Wheatstone Bridge 2

8/12/2019 Wheatstone Bridge 2

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11/11/2011 Electrical Measurement 1

ELECTRICALMEASUREMENT

ESRA SAATI


Bridges and theirApplications

CONTENTS DC Bridges

Wheastone Bridge

Kelvin Bridge

Microprocessor-Controlled Bridges

Bridge Controlled Circuits

Loop Test with portable test set


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Bridges Works as a null measurement technique: The null-measurement occurs when the reading on the

ammeter or voltmeter is zero. This is a huge practicalbenefit. Making a meter which is precisely linear, with anaccurate scale, and negligible resistance, is a challenge.None of these issue matter in a null measurement, sincethe purpose of the meter to determine the presence orabsence of current or voltage. It does not need to belinear; it is only important to detect the zero value. Theresistance does not matter, since there is no currentthrough the meter at the point of measurement.

The only concern is that the meter be able to detectfairly small currents, during the nulling step. This makesthe design much easier.


Bridges

A bridge is just two voltage dividers in parallel.The output is the difference between the twodividers.

Used for measuring component values, such as

resistance, inductance, or capacitance, and ofother circuit parameters directly derived fromcomponent values

Its accuracy can be very high Accuracy is directly related to the accuracy of

the bridge components, not to that of the nullindicator itself


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Wheastone Bridge

Figure 1. Simplified schematic of the Wheatstone bridge.

3 41 3 2 4

234

1

A BV V

E ER R

R R R R

RR R

R

=

=+ +

=

Measures resistance (from 1 to 1M)Upper limit is set by the reduction in sensitivity to unbalanceLower limit is set by the resistance of the connecting leads and thecontact resistance at the binding posts.


Wheastone Bridge

The main source of measurement errors are: Limiting errors of the three known resistors. Insufficient sensitivity of the null detector,

Changes in resistance of the bridge arms due tothe heating effect,

Thermal emfs in the bridge circuit or thegalvanometer circuit,

Errors due to the resistance of leads andcontacts exterior to the actual bridge.


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Wheastone Bridge

Figure 2. Application of Thevenin theorem to the Wheatstone bridge.

1 2

1 3 2 4th

R RE E

R R R R

=

+ +

1 3 2 4thR R R R R = +

thg

gth

EI

R R=

+


Thevenin Method

Find Vth (open circuit voltage)

Remove load if there is one so that load is open

Find voltage across the open load

Find Rth (Thevenin resistance)

Set voltage sources to zero (current sources toopen) in effect, shut off the sources

Find equivalent resistance from A to B

Vth

0

Rth

A

B


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Example

Figure 3 shows the schematic diagram of a Wheatstone bridge withvalues of bridge elements as shown. The battery voltage is 5V and itsinternal resistance negligible. The galvanometer has a currentsensitivity of 10mm/A and an internal resistance of 100. Calculatethe deflection of the galvanometer caused by the 5 unbalance inarm BC.

Figure 3. Wheatstone bridge.


Example

1 2

1 3 2 4

100 10005 2.77

100 200 1000 2005

th

th

R RE E

R R R R

E V mV

=

+ +

= =

+ +

Thevenin equivalent is determined with respect to galvanometer terminals A and B

1 3 2 4

100 200 1000 2005 730th

th

R R R R R

R

= +

= + =

2.773.34

730 100

thg

gth

g

EI

R R

mVI A

=+

= = +

3.34 10 33.4d A mm A mm = =


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Example

The galvanometer of Example 1 is replaced by one with an internalresistance of 500 and a current sensitivity of 1mm/A. Assuming that adeflection of 1mm can be observed on the galvanometer scale, determineif this new galvanometer is capable of detecting the 5 unbalance in armBC.

Since the bridge constants have not been changed, the equivalent circuit isagain represented by a Thevenin generator of 2.77mV and Theveninresistance of 730 . The new galvanometer is now connected to the outputterminals, resulting in a galvanometer current:


Example

2.772.25

730 500

thg

gth

g

EI

R R

mVI A

=+

= =

+

2.25 1 2.25d A mm A mm = =


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Wheastone Bridge Wheatstone bridge smoke detector


Wheastone Bridge Strain Gauge in a Bridge Circuit


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Example At 20oC, the Wheatstone bridge as shown in Figure is in balance condition

when R1=1000, R2=842, and R3=500 . Meanwhile, R4 is copper

Resistance Temperature Detector (RTD).The internal resistance of

galvanometer, Rg=100and the temperature coefficient of the RTD,

=0.0042/oC. If the RTD is dipped into boiling water (100oC), determine

the deflection of galvanometer if its sensitivity is 1mm/A

= = 0.0042 20 0.084RTD

R

= =

=

24 3

1

842500 0.084

1000420.916

RTD

RR R R

R

= =

= + = + =

'

'4

0.0042 100 0.42

420.916 0.42 421.336RTD

x RTD

R

R R R


Example

= + +

= =

+ +

1 2

1 3 2

1000 84210 1.77

1000 500 842 421.33

thx

th

R RE E

R R R R

E V mV

Thevenin equivalent is determined with respect to galvanometer terminals A and B

= +

= + =

1 3 2

1000 500 842 421.33 614.14th x

th

R R R R R

R

=+

= = +

1.772.47

614.14 100

thg

th g

g

EI

R R

VI A

= =2.47 1 2.47d A mm A mm


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Kelvin Bridge

Figure 4. Wheatstone bridge.

Modification of the Wheatstone bridgeMeasures low-value resistance (1)

If the galvanometer is connectedto a point p and the adjusted ratiois:

= 2

1

np

mp

R R

R R


Kelvin Bridge

Balance equation is:

+ = +23

1

( )x np mp

RR R R R

R

y mp np R R R= +

=+

1

1 2

y

mp

R RR

R R

=+

2

1 2

y

np

R RR

R R

= 23

1x

RR R

R

= 2

1

np

mp

R R

R R


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Kelvin DoubleBridge

Figure 5. Basic Kelvin double bridge circuit.

The galvanometer indication will bezero when Ekl = Elmp

G

R2 R1

R3 Rx

p

nm

Ry

l

b a

o

E

I

k


Kelvin DoubleBridge

The galvanometer indication will be zero when Ekl = Elmp

( )2 2 31 2 1 2

( )x yklR R

E E I R R a b R

R R R R

= = + + ++ +

3 ( ) ylmpb

E I R a b R a b

= + + +

( )2 3 31 2

( ) ( )x y yR b

I R R a b R I R a b R R R a b

+ + + = + + + +


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Kelvin DoubleBridge

1 3 1

2 2( )y

x

y

bRR R R aR

R a b R R b

= +

+ +

If we establish the condition that: 1

2

R a

R b=

13

2x

RR R

R=


Microprocessor-ControlledBridges

Ampli fier MicroprocessorDigital

Readout

R1 R2

R3 Rx

Programmableresistor

E

Digital Control Signal

Figure 6. Block diagram for a Wheastone bridge with amicroprocessor control.


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Example 3:

5k 5k

5k Rv

6V A B

Error signal

0 20 40 60 80 100

Temp(0C)

1

2

3

4

5

R(k)

(a) Circuit (b) variation of Rvwithtemperature

Resistor Rv isthermistor, withrelation between itsresistance andtemperature as shownin the figure.Calculate

a) At what temperaturethe bridge is balanced,

b) The amplitude of theerror signal at 60C.



2 3

1

5 55

5v

R R k kR k

R k

= = =

From the graph, the bridge is balanced at 80C.

a) the value of Rv when the bridge is balanced is calculated as:

b) From the graph, the resistance of Rv at 60C is 4.5k.

= + +

= =

+ +

1 2

1 3 2

5 56 158

5 5 5 4.5

thv

th

R RE E

R R R R

k kE V mV

k k k k

158g th

e E mV = =


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Loop Test with portable testset

The portable Wheatstone bridge is often used to locate faults inmulticore cables, telephone wires, or power transmission lines by means ofthe so-called Murray-loop

Figure 6. Locating a ground fault (short circuit) by the Murray-loop test

G

R2

R1

E

La

Lb

Lx

Metalsheath of

cable

Ground fault

ShortCircuit at

cabletermination

Faulty

conduct

Returnconduct



At balance:

Ra and Rb are the resistance of the return conduct and faulty conductrespectivelyRx is the resistance of the faulty conductor from the bridge terminal tothe location of the ground fault.

wire resistance is proportional tothe length and the cross sectionalarea of the conductor

( )( )

+ = = +

+2 1

1 1 2

a b x

x a bx

R R RR RR R R

R R R R

= ++

1

1 2

( )x a b

RL L L

R R


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In a multicore cable the return conductor La has the same lengthand the same cross section as the faulty core

La = Lb = L

=+

1

1 2

2x

RL L

R R



Figure 9. Wheastone bridge connected for a Varley loop test.


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To locate the fault, first set switch S to position a. balance thebridge by adjusting R3. When the bridge is balanced:

2 2

3

1 3 1

a ba b

R RR RR R R

R R R

+= + =

Now set the switch to position b and balance the bridge again.The equation for balance is now:

( ) ( )1 1 321 3 1 2

a b x a b

x

x

R R R R R R R RRR

R R R R R

+ + = =+ +

Wheatstone Bridge 2

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