Chapter 1 (Part 1) AC Bridges - Notes, Electrical Measurement, Electrical Engineering Notes - Electrical Engineering (EE)

Electrical Engineering (EE): Chapter 1 (Part 1) AC Bridges - Notes, Electrical Measurement, Electrical Engineering Notes - Electrical Engineering (EE)

The document Chapter 1 (Part 1) AC Bridges - Notes, Electrical Measurement, Electrical Engineering Notes - Electrical Engineering (EE) is a part of Electrical Engineering (EE) category.
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Chapter 1 (Part 1) AC Bridges

A.C. BRIDGES

v Introduction :  The “AC Bridges” is a natural outgrowth of the DC bridge (wheatstone bridge) in its basic form consists of Four bridge arms a source of excitation and a null or balanced detector.  These bridge methods are very useful for the measurement of : Þ Inductance (L) Þ Capacitance (C) Þ Frequency (f) Þ Mutual inductance (M) Þ Storage factor Þ Loss factor, etc. ¦ Types of Sources in AC Bridges :  For Low frequency measurement the power line supply can serve as the source of excitation.  For High frequency measurement the electronic oscillator is used as excitation voltage. ¦ Types of detectors in AC Bridges : n Head phones  It is used at frequencies of 250 Hz and over upto 3 to 4 KHz.  Most sensitive detector for this ranges of frequency. n Vibration galvanometer  It can be used from 5 Hz to 1000 Hz but suitable mainly upto 200 Hz.  They are extremely useful for power and low AF ranges. n Tuneable Amplifier Detector (TAD)  It can be used at 10 Hz to 100 KHz. n Cathode Ray Oscilloscope (CRO)  It is used for higher frequency more than 5 KHz.

Note : Þ F or a DC Bri dge , the “PMMC ” instrument acts as a detector.

 

AC bridges through which inductance (L) is measured : 1. Maxwell’s inductance bridge 2. Maxwell’s inductance-capacitance bridge 3. Hay’s bridge 4. Anderson’s bridge 5. Owen’s bridge

Maxwell’s Inductance Bridge :  This bridge measures an unknown unductance by comparison with a variable standard self unductance.

 

 

Let R1 and L1 are unknown quantity L2 = Variable inductance of fixed resistance ‘r2’ R2 = Variable resistance connected in series with “L2” R3 and R4 = Known non-inductive resistances.

At balance condition,

 

Z1Z4 = Z2Z3

Þ (R1 + JwL1).R4 = {(R2 + r) + JwL2} × R3 equation real and imaginary part we get,

 

Maxwell’s Inductance-capacitance Bridge :  This Bridge measures an unknown inductance in terms of a known capacitance.

 

Let R1 and L1 are unknown quantity R2, R3 and R4 are known non-inductive resistances and C4 = variable standard capacitor At balance condition, Z1Z4 = Z2Z3

Equating real part we get,

and equating imag. part we get,

 

 This bridge is suitable for the measurement of “medium-Q coils” (1 < Q < 10). n Advantages  Circuit is simple.  Obtained balance equations are free from the frequency term.  Balance equations are independent if we choose R4 and C4 as variable elements.  It is very useful for measurement of a wise range of inductances at power and audio frequencies.

Disadvantages  It requires variable standard capacitor which is very costly.  For high or low Q-coils, it is not suitable. v Hay’s Bridge :  It is a modification of Maxwell’s bridge.  This bridge uses a resistances in series with the standard capacitor as shown in figure below,

 

 

Let,R1 and L1 are unknown quantity R2, R3 and R4 are non-inductive resistances. andC4 = standard capacitor At balance condition, Z1Z4 = Z2Z3

 

Equating real and imaginary parts we get,

 

In this bridge, the expression for the unknown inductance and resistance involves the frequency term.

So, for the higher Q (i.e. Q > 10) 1 + (1/Q)2 » 1 and then,

 

So, we can say this bridge is suitable for high Q-coils (i.e. Q > 10). n Advantages  It gives a simple expression for Q-factor.  For high Q-coils it gives simple expression for unknown R1 and L1. n Disadvantages  It is not suitable for medium or low Q-coils. v Anderson’s Bridge:  It is a mod ific at ion of the M ax w ell ’s inductance-capacitance bridge.  In this bridge method, the self inductance is measured in terms of standard capacitor

 

At balanced condition, Vb = Ve So, ID = 0 Also for the Delta network

we can convert this in star form

 

Now the circuit of figure 3.5 (a) can be represented as,

For balance condition, Zab.Zc = ZaN.Zbc

 

Equating real part we get,

 

Now equating imaginary part we get, L1 R4 = R3C[R2 R4 + rR2 + rR4]

 

Phasor diagram for Anderson’s bridge n/w :

 

For Low Q-coil, L1 ¯ and C ¯ So, it is suitable for Low Q-coils (i.e. Q < 1). n Advantages  It may be used for accurate estimation of capacitance in terms of inductance.  It is relatively cheaper because here fixed capacitance is used.  It is much easier to obtain the balance. n Disadvantage  It is more complex circuit.  The balance equations are not simple and infact are much more tedious.  An additional junction point increases the difficulty of shielding the bridge network. v Own’s Bridge :  This bridge may also be used for the measurement of inductance in terms of capacitance.

 

Let R1 and L1 are the unknown quantity R2 = Variable non-inductive resistance R3 = Fixed non-inductive resistance C2 = Variable standard capacitor C4 = Fixed standard capacitor At balance condition, ZabZcd = Zad . Zbc Þ (R1 + JwL1) (1/JwC4) = {R2 + (1/JwC2}R3

Þ R1 + JwL1 = JwR2R3C4 +

Equating real and imaginary part we get,

and

 

The document Chapter 1 (Part 1) AC Bridges - Notes, Electrical Measurement, Electrical Engineering Notes - Electrical Engineering (EE) is a part of Electrical Engineering (EE) category.
All you need of Electrical Engineering (EE) at this link: Electrical Engineering (EE)

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