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Author’s name
Department of Electronics & Telecommunication Engineering,
St Francis Institute of technology,
Mt Poinsur, S V P Road, Borivali (W), Mumbai 400 076, India
Email: [email protected]
Abstract: The abstract will be in italic, Times New Roman Font, size 10.
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1.
2.1 Maxwell bridge
Introduction
Consider the Maxwell bridge shown in Fig 2. Using
eqns (2) and (3), we get
AC bridges have been known for quite some time for
finding the equivalent circuits of coils and capacitors
[1]. These bridges are now revisited in the context of
measuring quality factor (Q) of the coils and the
dissipation factor (tan  ) of the capacitors. One
method of measuring tan  of a capacitor is by phase
compensation [2].

1  jC3 R3 
Rx  Re  R2 R4

R3


R2 R4

,
R3
Note the following.
In the conventional bridge method of measuring these
quantities, one has to balance the bridge and then
perform manual calculations.
2.
(3)
1. The null conditions in eqns (6) and (7) are
independent of each other if R3 and C3 are chosen
as the variables because the adjustment of R3 to
satisfy eqn (6) does not affect eqn (7) and the
adjustment of C3 to satisfy eqn (7) does not affect
eqn (6). Such independent null conditions are
preferred in practice, because they lead to null
quickly.
AC Bridges
Consider the general ac bridge configuration shown in
Fig. 1. Under the null condition
3.
Proposed Methods
3.1 Quality factor measurement
Fig. 1: General ac bridge
Z1 
Z2Z4
Z3
.
Again consider the Hay bridge shown in Fig. 3. Qx can
be expressed aswhere VC3 and VR3 are the voltage
drops across C3 and R3, respectively, under the null
condition.
(1)
resistance Rx and reactance Xx, i.e., Z1= Rx + jXx. Then
from eqn (1)
Z Z 
Z Z 
Rx  jX x  Re 2 4   j Im 2 4 
 Z3 
 Z3 
Equating real and imaginary parts on the two sides of
the equation, we get
Z Z 
Rx  Re 2 4 ,
(2)
 Z3 
3.2 Dissipation factor measurement
Equation (14) can be expressed as
tan  x 
VC
1
 3.
C3 R3 VR3
Thus, tan  x of the unknown capacitor also equals
the ratio of voltages VC3 and VR3 under balance
condition.
1
4.
measured values of Q by the proposed voltage ratio
method were compared with those obtained from an
LCR meter and also using the results Qx = ωLx/Rx.
Voltage Ratio Measurement
Digital ratio measurement can be accomplished as
follows.
6.
4.1 Using voltage to time converter
It eliminates the need for calibrated variable elements
(highly accurate but costly decade boxes). Finally, the
reading is displayed directly in numerals.
A voltage to time converter converts input voltage Vx
4.2 Using voltage to frequency converter
References
A voltage to frequency converter converts input If V R
and Vx are replaced by VR3 and VC3, respectively, then
fx becomes proportional to the ratio VC3/VR3. Thus
voltage ratio VC3/VR3 can be measured digitally by
measuring the frequency fx as given in [3].
5.
Conclusions
[1]
[2]
M B Stout, Basic Electrical Measure-ments,
Englewood Cliffs, N J, Prentice-Hall, Inc., 1960
T Saegusa, T Wada and N Nagiwara, Phase
comparison digital tan delta meter, Electrical
Engg in Japan, 98, 98-106, 1978
Practical Results
Hay bridge was built in the laboratory and the
______________________________________
Brief Resume of all the authors
with photograph.
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