I2= 2 /(2 + 4 ) 30

A= 10

A


8/16


9/16

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


10/16

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


11/16

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.


12/16

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


13/16


14/16

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.


15/16


16/16

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.

Cours d'éléctronique pour les débutants 7

Documents

Transcript of Cours d'éléctronique pour les débutants 7