Unit-3
AC/DC BRIDGES AND
INSTRUMENTATION AMPLIFIERS
Part -A:
1. Write the two conditions to be satisfied for balancing AC bridges
and DC bridges.
(1) the current I may be held at a fixed value and
the resistance R across which the IR drop is opposed to the unknown
may be varied.
(2) current may be varied across a fixed resistance
to achieve the needed IR drop.
2. Write any two limitation of wheat stone bridge.
1.The resistance of the bridge arms can vary
with temperature, affecting the accuracy of the measurements.
2. It is most effective for detecting small
changes in resistance; large resistance variations may cause the bridge
to become unbalanced and less accurate.
3. 12V Dc was input to a wheat stone bridge. The ratio arm
impedances were 400 ohm and 200 ohm. A 560 ohm standard was
connected in the third arm. Find the magnitude of resistance in the
unknown arm.
Soln:
R1/R2 = R3/R4
400/200 = 560/R4
2 = 560/R4
R4 = 560/2 = 280 ohm.
4. What type of AC bridges is used for measurement of capacitance?
Also writes its formula.
A Schering Bridge is a bridge circuit used for
measuring an unknown electrical capacitance and its dissipation factor.
The dissipation factor of a capacitor is the the ratio of its resistance to
its capacitive reactance.
when the bridge is balanced,
C2/C3 = R2/R1 or C3 = R1C2 / R2
5. List the various errors observed in AC bridges.
- Unwanted capacitance or inductance between
bridge components or leads can distort measurements.
- Electromagnetic interference from nearby
components or wires may cause signal distortion.
- In capacitive bridges, dielectric losses in
components can affect the accuracy of capacitance measurement.
- Changes in temperature can alter resistance or
capacitance values of components in the bridge.
6. Give the role of instrumentation amplifier.
An instrumentation amplifier (IA) is a type of
amplifier designed to amplify very weak signals while rejecting noise
and other unwanted signals.
7. Specify the purpose of Wagner Earthing devices.
1.When measuring small capacitance and
large integrance values at high frequency an error is produced due
to stray capacitance.
2.The wagner electric device is used to
remove these stray capacitance and the capacitance between the
bridge arms.
8. What is meant by self-balancing bridge? Give two examples.
A self-balancing bridge is a type of bridge
circuit that automatically adjusts its components to maintain a balanced
state.This is achieved by using feedback mechanisms, often involving
amplifiers, to correct any imbalances.
examples of self-balancing bridges are bolometer bridge and the Kelvin
double bridge.
9. What are the sources of electromagnetic interference? How are the
AC bridges protected from electrostatic and electromagnetic
interference?
The sources of EMI are Lightning, motors and
generators, radio transmitters ,etc.
The AC bridges protected from electrostatic and electro magnetic
interference by Ensuring all closures and shielding are connected to the
low impedence ground.
10. List the application of AC bridges.
1.It is used to measure inductance.
2.It is used to measure capacitance.
3.It is used to measure frequency.
4.It is used to measure resistance.
11. How kelvins double bridges differ from wheat stone bridge?
The Kelvin double bridge is a modified version of
the Wheatstone bridge specifically designed for accurately measuring
very low resistances, typically below 1 ohm, while the Wheatstone
bridge is suitable for a wider range of resistances.
12. Identify the detectors used in AC bridges.
The detectors used in AC bridges are vibration
galvanometers, tuned amplifiers and Cathode Ray Oscilloscopes (CRO’s).
PART: B
1. Draw the circuit diagram of a schering’s bridge and derive the
expressions for the unknown quantities.
A Schering Bridge is a bridge circuit used for
measuring an unknown electrical capacitance and its dissipation factor.
The dissipation factor of a capacitor is the the ratio of its resistance to its
capacitive reactance. The Schering Bridge is basically a four-arm
alternatingcurrent (AC) bridge circuit whose measurement depends on
balancing the loads on its arms.
Figure 1 below shows a diagram of the Schering Bridge. Diagram
Figure 1.7.2. Schering Bridge
Explanation
In the Schering Bridge above, the resistance values of
resistors R1 and R2 are known, while the resistance value of
resistor R3 is unknown.
The capacitance values of C1 and C2 are also known,
while the capacitance of C3 is the value being measured.
To measure R3 and C3, the values of C2 and R2 are
fixed, while the values of R1 and C1 are adjusted until the current
through the ammeter between points A and B becomes zero.
This happens when the voltages at points A and B are
equal, in which case the bridge is
said to be 'balanced'.
When the bridge is balanced, Z1/C2 = R2/Z3, where Z1
is the impedance of R1 in parallel with C1 and Z3 is the
impedance of R3 in series with C3.
In an AC circuit that has a capacitor, the capacitor contributes a
capacitive reactance to the impedance.
Z1 = R1/[2πfC1((1/2πfC1) + R1)] = R1/(1 + 2πfC1R1) while Z3 =1/2πfC3
+ R3. 2πfC2R1/ (1+2πfC1R1) = R2/(1/2πfC3 + R3); or 2πfC2 (1/2πfC3 +
R3) = (R2/R1) (1+2πfC1R1); or
C2/C3 + 2πfC2R3 = R2/R1 + 2πfC1R2.
When the bridge is balanced, the negative and positive
reactive components are equal and cancel out, so
2πfC2R3 = 2πfC1R2 or R3 = C1R2 / C2.
Similarly, when the bridge is balanced, the purely
resistive components are equal, so C2/C3 = R2/R1 or C3 =
R1C2 / R2.
Note that the balancing of a Schering Bridge is
independent of frequency.
Advantages:
Balance equation is independent of frequency
Used for measuring the insulating properties of electrical cables
and equipment’s
2. Explain how inductance is measured in terms of known capacitance
using Maxwell’s bridge and also derive the equation for balance
condition.
Definition
A Maxwell bridge (in long form, a Maxwell-Wien
bridge) is a type of Wheatstone bridge used to measure an unknown
inductance (usually of low Q value) in terms of calibrated resistance
and capacitance. It is a real product bridge.
The maxwell bridge is used to measure unknown inductance in terms
of calibrated resistance and capacitance. Calibration-grade inductors
are more difficult to manufacture than capacitors of similar precision,
and so the use of a simple "symmetrical" inductance bridge is not
always practical.
Circuit Diagram
Figure 1.7.1. Maxwell Bridge
Explanation
With reference to the picture, in a typical application R1
and R4 are known fixed entities, and R2 and C2 are known
variable entities.
R2 and C2 are adjusted until the bridge is balanced.R3
and L3 can then be calculated based on the values of the other
components:
As shown in Figure, one arm of the Maxwell bridge
consists of a capacitor in parallel with a resistor (C1 and R2) and
another arm consists of an inductor L1 in series with a resistor
(L1 and R4). The other two arms just consist of a resistor each
(R1 and R3).
The values of R1 and R3 are known, and R2 and
C1 are both adjustable. The unknown values are those of L1 and
R4.
Like other bridge circuits, the measuring ability of a
Maxwell Bridge depends on
'Balancing' the circuit.
Balancing the circuit in Figure 1 means adjusting C1 and R2 until
the current through the bridge between points A and B becomes zero.
This happens when the voltages at points A and B are equal.
Mathematically,
Z1 = R2 + 1/ (2πfC1); while Z2 = R4 + 2πfL1. (R2 + 1/ (2πfC1))
/ R1 = R3 / [R4 + 2πfL1]; or
R1R3 = [R2 + 1/ (2πfC1)] [R4 + 2πfL1]
To avoid the difficulties associated with determining the
precise value of a variable capacitance, sometimes a fixed-value
capacitor will be installed and more than one resistor will be
made variable.
The additional complexity of using a Maxwell bridge
over simpler bridge types is warranted in circumstances where
either the mutual inductance between the load and the known
bridge entities, or stray electromagnetic interference, distorts the
measurement results.
The capacitive reactance in the bridge will exactly
oppose the inductive reactance of the load when the bridge is
balanced, allowing the load's resistance and reactance to be
reliably determined.
Advantages:
The frequency does not appear
Wide range of inductance Disadvantages:
Limited measurement
It requires variable standard capacitor.
