Transcript CHAPTER 1

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7.1 Introduction to AC Bridge.
 AC bridges are used to measure inductance and
capacitance.
 All the AC bridges are based on the Wheatstone
bridge.
 In the AC bridge the bridge circuit consists of four
impedances and an ac voltage source.
 The impedances can either be pure resistance or
complex impedance.
 Other than measurement of unknown impedance, AC
bridge are commonly used for shifting phase.
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Cont’d…
Operation of AC Bridge:
When the specific circuit conditions apply,
the detector current becomes zero, which
is known as null or balance condition.
 Since zero current, it means that there is no
voltage difference across the detector,
Figure 7.2.
 Voltage at point b and c are equal.


The same thing at point d.
I 1 Z1  I 2 Z 2

From two above equation yield general
bridge equation;
I1 Z 3  I 2 Z 4
Figure 7.2: Equivalent of Balance
(nulled) AC Bridge.
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Cont’d…
 Figure 7. 3(a) and 7.3 (b) is a simple AC Bridge circuit.
Figure 7.3: (a) and (b) are Simple AC Bridge Circuit.
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7.5 Wein Bridge
 The Wein Bridge is versatile where it can measure either the
equivalent –series components or the equivalent-parallel
components of an impedance, Figure 7.8.
 This bridge is used extensively as a feedback for the Wein bridge
oscillator circuit.
Figure 7.8: Wein Bridge.
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•
It is used extensively for the
measurment of capacitors.
900
• It is also useful for measuring insulating
properties i.e. phase angles very nearly
• fig. shows basic circuit arrengement.
• One of the ratio are consists of a
resistance in parrallel with a capacitor
and standard arm consists only a
capacitor.
• The standard capacitor is high quality
mica capacitor or an air capacitor for
insulation measurement .
• The general bridge balance equation is ,
z1 z x  z 2 z3
z x  z 2 z3 z1
1
 j
1
y1 
 jC1 , Z 2  R2 , Z 3 
, Z x  Rx 
R1
C3
jC x
Substituting ,
 Separating real and imaginary terms ,The equation gives
the value
Of unknown capacitance Cx inTerms of standard capacitorC3
, R1 ,anR2 .
The bridge can be used to define the quality
Of capacitor by obtaining

Rx
 1


 R  jC1 

1


R2
R2C1
  j

R1C3
C3
j
 j

 R2 
C x
C3
Rx 
j
C x
Rx 
R2 C1
C3
1
C x

Cx 
R1C3
R2
R2
R1C3
 Power
factor : it is defined as the cosine of the
phase angle of the circuit .
p.f. =
R
cos  x  x
x
for phase angles Zclose
to
, the reactance is equal to
impedance.
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p.f. =
Rx
Rx

Xx  1 
P.f. =


Cx 

 Dissipation factor : it is defined as the cotangent of the
phase angle.RxCx
 Rx 
D  cot  x   
 Zx 
Rx
D
Xx
D  R x C x
Q
define
Xl
as
R
The quality of a coil is
. The
dissipation factor is the reciprocal of quality factor .
1
D
Q
Putting values of Rx and Cx .
R2C3 R1C3
D 

C3
R2
D  R1C1
 If
R1 is fixed then C1 may be calibrated to give
dissipation D i.e. quality of capacitor .
 The calibration of C1 is good only for particular
frequency , as Ѡ term is present in the equation .
 Commercial schering bridge measures capacitors
from 100 pf -1 F with
accuracy .
 The bridge is widely used for testing small
capacitors at low voltages with high
 precision
 2% .
 The
Anderson’s Bridge is a modification of
the Maxwell’s inductance capacitance
bridge.
 In
this method, the self-inductance is
measured in terms of a standard capacitor.
 This
method is applicable for precise
measurement of self-inductance over a very
wide range of values.
The
connection of the bridge for balanced
condition is shown below:-
 The
phasor diagram of the bridge for balanced condition
is given below:-
 Let,
L1= self-inductance to be measured
R1= resistance of self-inductor
r1= resistance connected in series with self-inductor
R, R2, R3, R4= known non-inductive resistances
C= fixed standard capacitor
At balance,
I1=I3 & I2=Ic+I4,
Now,
Writing the other balance equations
And,
Substituting the value of Ic in the above equations we have,
Or,
……..(1)
And,
Or,
From equations (1) & (2) we obtain,
Equating the real & imaginary parts,
And,
……………(2)
A
fixed capacitor can be used instead of a
variable capacitor as in the case of Maxwell’s
bridge.
 This bridge may be used for accurate
determination of capacitor in terms of
inductance.

The Anderson’s bridge is more complex than its
prototype Maxwell’s bridge .The Anderson’s bridge
has more parts and is more complicated to set up
and manipulate. The balance equations are not
simple and in facts are much more tedious.

An additional junction point increases the difficulty
of shielding the bridge.
 The
Maxwell’s bridge measures an unknown
inductance in terms of a known capacitance.
 One of the ratio arms has a resistance and
capacitance in parallel. we know that the general
equation of bridge balance is,
•
Z1 ZX = Z2 Z3
•
ZX = Z2 Z3 * 1/Z1
=Z2 Z3 Y1
Here, Y1=Admittance of arm 1
•
•
Z2 = R2
 Z3 = R3
 Y1 = 1/R1 + jωC1

Substituting these values,
Zx = Rx + jωLx = R2 R3 ( 1/R1 + jωC1)
Zx = R2 R3/R1 + jωR2 R3 C1
Separating real and imaginary parts,
Rx = R2 R3/R1
Lx = R2 R3 C1
 To obtain bridge balance, first R3 is adjusted for
inductive balance and R1 is adjusted for resistive
balance.
 The quality factor of the coil is given by,
Q = ωLx/Rx = ωR2 R3 C1/(R2 R3 /R1)
Q = ω R1 C1
The balance equation is independent of
frequency.
 The two balance equation are independent.
 The scale of resistance can be calibrated to
read the inductance and Q value.
 It is useful for measurement of wide range of
inductance at power and audio frequencies.

It cannot be used for measurement of high Q
values. it is limited to measure low Q values
(1<Q>10)
 It cannot be used for measurement of very low Q
values ,because of balance converge problem.
Commercial Maxwell’s bridge measures the
inductance from 1-100H , with ± 2% error.

 Used
to measure the L and R of an inductor having
a small series resistance
Lx 
R 2 R 3C
 2 R1 2C 2  1
 2 R1R 2 R 3C 2
Rx 
 2 R1 2C 2  1
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