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AB-11MAXWELL’S CAPACITANCE BRIDGE

ANALOG LABEXPERIMENT BOARD

Ver. 1.0

QUALITY POLICY

To be a Global Provider of Innovative and Affordable Electronic Equipments for Technology Training by enhancing Customer Satisfaction based on Research, Modern manufacturing techniques and continuous improvement in Quality of the products and Services with active participation of employees.

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94-101, Electronic Complex, Pardesipura INDORE-452010, India.Tel.: 91-731-2570301 Fax: 91-731-2555643

AB-11

Email: [email protected] Web: www.scientech.bz

Scientech Technologies Pvt. Ltd. 2

http://www.scientech.bz/

mailto:[email protected]

AB-11


AB-11

MAXWELL’S CAPACITANCE BRIDGE

AB-11

TABLE OF CONTENTS

1. Introduction 4

2. Theory 6

3. Experiment 10To study the operation of Maxwell’s Capacitance Bridge and to measure the value of unknown Inductance and Q factor.

Datasheet 12

4. Warranty 14

5. List of service Centers 15

6. List of Accessories with AB-11 16


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INTRODUCTION

AB-11 is a compact, ready to use MAXWELL’S CAPACITANCE BRIDGE experiment board. This board is useful for students to understand the working and operation of A.C. Bridges. It can be used as stand alone unit with external DC power supply or can be used with SCIENTECH Analog Lab ST-2612 which has built in DC power supply, AC power supply, function generator, modulation generator, continuity tester, toggle switches, and potentiometer.

List of Boards :

Model Name

AB-01 Diode characteristics (Si, Zener, LED)AB-02 Transistor characteristics (CB NPN)AB-03 Transistor characteristics (CB PNP)AB-04 Transistor characteristics (CE NPN)AB-05 Transistor characteristics (CE PNP)AB-06 Transistor characteristics (CC NPN)AB-07 Transistor characteristics (CC PNP)AB-08 FET characteristicsAB-09 Rectifier CircuitsAB-10 Wheatstone Bridge AB-14 Darlington PairAB-15 Common Emitter AmplifierAB-16 Common Collector AmplifierAB-17 Common Base AmplifierAB-18 Cascode AmplifierAB-19 RC-Coupled AmplifierAB-21 Class A AmplifierAB-22 Class B Amplifier (push pull emitter follower)AB-23 Class C Tuned AmplifierAB-25 Phase Locked Loop (FM Demodulator & Frequency

Divider / Multiplier)AB-28 Multivibrator ( Monostable / Astable)AB-29 F-V and V-F ConverterAB-30 V-I and I-V ConverterAB-31 Zener Voltage Regulator AB-32 Transistor Series Voltage RegulatorAB-33 Transistor Shunt Voltage RegulatorAB-41 Differential Amplifier (Transistorized)


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AB-42 Operational Amplifier (Inverting / Non-inverting / Differentiator)

AB-43 Operational Amplifier (Adder/Scalar)AB-44 Operational Amplifier (Integrator/ Differentiator)AB-45 Schmitt Trigger and ComparatorAB-51 Active filters (Low Pass and High Pass)AB-52 Active Band Pass Filter AB-53 Notch Filter AB-54 Tschebyscheff Filter AB-56 Fiber Optic Analog LinkAB-65 Phase Shift OscillatorAB-66 Wien Bridge OscillatorsAB-67 Colpitt OscillatorAB-68 Hartley OscillatorAB-80 RLC Series and RLC Parallel Resonance AB-81 Kirchoff’s Laws (Kirchoff’s Current Law & Kirchoff’s

Voltage Law)AB-82 Thevenin’s and Maximum power Transfer TheoremAB-83 Reciprocity and Superposition TheoremAB-84 Tellegen’s TheoremAB-85 Norton’s theoremAB-88 Diode ClipperAB-89 Diode ClampersAB-90 Two port network parameterAB-91 Optical Transducer (Photovoltaic cell)AB-92 Optical Transducer (Photoconductive cell/LDR)AB-93 Optical Transducer (Phototransistor)AB-96 Temperature Transducer (RTD & IC335)AB-97 Temperature Transducer (Thermocouple)AB-101 DSB Modulator and DemodulatorAB-102 SSB Modulator and DemodulatorAB-106 FM Modulator and Demodulator

………… and many more


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THEORY

Alternating current Bridge methods are of outstanding importance for measurement of electrical quantities measurement of inductance, capacitance, storage factor, loss factor may be made conveniently and accurately by employing a.c. bridge networks.

An a.c. bridge, in its basic form, consists of four arms, a source of excitation and a balance detector. In an a.c. bridge each of four arms is impedance, and the a.c. source and a detector sensitive to small alternating potential differences.

The usefulness of a.c. bridge circuits is not restricted to the measurement of unknown impedances and associated parameters like inductance, capacitance, storage factor etc. These circuits find other application in communication system and complex electronics circuits. Alternating current bridge circuits are commonly used for phase shifting, providing feedback paths for oscillators and amplifiers, filtering out undesirable signals ad measuring the frequency of audio signals.

For measurement at low frequencies, the power line may act as the source of the supply to bridge circuits. For higher frequencies electronic oscillators are universally used as bridge source supplies. These oscillators have the advantage that the frequency is constant, easily adjustable and determinable with accuracy .The waveform is very close to a sine wave, and their power output is sufficient for most bridge measurements.

Detectors most commonly used for a.c. bridges are:

a. Head phones

b. Vibration galvanometers

c. Tuneable amplifiers detectors

Headphones are widely used as detectors at frequencies of 250 Hz and up to 3 or 4 kHz. They are most sensitive detectors for this range

When working at a single frequency a tuned detector normally gives the greatest sensitivity and discrimination against harmonics in the supply. Vibration galvanometers are extremely used for power and low audio frequency ranges. Vibration galvanometers are manufactures to work at various frequencies ranging from 5 Hz to 1000 Hz but are most commonly used below 200 Hz as below this frequency they are more sensitive that the head phones.


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Tuneable amplifiers detectors are the most versatile of the detectors .The transistors amplifiers can be tuned electrically and thus can be made to respond to a narrow bandwidth at the bridge frequency .The output of the amplifier is fed to a pointer type instrument this detector can be used, over a frequency range of 10 Hz to 100 kHz.

General equation for bridge balance:

Basic a.c. bridge circuit is shown below in fig.1

The four arm of the bridge are impedance Z1, Z2, Z3, Z4.

Basic A.C. bridge network Fig.1

The condition for balance of bridge require that there should be no current through the detector .This requires that the potential difference between points b and d should be zero. This will be the case when the voltage drop from a to b equals the voltage drop from a to d, both in magnitude and phase. In complex notation we can, thus, write:

E1 = E2 …………….(1)

I1Z1 =I2Z2 …………….(2)

Also at balance, I1=I3 =E/Z1+Z2 …………….(3)

I2=I4=E/Z2+Z4 …………….(4)

Substituting the value of I1and I2 in eq.2, we get

Z1Z4=Z2Z3 …………….(5)


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Eq.5 states that the product of impedances of one pair opposite arms must equal the product of impedance of the other pair of opposite arms in complex notation .This means that both magnitude and phase angle of the impedance must be taken into account.

Two conditions must be satisfied simultaneously when balancing the a.c. bridge

1. The first condition is that the magnitude of impedances satisfies the relationship:

Z1 Z4=Z2Z3 …………….(6)2. The second condition is that the phase angles of impedance satisfy

the relationship:θ1+θ4=θ2+θ3 …………….(7)

The phase angles are positive for inductive impedance and negative for capacitance impedance.

Measurement of self inductance by Maxwell’s capacitance bridge:

In this bridge, an inductance is measured by comparison with a standard or variable capacitance.

Maxwell’s Capacitance Bridge

Fig.2

L1 =unknown inductanceR1 =effective resistance of inductor L1

R2, R3, R4= unknown non-inductive resistancesC4= standard capacitor


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And writing the eq. for balance

(R1+jωL1)(R4/1+jωC4R4)=R2R3 ………….(8)

or

R1R4+jωL1R4=R2R3+jωR2R3C4R4 …………….(9)

Separating the real and imaginary terms, we have

R1 =R2R3/R4 ……………(10)

and L1=R2R3C4 ……………(11)

The expression for Q factor

Q=ωL1/R1=ωC4R4 ……………(12)

Advantages of this bridge are :

1. The frequency does not appear in any of the two equations i.e value of L and R independent of the frequency.

2. The Maxwell’s capacitance bridge is very useful for measurement of a wide rage of inductance at power and audio frequencies.

Disadvantages :

The main disadvantage is the bridge is limited to measurement of low Q coils (1<Q<10) thus for values of Q>10 the Maxwell’s bridge is unsuitable. The Maxwell’s bridge is also unsuited for coils with a very low value of Q (i.e. Q<1). Q value of this magnitude occur in inductive resistors or in R.F. coil if measured at low frequencies .The difficulty in measurement occurs on amount of labour involved in obtaining balance. Only medium Q coils measurements are suited with the Maxwell’s capacitance bridge.


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EXPERIMENT 1Object : To study the operation of Maxwell’s Capacitance Bridge and to

measure the value of unknown inductance and Q factor.Apparatus Required :

1. Analog board AB-11.

2. DC power supply +12V from external source or ST-2612 Analog Lab.

3. Function Generator ST- 4064.

4. Oscilloscope.

5. Multimeter.

6. 2mm patch chords.

Circuit Diagram :Circuit used to study the operation of Maxwell’s Capacitance Bridge and to

measure the value of unknown inductance is shown in fig3.

Fig.3


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Procedure :

• Connect +12V,-12V power supplies and gnd at their indicated position from external source or ST-2612 Analog Lab.

1. Adjust the pot in the minimum position so that the resistance R3 between the arm is minimum by measuring it with help of multimeter.

2. Connect 10Vp-p, 1 KHz sine wave signal at the input Vin (positive and negative terminal) of Maxwell’s Capacitance Bridge AB-11 board.

3. Connect the unknown inductor with 2mm patch cord with arm consisting resistance R2.

4. Now vary the resistance R3 with the help of pot till the null position (or the first minimum sound position) is achieved.

5. Now switch off the power supply and remove all the patch cord and measure the resistance R3 with the help of multimeter.

6. Calculate the value of unknown inductor using eq.11

7. Calculate the value for Q factor by using eq.12

8. Verify the result for calculation of Q factor using both the formula in eq.12

9. Verify the result for unknown value of resistance Rx1 by measuring it with help of multimeter and calculating it using eq.10

10. Repeat the process for different values of inductors.

Result :

The unknown value of Inductor L1, Resistance Rx1 and Q factor are ……

The unknown value of Inductor L2, Resistance Rx2 and Q factor are ....….

The unknown value of Inductor L3, Resistance Rx3 and Q factor are …….

Note :

1. The value of inductor L1, L2 and L3 are 10mH, 20mH and 58.8mH.

2. Small amount of error would be there due to component variations and also due to human error.


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DATASHEET


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AB-11

WARRANTY

1. We guarantee the instrument against all manufacturing defects during 24 months from the date of sale by us or through our dealers.

2. The guarantee covers manufacturing defects in respect of indigenous components and material limited to the warranty extended to us by the original manufacturer, and defect will be rectified as far as lies within our control.

3. The guarantee will become INVALID.a. If the instrument is not operated as per instruction given in the

instruction manual. b. If the agreed payment terms and other conditions of sale are not

followed.c. If the customer resells the instrument to another party.d. Provided no attempt have been made to service and modify the

instrument.

4. The non-working of the instrument is to be communicated to us immediately giving full details of the complaints and defects noticed specifically mentioning the type and sr. no. of the instrument, date of purchase etc.

5. The repair work will be carried out, provided the instrument is dispatched securely packed and insured with the railways. To and fro charges will be to the account of the customer.

DISPATCH PROCEDURE FOR SERVICE

Should it become necessary to send back the instrument to factory please observe the following procedure:

1. Before dispatching the instrument please write to us giving full details of the fault noticed.

2. After receipt of your letter our repairs dept. will advise you whether it is necessary to send the instrument back to us for repairs or the adjustment is possible in your premises.

Dispatch the instrument (only on the receipt of our advice) securely packed in original packing duly insured and freight paid along with accessories and a copy of the details noticed to us at our factory address.


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LIST OF SERVICE CENTERS

1. Scientech Technologies P. Ltd.90, Electronic Complex Ph: (0731) 5202959Pardesipura, Email: [email protected] INDORE – 452010

2. Scientech Technologies P. Ltd. Ph.: (011) 26513912, 26864943First Floor, 14, Uday Park, Fax: (011) 26864943.NEW DELHI – 110049 Email: [email protected]

3. Scientech Technologies P. Ltd.New no.2, Old no.10, 4th street Ph.: (044) 52187548, 52187549

Venkateswara nagar, Adyar Fax: (044) 52187549CHENNAI – 600025 Email: [email protected]

4. Scientech Technologies P. Ltd. 202/19, 4th main street Ph.: (080) 51285011 Ganganagar, Fax: (080) 51285022 BANGALORE- 560032 Email: [email protected]. Scientech Technologies P. Ltd. Ph.: (022) 56299457 8,1st floor, 123-Hariram Mansion, Fax: (022) 24168767 Dada Saheb Phalke road, Email: [email protected] Dadar (East), MUMBAI –400014 6. Scientech Technologies P. Ltd. 988, Sadashiv Peth, Ph.: (020) 24461673 Gyan Prabodhini Lane, Fax: (020) 24482403 PUNE – 411030 Email: [email protected]. Scientech Technologies P. Ltd SPS Apartment, 1st Floor Ph. +913355266800 2, Ahmed Maooji Street, E mail : [email protected]

Behind Jaiswal Hospital, Liluah, HOWRAH-711204

W.B.


AB-11

LIST OF ACCESSORIES

1. 2mm patch cord (red)................................................................ 3 Nos.

2. 2mm patch cord (blue).............................................................. 2 Nos.

3. 2mm patch cord (black)............................................................ 3 Nos.


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