An overview of bridge circuits

1. NAME - GARVIT ARYA
COLLEGE- MAIT
STREAM - CSE
SUBJECT - APPLIED PHYSICS
+
-
G
R3 R4
R1 R2
I2
I4
Vbias
I3
Standard
Arm
Unknown
Arm
Ratio
Armsa
b
c d
I1

2. ::INTRODUCTION::
 Bridge circuits are extensively used for measuring
component values, such as resistance, inductance, or
capacitance, and of other circuit parameters directly
derived from component values
 Its accuracy can be very high.
 A bridge is just two voltage dividers in parallel. The output
is the difference between the two dividers.

3. ::GENERAIZED BRIDGE::
2211 RIRI 
31
31
RR
Vbias
II


42
1
RR
Vbias
II x


31
3
42
4
RR
R
RR
R



4132 RRRR 
4
2
3
1
R
R
R
R

+
-
G
R3 R4
R1 R2
I2
I4
Vbias
I3
Standard
Arm
Unknown
Arm
Ratio
Armsa
b
c d
I1

4. ax RIRI  21
ba RR
Vbias
II

 32
x
x
RR
Vbias
II

1
xba
b
RR
R
RR
R



axb RRRR 
b
a
x
R
RR
R


+
-
V
Rb R
Ra Rx
I1
Ix
Vbias
I3
Standard
Arm
Unknown
Arm
Ratio
Armsa
b
c d
I2
::WHEATSTONE BRIDGE::

5. • Used to determine the L and R
of an inductor having a large
series resistance
• Lx = R2R3C
• Rx = R2R3/R1
• Appears to work best when
ωL/R<10
::MAXWELL BRIDGE::

6. ::HAY BRIDGE::
 Used to measure the L
and R of an inductor
having a small series
resistance
 Appears to work best
when ωL/R>10
1
32
32
R
RR
R
CRRL
x
x


1
1
22
1
2
2
321
2
22
1
2
32




CR
CRRR
R
CR
CRR
L
x
x




7. ::SCHERING BRIDGE::
• Used to determine an unknown capacitance
3
21
2
31
C
RC
R
R
CR
C
x
x



8. ::CALLENDER & GRIFFITH’S
BRIDGE::
 They are used to measure the
resistance of RTD (Resistance
temperature detectors), to minimize
loading errors, and to provide low
uncertainties in measured resistance
values.
 It usually have 3 wires.
 Leads 1, 2, 3 have resistance r1, r2, r3,
where r2 does not affect the circuit,
since there is no current through the
galvanometer at balance conditions.

9. ::CAREY FOSTER BRIDGE::
 In electronics, the Carey Foster bridge is a bridge circuit
used to measure low resistances, or to measure small
differences between two large resistances
Circuit diagram for the Carey Foster bridge

10. OVERVIEW OF
WHEATSTONE BRIDGE
A “Wheatstone Bridge” circuit is simply a parallel circuit with
2 branches. Each branch is a potential divider.
The “bridge” connects the branches as follows…
R1 R2
R3 R4
Vs
V

11. ::HISTORY::
 The Wheatstone Bridge was invented in 1833 by Samuel
Hunter Christie
 Later named after Sir Charles Wheatstone for his many
applications of the circuit through the 1840s
 The most common procedure for the bridge remains the
testing of unknown electrical resistance

12. ::HOW DOES IT WORK::
 Uses ratio of 3 known resistors
 Measures fourth unknown resistance
 Balanced voltage between point 1 and battery’s negative,
and between point 2 and battery’s negative allows the
measurement
 By changing resistors to adjusting variable resistors to
balance the device, the mathematical ratio is used to
calculate the fourth (unknown) resistance.

13. ::IMPACT::
 The Wheatstone Bridge is a very simple design, although there
are more complex versions of achieving the same outcome
 Can be adjusted easily
 Fairly inexpensive to produce
 Electrical power distributors use the Wheatstone Bridge to
locate breaks in the power lines
 Also indirectly measures any variable that would change the
resistance of a material
 Ex: temperature, force, pressure

14. OVERVIEW OF CAREY
FOSTER’S BRIDGE
Laclanche cell Rheostat
One way key
Jockey
GalvanometerFractional
resistance box

15. ::INTRODUCTION::
 The Carey Foster bridge is a bridge circuit used to measure
low resistances, or to measure small differences between two
large resistances.
 It was invented by Carey Foster as a variant on the
Wheatstone bridge.
 It works on the same principle as Wheatstone’s bridge.
 The Carey Foster bridge is a modified form of the meter
bridge in which the effective length of the wire is considerably
increased by connecting a resistance in series with each end
of the wire. This increases the accuracy of the bridge.

16. ::DIFFERENCE BETWEEN CAREY
FOSTER’S BRIDGE AND METER
BRIDGE::
• Carey Foster bridge is a modified form of the meter bridge in which
the effective length of the wire is considerably increased by connecting
a resistance in series with each end of the wire.
• This increases the sensitivity of the bridge, because sensitivity of
bridge is directly proportional to length of bridge wire.

17. There are four gaps in this arrangement.
•Standard low resistances, P and Q, of 2 Ω each are connected in inner
gaps 2 and 3.
• Known resistance, i.e., fractional resistance box X and unknown
resistance Y are connected in outer gaps 1 and 4, respectively.
•One meter long resistance wire EF of uniform area of cross section is
soldered to the ends of two copper strips.
• Galvanometer G is between terminal B and jockey D .
::CAREY FOSTER’S BRIDGE::

18. • Laclanche cell with a key K in series between terminals A & C.
• Position of jockey D is adjusted to locate the position where there is no
deflection of the galvanometer when jockey is pressed to make
electrical contact with the wire; this position is called the balance point
or null point.
• Bridge has highest sensitivity when all four resistances, P, Q, X and Y,
have similar magnitudes.
• I f balance point is located at a distance from E, then applying
Wheatstone bridge principle , condition of balance can be written as
P = R = ( X + α + ρ )_ (1)
Q S {Y + β + (100 - ) ρ}

19. where α and β are end corrections at left and right ends.
These end corrections are contact resistances between wire and
strips.
Interchanging the positions of X and Y, let the balancing length
obtained be then,
P = R = ( Y + α + ρ ) _ (2)
Q S { X + β + (100 - ) ρ }
Combining equations 1 and 2 , we obtain
_(X + α + ρ ) __ = __( Y + α + ρ )__ (3)
{ Y + β + (100 - ) ρ } = { X + β + (100 - ) ρ }

20. We can write ,
{ Y + β +(100 - ) ρ } = { X + β + (100 - ) ρ } (4)
X – Y = ( - ) ρ (5)
Y = X – ( - ) ρ (6)
If Y=0 , then eq. 5 leads to ,
p = ____X_____ (7)
-
Thus if Y is effectively a short circuit, then we can determine the
resistance per unit length from knowledge of X and the measured
values of and .

21. ::PRECAUTIONS::
• In order that the bridge may have high sensitiveness,
resistance of four arms should be of same order.
• plug key should be included in cell circuit and should be closed
when observations are being made.
• Jockey should be pressed gently and momentarily, otherwise it
will spoil the uniformity of diameter of bridge wire.
• In checking null point , the cell circuit must be completed
before galvanometer circuit.
• While determining the value of p , the value of R should be
comparable with resistance of bridge wire.