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:
2. Vibration Galvanometer
3. Tuneable Amplifier Detector (TAD)
4. Cathode Ray Oscilloscope (CRO)
Note: For a DC Bridge , the “PMMC ” instrument acts as a detector.
This bridge measures an unknown inductance by comparison with a variable standard self inductance.
Let R_{1} and L_{1} are unknown quantities.
L_{2} = Variable inductance of fixed resistance ‘r_{2}’
R_{2} = Variable resistance connected in series with “L_{2}”
R_{3} and R_{4} = Known noninductive resistances.
At balance condition,
equation real and imaginary part we get,
and
This Bridge measures an unknown inductance in terms of a known capacitance.
Let R_{1} and L_{1 }are unknown quantity R_{2}, R_{3} and R_{4 }are known noninductive resistances and C_{4} = variable standard capacitor
At balance condition, Z_{1}Z_{4} = Z_{2}Z_{3}
Equating real part we get,
and equating 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 R_{4} and C_{4} 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.
• The bridge is limited to measurement of low quality coils (1 < Q < 10) and it is also unsuitable for low value of Q (i.e. Q < 1) from this we conclude that a Maxwell bridge is used suitable only for medium Q coils.
Let,R_{1} and L_{1} are unknown quantity
R_{2}, R_{3} and R_{4} are noninductive resistances.
and C_{4} = standard capacitor
At balance condition,
Z_{1}Z_{4 }= Z_{2}Z_{3}
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 Qcoils (i.e. Q > 10)
Advantages:
• It gives a simple expression for Qfactor.
• For high Qcoils it gives simple expression for unknown R_{1} and L_{1}.
Disadvantages:
• It is not suitable for medium or low Qcoils.
• It is a modification of the Maxwell ’s inductancecapacitance bridge.
• In this bridge method, the self inductance is measured in terms of standard capacitor
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_{a}N.Z_{bc}
Equating real part we get,
Now equating imaginary part we get,
L_{1} R_{4} = R_{3}C[R_{2} R_{4} + rR_{2} + rR_{4}]
Phasor diagram for Anderson’s bridge n/w:
Quality factor =
• For Low Qcoil, L_{1} and C So, it is suitable for Low Qcoils (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 more complex circuit.
• The balance equations are not simple and in fact are much more tedious.
• An additional junction point increases the difficulty of shielding the bridge network.
• This bridge may also be used for the measurement of inductance in terms of capacitance.
Let R_{1} and L_{1} are the unknown quantity
R_{2} = Variable noninductive resistance
R_{3} = Fixed noninductive resistance
C_{2} = Variable standard capacitor
C_{4 }= Fixed standard capacitor
At balance condition,
Z_{ab}Z_{cd} = Z_{ad} . Z_{bc}
Equating real and imaginary part we get,
and
L_{1} = R_{2} R_{3} C_{4}
Quality factor =
Advantages:
• It has independent balance equations.
• The unknown quantities expressions are free from frequency term.
This can be used over a wide range of measurement of inductances.
Disadvantages:
• It requires a variable capacitor so it is very costly network.
• Its accuracy is about only 1%.
AC bridges through which capacitances are measured
1. De Sauty’s bridge
2. Schering bridge
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).
Note:
then D = tan δ = ωC_{s} r_{s}
then D = tan
δ = 1/ωC_{p} r_{p}
Considering ideal capacitors, the bridge circuit is,
Let C_{1 }= unknown capacitor
C_{2} = a standard capacitor
R_{3} and R_{4} = noninductive 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 “Dissipation Factor (D)”, so some modification are needed in the above bridge.
Now we consider the lossy capacitor and bridge in becomes “Modified DeSauty’s Bridge”.
• Given C_{2} so, D_{2} = ωC_{2}r_{2} and we have to estimate C_{1} and hence D_{1} = ωC_{1}r_{1 }
At balance condition,
Z_{ab} . Z_{cd }= Z_{bc} . Z_{ad}
Equating real part we get, (R_{1} + r_{1})R_{4 }= (R_{2} + r_{2})R_{3}
Now equating imaginary part we have,
and
Also,
• This bridge can not determine the accurate result for dissipation factor because we have,
D _{2} – D_{1} = ω[C_{2}r_{2} – C_{1}r_{1}]
Since (D_{2} – D_{1}) is veryvery small so its is difficult to determine “D_{1}” accurately.
2. Schering Bridge
The Schering bridge use 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 bridge. The Schering bridge works on the principle of balancing the load on its arm.
In this diagram:
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
Z_{1}/Z_{2} = Z_{3}/Z_{4}
Z_{1}Z_{4} = Z_{2}Z_{3}
Substituting the values of z_{1}, z_{2}, z_{3} and z_{4} in the above equation, we get
Equating the real and imaginary parts and the separating we get,
Let us consider the phasor diagram of the above Schering bridge circuit and mark the voltage drops across ab,bc,cd and ad as e_{1}, e_{3},e_{4} and e_{2} 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.
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