DEE 514�ELECTRONIC INSTRUMENTATION�

UNIT-4 �(We will study this unit after Unit-1)

• Impedance Bridges and Q-meters;
• Block diagram and working principle of laboratory types RLC bridge;
• Specification;
• Digital RLC bridge.
• Block diagram and working principle of Q-meter,
• Definition and concept of Q of a component and circuit.

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Rearranging the syllabus �(Topics Wise)

I) Introduction

• 1.General form of A.C. bridge

II) Measurements of inductance

• 2. Maxwell’s inductance bridge
• 3. Maxwell’s inductance capacitance bridge
• 4. Hay’s bridge
• Owen’s bridge
• Anderson’s bridge

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• Note: Red colour topics will not be discussed

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III) Measurement of capacitance and loss angle.

5. Introduction to Dissipation factor

6. Schering bridge

Desauty’s Bridge

Modified desauty’s bridge

IV) Measurements of frequency

• 7. Wein’s bridge
• High Voltage Schering Bridge

V) Measurement of electrical property of coil and capacitors

• 8.Q-Meter
• 9. Digital RLC meter

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1.General form of A.C. bridge

• AC bridge are similar to D.C. bridge in topology(way of connecting).It consists of four arm
• AB,BC,CD and DA .Generally the impedance to be measured is connected between ‘A’ and ‘B’.
• A detector is connected between ‘B’ and ’D’. The detector is used as null deflection instrument (See fig in next slide).
• Some of the arms are variable element. By varying these elements, the potential values at ‘B’ and
• ‘D’ can be made equal. This is called balancing of the bridge.

• At the balance condition, the current through detector is zero.
• Therefore, I1=I3
• I2=I4

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• ---------------(1)

• At balance condition,
• Voltage drop across ‘AB’=voltage drop across ‘AD’.
• (i.e) E₁ = E₂
• Therefore, I₁Z₁= I₂Z₂ -------(2)
• I₁/I₂=Z₂/Z₁ -------(3)
• Similarly,

Voltage drop across ‘BC’=voltage drop across ‘DC’

(i.e) E₃ = E₄

Therefore, I₃Z₃= I₄Z₄ -------(4)

I₃/I₄=Z₄/Z₃ -------(5)

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From equation -1, it can be seen that, equation -3 and equation-5 are equal.

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• Products of impedances of opposite arms are equal.

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• * For balance condition, magnitude on either side must be equal.
• * Angle on either side must be equal.
• Summary
• For balance condition,

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• Types of detector
• The following types of instruments are used as detector in A.C. bridge.
• • Vibration galvanometer
• • Head phones (speaker)
• • Tuned amplifier
• 1 Vibration galvanometer
• Between the point ‘B’ and ‘D’ a vibration galvanometer is connected to indicate the bridge balance condition. This A.C. galvanometer which works on the principle of resonance. The A.C. galvanometer shows a dot, if the bridge is unbalanced.
• 2. Head phones
• Two speakers are connected in parallel in this system. If the bridge is unbalanced, the speaker produced more sound energy. If the bridge is balanced, the speaker do not produced any sound energy.
• 3 Tuned amplifier
• If the bridge is unbalanced the output of tuned amplifier is high. If the bridge is balanced, output of amplifier is zero.

Maxwell’s inductance bridge

• The choke for which R1 and L1 have to measure connected between the points ‘A’ and ‘B’.
• In this method the unknown inductance is measured by comparing it with the standard inductance.
• L2 is adjusted, until the detector indicates zero current.(See Fig in next slide)

Let

• R1= unknown resistance
• L1= unknown inductance of the choke.
• L2= known standard inductance
• R2,R3,R4= known resistances.

Comparing real part,

• Comparing the imaginary parts,
• wL1R4 = wL2R3, then

• Advantages
• Expression for R1 and L1 are simple.
• Equations area simple
• They do not depend on the frequency (as w is cancelled)
• R1 and L1 are independent of each other.
• Disadvantages
• Variable inductor is costly.
• Variable inductor is bulky.

Maxwell’s inductance capacitance bridge

• Unknown inductance is measured by comparing it with standard capacitance.
• In this bridge, balance condition is achieved by varying ‘C4’.
• From Fig (shown in next slide)
• Z1= R1+jwL1
• Z2=R2
• Z3=R3
• and

• At balance condition, Z1Z4=Z3Z2

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Substitute the values of Z1,Z2,Z3 and Z4 in the balance condition

we get

• (R1 + jwL1)R4 = R2R3(1+ jwR4C4 )
• R1R4 + jwL1R4 = R2R3 + jwC4R4R2R3
• Comparing real parts, we get
• R1R4 = R2R3

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• Comparing imaginary part,
• wL1R4 = wC4R4R2R3
• L1 = C4R2R3

Q-factor of choke,

• Advantages
• Equation of L1 and R1 are simple.
• They are independent of frequency.
• They are independent of each other.
• Standard capacitor is much smaller in size than standard inductor.
• Disadvantages
• Standard variable capacitance is costly.
• It can be used for measurements of Q-factor in the ranges of 1 to 10.
• It cannot be used for measurements of choke with Q-factors more than 10.
• We know that Q =wC4R4

• For measuring chokes with higher value of Q-factor, the value of C4 and R4 should be higher.
• Higher values of standard resistance are very expensive.
• Therefore this bridge cannot be used for higher value of Q-factor measurements.

Hay’s bridge

• From Fig
• Z1= R1+jwL1
• Z2=R2
• Z3=R3

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• At balance condition, Z1Z4=Z3Z2

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• Comparing the imaginary terms,
• wC4R4R1 + wL1 = wC4R2R3
• C4R4R1 + L1 = C4R2R3
• L1 = C4R2R3 −C4R4R1

Substituting the value of R1 in above equation, then we get

Substitute L1 in R1

• Advantages
• Fixed capacitor is cheaper than variable capacitor.
• This bridge is best suitable for measuring high value of Q-factor.
• Disadvantages
• Equations of L1and R1 are complicated.
• Measurements of R1 and L1 require the value of frequency.
• This bridge cannot be used for measuring low Q- factor.