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DC & AC BRIDGES
Part 2 (AC Bridge)
Objectives
• Ability to explain operation of ac
bridge circuit.
• Ability to identify bridge by name
• Ability to compute the values of
unknown impedance following ac
bridges.
AC Bridges
AC bridges are used to measure inductance and
capacitances and all ac bridge circuits are based on
the Wheatstone bridge. The general ac bridge circuit
consists of 4 impedances, an ac voltage source, and
detector as shown in Figure below. In ac bridge
circuit, the impedances can be either pure
resistance or complex impedances.
Z1 Z 2

Z3 Z4
Fig. 5-7: General ac bridge circuit
A simple bridge circuits are shown
below;
Inductance
Capacitance
Cont.
Applications - in many communication system and
complex electronic circuits. AC bridge circuits - are
commonly used for shifting phase, providing feedback
paths for oscillators and amplifiers, filtering out
undesired signals, and measuring the frequency of
audio signals.
The operation of the bridge depends on the fact that
when certain specific circuit conditions apply, the
detector current becomes zero. This is known as the
null or balanced condition. Since zero current means
that there is no voltage difference across detector, the
bridge circuit may be redrawn as in Fig. 5-8. The
voltages at point a and b and from point a to c must be
equal.
Definition of electrical impedance
• The impedance of a circuit element is defined as the ratio of the
phasor voltage across the element to the phasor current through the
element:
ZR 
Vr
Ir
• It should be noted that although Z is the ratio of two phasors, Z is not
itself a phasor. That is, Z is not associated with some sinusoidal
function of time.
• For DC circuits, the resistance is defined by Ohm's law to be the ratio
of the DC voltage across the resistor to the DC current through the
resistor:
R
VR
IR
• where the VR and IR above are DC (constant real) values.
Definition of Reactance, X
Reactance is the imaginary part of impedance, and is caused by the presence of
inductors or capacitors in the circuit. Reactance is denoted by the symbol X
and is measured in ohms.
• A resistor's impedance is R (its resistance) and
its reactance, XR is 0.
• A capacitance impedance: XC = -1/C
= -1/(2fC)
• An inductive impedance: XL = L = 2fL
Z and Y passive elements
Element
Impedance
Admittance
R
Z= R
Y= 1/R
L
Z= jωL
Y=1/j ωL
C
Z=-j(1/ωc)
Y=j ωc
Cont.
Fig. 5-7: General ac bridge circuit
Fig. 5-8: Equivalent of balanced
ac bridge circuit
Cont.
I1Z1 = I2Z2
(1)
Similarly, the voltages from point d to point b and point
d to point c must also be equal, therefore
I1Z3 = I2Z4
equation (1) divided by equation (2)
Z1 Z 2

Z3 Z4
(2)
• If impedance is written in the form Z  Z
where Z represents magnitude and 
the phase angle of complex impedance, its
can be written as,
( Z 11 )( Z 11 )  ( Z 2  2 )( Z 11 )
where
Z 1 Z 4 (1   4 )  Z 2 Z 3 ( 2   3 )
Example 5-5
The impedances of the AC bridge in Fig.
5-7 are given as follows:
Z1  20030 
0
Z 2  1500 
0
Z 3  250  40 0 
Z x  Z 4  unknown
Determine the constants of the unknown arm.
Solution
The first condition for bridge balance
requires that
Z1Zx =Z2Z3
Zx = (Z2Z3/Z1)=[(150x250)/200]
= 187.5
Cont.
The second condition for balance requires
that the sums of the phase angles of
opposite arms be equal
1+ x = 2 + 3
x = 2 + 3 - 1
= 0 + (-40) – 30
= -70o
Cont.
Hence, the unknown impedance Zx, can be
written as
Zx = 187.5 -700 = (64.13 – j176.19) 
Where
Zx  = Zx cos  + j Zx sin 
Indicating that we are dealing with a
capacitive element, possibly consisting of a
series resistor and a capacitor
Example 5-6
Fig. 5-9: AC bridge in balance
Given the AC bridge of Fig. 5-8 in balance, find the
components of the unknown arms Zx.
Similar Angle Bridge
The similar angle bridge (refer figure below) is used to
measure the impedance of a capacitive circuit. This bridge is
sometimes called the capacitance comparison bridge of the
series resistance capacitance bridge.
Z1 = R1
Z2 = R2
Z3 = R3 –jXc3
Zx = Rx –jXcx
Rx 
R2
R3
R1
Cx 
R1
C3
R2
Maxwell Bridge
• to determine an unknown inductance with capacitance standard
Z1 
1
1
 jC1
R1
Z 2  R2
Z 3  R3
Z x  Rx  jX Lx
R2 R3
Rx 
R1
Lx  R2 R3C1
X - reactance
Z = R + jX
Opposite Angle Bridge
The Opposite Angle Bridge or Hay Bridge (see Figure below) is
used to measure the resistance and inductance of coils in which
the resistance is small fraction of the reactance XL, that is a coil
having a high Q, meaning a Q greater than 10.
 2 R1 R2 R3C12
Rx 
1   2 R12 C12
R2 R3C1
Lx 
1   2 R12 C12
Wein Bridge
The Wein Bridge shown in Figure below has a series RC combination in
one arm and a parallel combination in the adjoining arm. It is designed to
measure frequency (extensively as a feedback arrangement for a circuit). It
can also be used for the measurement of an unknown capacitor with
great accuracy.
Z1  R1
Z 2  R2
Z3 
1
1
1

R3
jX c 3
Z 4  R4  jX c 4
Cont..
Equivalent
parallel
component
R1 
1
 R4  2
R3 
R2 
 R4C42
R2
1
C3  (
)C4
2 2
2
R1 1   R4 C4
R1 
1 
C4   C3  2 2 2 
R2 
 R3 C3 
Equivalent series
component

R2 
R3

R4  
2 2 2 
R1  1   R3 C3 



Radio Frequency Bridge
The radio frequency bridge shown in figure below is often
used in laboratories to measure the impedance of both
capacitance and inductive circuits at higher frequencies.
Rx 
Xx 
R3 '
(C1  C1 )
C2
1
1
1

)
'
 C4 C4
(
C’1 & C’4 : new values of
C1 & C4 after rebalancing
Schering Bridge
• used for measuring capacitors and their insulating properties
for phase angle of nearly 90o.
Zx =Rx –j/Cx
Z2 = R2
Z3 = -j/C3
Z1 = 1/(R1 + jC1)
R2 C1
Rx 
C3
R1C3
Cx 
R2
Summary
• The Wheatstone Bridge – most basic bridge
circuit. Widely used to measure instruments and
control circuits. Have high degree of accuracy.
• Kelvin Bridge – modification of Wheatstone Bridge
and widely used to measure very low resistance.
• Thevenin’s theorem – analytical tool to analyzing
an unbalance Wheatstone bridge.
• AC bridge – more general form of Wheatstone
bridge.
• Different types of AC bridges differ in the types of
impedances in the arms