AC BRIDGESResistance, Capacitance and Inductance

Measurement

EKT 112

Principles of Measurement and Instrumentation

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 BRIDGESAC 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.

4

2

3

1

Z

Z

Z

Z

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 thatwhen certain specific circuit conditions apply, thedetector current becomes zero. This is known as thenull or balanced condition. Since zero current meansthat there is no voltage difference across detector, thebridge circuit may be redrawn as in Fig. 5-8. Thevoltages at point a and b and from point a to c must beequal.

DEFINITION OF ELECTRICAL IMPEDANCE

The impedance of a circuit element is defined as the ratio of the phasorvoltage across the element to the phasor current through the element:

It should be noted that although Z is the ratio of two phasors, Z is notitself a phasor. That is, Z is not associated with some sinusoidal functionof time.

For DC circuits, the resistance is defined by Ohm's law to be the ratio ofthe DC voltage across the resistor to the DC current through the resistor:

where the VR and IR above are DC (constant real) values.

r

rR

I

VZ

R

R

I

VR

DEFINITION OF REACTANCE, X

A resistor's impedance is R (its resistance) and its

reactance, XR is 0.

A capacitance impedance: XC = -1/C

= -1/(2fC)

An inductive impedance: XL = L = 2fL

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.

Z AND Y PASSIVE ELEMENTS

Element Impedance Admittance

R Z= R Y= 1/R

L Z= jL Y=1/j L

C Z=-j(1/c) Y=j c

CONT.

Fig. 5-8: Equivalent of balanced

ac bridge circuit

Fig. 5-7: General 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 (2)

equation (1) divided by equation (2)

4

2

3

1

Z

Z

Z

Z

If impedance is written in the form

where Z represents magnitude and the

phase angle of complex impedance, its can

be written as,

ZZ

)()(

))(())((

32324141

11221111

ZZZZ

where

ZZZZ

EXAMPLE 5-5

The impedances of the AC bridge in Fig. 5-7 are given as follows:

Determine the constants of the unknown arm.

01 30200Z

02 0150Z

03 40250Z

unknownZZ x 4

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

Given the AC bridge of Fig. 5-8 in balance, find the

components of the unknown arms Zx.

Fig. 5-9: AC bridge in balance

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 = R1Z2 = R2

Z3 = R3 jXc3Zx = Rx jXcx

3

1

2 RR

RRx

3

2

1 CR

RCx

MAXWELL BRIDGE

to determine an unknown inductance with capacitance standard

1

1

1 1

1

CjR

Z

22 RZ

33 RZ

LxxxjXRZ

1

32

R

RRRx 132 CRRLx 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

1

2

1

2

2

1321

2

1 CR

CRRRRx

2

1

2

1

2

132

1 CR

CRRLx

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.

444 cjXRZ

11RZ

33

3 11

1

cjXR

Z

22RZ

Cont..

2

44

24

2

1

3

1

CRR

R

RR

42

4

2

4

2

1

2

3)

1

1( C

CRR

RC

2

3

2

3

23

2

1

4

1

CRC

R

RC

2

3

2

3

2

3

1

2

41 CR

R

R

RR

Equivalent

parallel

component

Equivalent series

component

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.

)( 1'

1

2

3 CCC

RRx

)11

(1

4

'

4CC

X x

C1 & C4 : new values of C1 & C4 after rebalancing

SCHERING BRIDGE

used for measuring capacitors and their insulating properties

for phase angle of nearly 90o.

3

12

C

CRRx

2

31

R

CRCx

Zx =Rx j/CxZ2 = R2

Z3 = -j/C3Z1 = 1/(R1 + jC1)

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.

Thevenins 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