ELECTRICAL MEASUREMENT & INSTRUMENTATION

AC BRIDGE

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Amrendra kumarRegd.no-14781A0203

Synopsis• Comparison between AC and DC Bridge• Maxwell’s Inductance bridge• Maxwell’s capacitance bridge• Anderson bridge• De Sauty’s bridge• Schering bridge

Comparison between AC & DC Bridge

For DC Bridge(a) R1 * R3 = R2 * R4

For AC Bridge(b) Z1 *Z3 = Z2 * Z4

Maxwell’s inductance bridge

• The bridge circuit is used for medium inductances and can be arranged to yield results of considerable precision.• As shown in Fig., in the two arms, there are two

pure resistances so that for balance relations, the phase balance depends on the remaining two arms.

Conti.

• L1 = unknown inductance of resistance R1

• L4 = variable inductance of fixed resistance R4

• R4 = variable resistance connected in serieswith inductor L4.

R2 and R3 are fixed known resistances

• At balance, (R1 + jωL1)R3 = (R4 + jωL4 )R2

• Finally, L1 = L4(R2/R3) R1 = R4(R2/R3)

Phasor Diagram

Maxwell’s inductance capacitance bridge

• In this bridge, an inductance is measured by comparison with a standard variable capacitance.• The connection is shown in figure.• One of the ratio arms has a resistance and

capacitance in parallel.

Conti.

• L3 = unknown inductance• C = variable standard capacitor

• R1, R2, R4 = known pure resistances.

• R3 =effective resistance of inductor L3

• At balance, R1(R3 + jωL3) = R2R4

(1 + jωCR1)• Finally, L3 = CR2R4

R3 = R4R2/R1

Q = ωL3/R3

Advantages

• The balance equation is independent of frequency.

• It is useful for measurement of wide range of inductance at power and audio frequency.

Disadvantages

• It cannot be used for measurement of high Q values (Q≥10).

• It cannot be used for measurement of very low Q values, because of balance converge problem.

Anderson’s bridge• This bridge, in fact, is a modification of the Maxwell’s

inductance-capacitance bridge.• In this method, the self-inductance is measured in terms

of a standard capacitor.• Figure shows the connections and the phasor diagram of

the bridge for balanced conditions.

Conti.

• L1 = self inductance to be measured.

• C = fixed standard capacitor

• R2, R3, R4 , R5 = known pure resistances.• R1 = resistance connected in series with L1.

• At balance, (R1 + jωL1) (R3/jωC) = R2 R4+ R3R5

(R3 + R5 + 1/jωC) (R3 + R5 + 1/jωC)• Finally, R1 = R2R4/R3

L1 = CR2 + R4 + R5 + (R5R4/R3 )

Advantages

• Anderson’s bridge balance is easily obtained for low Q coils.

• The bridge can be used for accurate determination of capacitance in terms of inductance.

Disadvantages

• It is complex.• The bridge balance

equations are not simple. They are rather more tadious.

De Sauty’s bridge• This bridge is the simplest method of comparing two

capacitances.• The connection diagram of this bridge is shown in figure.

Conti.

• C2 = capacitor whose capacitance is to be measured• C3 = a standard capacitor.

• R3, R4 = pure resistances.

• At balance, R1 -j = R4 -j ωC3 ωC2

• Finally, C2 = C3R4

R1

Advantages

• The bridge is simple.• It is economical.

Disadvantages

• If both the capacitors are not free from dielectric loss , then it is not possible to achieve bridge balance. This method is only suitable for the measurement of lossless capacitors.

Schering bridge• It is used extensively fo the measurement of capacitors.• It is also useful for measuring insulating properties i.e.

phase angles very nearly 90o.• One of the ratios are consists of a resistance in parallel

with a capacitor and standard arm consists only a capacitor.

• The standard capacitor is a high quality mica capacitor or an air capacitor for insulation measurement.

Conti.

• C2 = capacitor of unknown capacitance.• r = a series resistance representing the loss in the capacitor C1.• C1 = a standard capacitor.• R3 = a pure resistance.• C4 = a variable capacitor.• R4 = a variable pure resistance.• At balance , r + 1 R4 = 1 R3

jωC2 (1 + jωC4R4) jωC1

• Finally, r = R3C4 & C2 = C1 R4 & D = ωC4R4

C1 R3

Advantages

• The bridge is widely used for testing small capacitors at low voltages with high precision.

• Since C4 is a variable decade capacitance box, its setting in μF directly gives the value of the dissipation factor.

Disadvantages

• The calibration of C4 is only for particular frequency, as ω term present in the equation.

• Commercial Schering bridge measures capacitors from 100 pF -1μF with ±2% accuracy.