AC Bridges - 1 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE) PDF Download

What are AC Bridges?

The “AC Bridge” is a natural outgrowth of the DC bridge (Wheatstone bridge) in its basic form consisting of Four bridge arms, a source of excitation, and a null or balanced detector.

These bridge methods are very useful for the measurement of:

• Inductance (L)
• Capacitance (C)
• Frequency (f)
• Mutual inductance (M)
• Storage factor
• Loss factor, etc.

Types of Sources in AC Bridges

1. For Low frequency measurement the power line supply can serve as the source of excitation.
2. For High frequency measurement the electronic oscillator is used as excitation voltage.

Types of Detectors in AC Bridges

1. Headphones

• It is used at frequencies of 250 Hz and over upto 3 to 4 KHz.
• Most sensitive detector for this ranges of frequency.

2. 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.

3. Tuneable Amplifier Detector (TAD)

• It can be used at 10 Hz to 100 KHz.

4. Cathode Ray Oscilloscope (CRO)

• It is used for higher frequencies more than 5 KHz.

Note: For a DC Bridge , the PMMC(Permanent Magnet Moving Coil)  instrument acts as a detector.

AC Bridges through which Inductance (L) is Measured

1. Maxwell’s Inductance Bridge

This bridge measures an unknown inductance by comparison with a variable standard self-inductance.

Maxwell's Inductance Bridge

Let R₁ and L₁ be unknown quantities.
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,

equating real and imaginary parts we get,

2. Maxwell’s Inductance-Capacitance Bridge

This Bridge measures an unknown inductance in terms of a known capacitance.

Maxwell Inductance Capacitance Bridge 

Phasor Diagram for Maxwell Inductance Capacitance Bridge

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 the real part we get,

and equating the imaginary part we get,

Quality Factor:

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 a variable standard capacitor which is very costly.
• The bridge is limited to the measurement of low-quality coils (1 < Q < 10) and it is also unsuitable for the low value of Q (i.e. Q < 1) from this we conclude that a Maxwell bridge is suitable only for medium Q coils.
  
  Question for AC Bridges - 1

  Try yourself:Which of the following statements is true regarding the Maxwell’s Inductance-Capacitance Bridge?
   

  • A.

    It measures an unknown inductance in terms of a known resistance.
     
  • B.

    It requires a variable standard inductor which is very costly.
     
  • C.

    The balance equations are dependent on the frequency term.
     
  • D.

    It is very useful for measurement of a wide range of inductances at power and audio frequencies.
     

  Explanation

  According to the information provided, the Maxwell’s Inductance-Capacitance Bridge measures an unknown inductance in terms of a known capacitance, not resistance. It requires a variable standard capacitor, not an inductor. The balance equations obtained from this bridge are free from the frequency term, meaning they are independent of it. Lastly, it is stated that this bridge is very useful for measuring a wide range of inductances at power and audio frequencies, making the correct answer choice D.

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3. HAY’s Bridge

• This bridge uses resistances in series with the standard capacitor as shown in figure below,

Hay's Bridge

Phasor Diagram of Hay's Bridge

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

Equating real and imaginary parts we get, and  
 
Quality factor =  
i.e.  Now   and  

• 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)

Advantages:

•  It gives a simple expression for the Q-factor.
• For high Q-coils, it gives a simple expression for unknown R₁ and L₁.

Disadvantages:

• It is not suitable for medium or low Q-coils.

4. Anderson’s Bridge

• It is a modification of the Maxwell’s inductance-capacitance bridge.
• In this bridge method, the self-inductance is measured in terms of standard capacitor

 Anderson's Bridge

At balanced condition, V_b = V_e 

So, I_D = 0
Also for the Delta network

we can convert this in star form

 as 

So, 

For balance condition, Z_ab.Z_c = Z_aN.Z_bc

Equating the real part we get,

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

Phasor diagram for Anderson’s bridge:

Phasor Diagram for Anderson's Bridge

Quality factor = 

• It is suitable for Low Q-coils (i.e. Q < 1).
  

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.

Disadvantage:

• It is a more complex circuit.
• The balance equations are not simple and are much more tedious.
• An additional junction point increases the difficulty of shielding the bridge network.

5. Owen’s Bridge

• This bridge may also be used for the measurement of inductance in terms of capacitance.

Owen's Bridge

               Phasor Diagram for Owen's Bridge

Let R₁ and L₁ be the unknown quantity

R₂ = Variable non-inductive resistance

R₃ = Fixed non-inductive resistance

C₂ = Variable standard capacitor

C₄ = Fixed standard capacitor

At balance condition,

Z_abZ_cd = Z_ad. Z_bc

Equating real and imaginary parts we get,

and

L₁ = R₂ R₃ C₄
Quality factor  =
Advantages:

• It has independent balance equations.
• The unknown quantities expressions are free from frequency terms.
  This can be used over a wide range of measurements of inductances.

Disadvantages:

• It requires a variable capacitor so it is a very costly network.
• Its accuracy is about only 1%.

AC bridges through which capacitances are measured

1. De Sauty’s Bridge

• It is the simplest method of comparing two capacitances.
• It may also be used for determining the dissipation factor (D).
  

Considering ideal capacitors, the bridge circuit is,
  De Sauty BridgeLet C₁ = unknown capacitor
C₂ = a standard capacitor
R₃ and R₄ = non-inductive resistors
At balance condition:
Z_ab . Z_cd = Z_ad . Z_bc

The advantage of this bridge is its simplicity but from this we can not determine the “Dissipation Factor (D)”, so some modifications are needed in the above bridge.
Now we consider the lossy capacitor and bridge to become “Modified De-Sauty’s Bridge”.
Modified De Sauty Bridge

• Given C₂ so, D₂ = ωC₂r₂ and we have to estimate C₁ and hence D₁ = ωC₁r₁ 
  At balance condition,
  Z_ab . Z_cd = Z_bc . Z_ad
  
  Equating real part we get, (R₁ + r₁)R₄ = (R₂ + r₂)R₃
  Now equating the imaginary part we have,
     and  
  Also,
    
• This bridge can not determine the accurate result for the dissipation factor because we have,
  D ₂ – D₁ = ω[C₂r₂ – C₁r₁]
  
  Since (D₂ – D₁) is very- very small it is difficult to determine “D₁” accurately.

2. Schering Bridge

The Schering bridge is used for measuring the capacitance of the capacitor, dissipation factor, properties of an insulator, capacitor bushing, insulating oil, and other insulating materials. It is one of the most commonly used AC bridges. The Schering bridge works on the principle of balancing the load on its arm.

In this diagram:
Schering Bridge

• C₁ = capacitor whose capacitance is to be determined
• R₁ = a series resistance representing the loss in the capacitor C₁
• C₂ = a standard capacitor
• R₃ = a variable non-inductive resistance
• C₄ = a variable capacitor
• R₄ = a non-inductive resistance in parallel with the variable capacitor C₄

When the bridge is in the balanced condition, zero current passes through the detector, which shows that the potential across the detector is zero. At balance condition
Z₁/Z₂ = Z₃/Z₄
Z₁Z₄ = Z₂Z₃

Substituting the values of z₁, z₂, z₃ and z₄ in the above equation, we get

Equating the real and imaginary parts and the separating we get,

Phasor Diagram for Schering Bridge

Let us consider the phasor diagram of the above Schering bridge circuit and mark the voltage drops across ab, bc, cd, and ad as e₁, e₃,e_4, and e₂ respectively. From the above Schering bridge phasor diagram, we can calculate the value of tanδ which is also called the dissipation factor.

The equation that we have derived above is quite simple and the dissipation factor can be calculated easily.

Advantages of Schering Bridge:
1. Balance equations are free from frequency.
2. The arrangement of the bridge is less costly as compared to the other bridges.