D.C & A.C Bridges
Bridge circuits are used very commonly as a variable conversion element in
measurement systems and produce an output in the form of a voltage level that
changes as the measured physical quantity changes. They provide an accurate
method of measuring resistance, inductance and capacitance values, and enable
the detection of very small changes in these quantities about a nominal value.
They are of immense importance in measurement system technology because so
many transducers measuring physical quantities have an output that is expressed
as a change in resistance, inductance or capacitance. The displacement-measuring
strain gauge, which has a varying resistance output, is but one example of this
class of transducers. Normally, excitation of the bridge is by a d.c. voltage for
resistance measurement and by an a.c. voltage for inductance or capacitance
measurement. Both null and deflection types of bridge exist, and, in a like manner
to instruments in general, null types are mainly employed for calibration purposes
and deflection types are used within closed-loop automatic control schemes.
Null-type, d.c. bridge (Wheatstone bridge)
A null-type bridge with d.c. excitation, commonly known as a Wheatstone bridge,
has the form shown in Figure 7.1. The four arms of the bridge consist of the
unknown resistance Ru, two equal value resistors R2 and R3 and a variable resistor
Rv (usually a decade resistance box). A d.c. voltage Vi is applied across the points
AC and the resistance Rv is varied until the voltage measured across points BD is
zero. This null point is usually measured with a high sensitivity galvanometer.
To analyses the Whetstone bridge, define the current flowing in each arm to be I 1 .
. . I4 as shown in Figure 7.1. Normally, if a high impedance voltage-measuring
instrument is used, the current Im drawn by the measuring instrument will be very
small and can be approximated to zero. If this assumption is made, then, for Im
D 0:
I1 =I3 and I2 =I4
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,Deflection-type d.c. bridge
A deflection-type bridge with d.c. excitation is shown in Figure 7.2. This differs
from the Wheatstone bridge mainly in that the variable resistance R vis replaced
by a fixed resistance R1 of the same value as the nominal value of the unknown
resistance Ru . As the resistance Ru changes, so the output voltage V0 varies, and
this relationship between V0 and Ru must be calculated.
This relationship is simplified if we again assume that a high impedance voltage
measuring instrument is used and the current drawn by it, Im , can be
approximated to zero. (The case when this assumption does not hold is covered
later in this section.) The analysis is then exactly the same as for the preceding
example of the Wheatstone bridge, except that Rv is replaced by R1. Thus, from
equation (7.1), we have:
V0= Vi * ( Ru / Ru + R3)- ( R1 / R1+ R2)
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, When Ru is at its nominal value, i.e. for Ru D R1, it is clear that V0 D0 (since R2 D
R3). For other values of Ru, V0 has negative and positive values that vary in a
non-linear way with Ru.
A.C bridges
Bridges with a.c. excitation are used to measure unknown impedances. As for d.c.
bridges, both null and deflection types exist, with null types being generally
reserved for calibration duties.
Null-type impedance bridge
A typical null-type impedance bridge is shown in Figure 7.7. The null point can
be conveniently detected by monitoring the output with a pair of headphones
connected via an operational amplifier across the points BD. This is a much
cheaper method of null detection than the application of an expensive
galvanometer that is required for a d.c. Wheatstone bridge.
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Bridge circuits are used very commonly as a variable conversion element in
measurement systems and produce an output in the form of a voltage level that
changes as the measured physical quantity changes. They provide an accurate
method of measuring resistance, inductance and capacitance values, and enable
the detection of very small changes in these quantities about a nominal value.
They are of immense importance in measurement system technology because so
many transducers measuring physical quantities have an output that is expressed
as a change in resistance, inductance or capacitance. The displacement-measuring
strain gauge, which has a varying resistance output, is but one example of this
class of transducers. Normally, excitation of the bridge is by a d.c. voltage for
resistance measurement and by an a.c. voltage for inductance or capacitance
measurement. Both null and deflection types of bridge exist, and, in a like manner
to instruments in general, null types are mainly employed for calibration purposes
and deflection types are used within closed-loop automatic control schemes.
Null-type, d.c. bridge (Wheatstone bridge)
A null-type bridge with d.c. excitation, commonly known as a Wheatstone bridge,
has the form shown in Figure 7.1. The four arms of the bridge consist of the
unknown resistance Ru, two equal value resistors R2 and R3 and a variable resistor
Rv (usually a decade resistance box). A d.c. voltage Vi is applied across the points
AC and the resistance Rv is varied until the voltage measured across points BD is
zero. This null point is usually measured with a high sensitivity galvanometer.
To analyses the Whetstone bridge, define the current flowing in each arm to be I 1 .
. . I4 as shown in Figure 7.1. Normally, if a high impedance voltage-measuring
instrument is used, the current Im drawn by the measuring instrument will be very
small and can be approximated to zero. If this assumption is made, then, for Im
D 0:
I1 =I3 and I2 =I4
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,Deflection-type d.c. bridge
A deflection-type bridge with d.c. excitation is shown in Figure 7.2. This differs
from the Wheatstone bridge mainly in that the variable resistance R vis replaced
by a fixed resistance R1 of the same value as the nominal value of the unknown
resistance Ru . As the resistance Ru changes, so the output voltage V0 varies, and
this relationship between V0 and Ru must be calculated.
This relationship is simplified if we again assume that a high impedance voltage
measuring instrument is used and the current drawn by it, Im , can be
approximated to zero. (The case when this assumption does not hold is covered
later in this section.) The analysis is then exactly the same as for the preceding
example of the Wheatstone bridge, except that Rv is replaced by R1. Thus, from
equation (7.1), we have:
V0= Vi * ( Ru / Ru + R3)- ( R1 / R1+ R2)
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, When Ru is at its nominal value, i.e. for Ru D R1, it is clear that V0 D0 (since R2 D
R3). For other values of Ru, V0 has negative and positive values that vary in a
non-linear way with Ru.
A.C bridges
Bridges with a.c. excitation are used to measure unknown impedances. As for d.c.
bridges, both null and deflection types exist, with null types being generally
reserved for calibration duties.
Null-type impedance bridge
A typical null-type impedance bridge is shown in Figure 7.7. The null point can
be conveniently detected by monitoring the output with a pair of headphones
connected via an operational amplifier across the points BD. This is a much
cheaper method of null detection than the application of an expensive
galvanometer that is required for a d.c. Wheatstone bridge.
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