chapter 5 bridges and their application · this bridge circuit is used for medium inductances and...
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CHAPTER 5 - PART 3
AC – BRIDGES
Comparison Bridges
Inductance
Measurements 1
Dr. Wael Salah
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2. INDUCTANCE BRIDGES
The circuit of the inductance comparison bridge is
similar to that of the capacitance bridge except that
inductors are involved instead of capacitors.
There are two pure resistive arms. So, the phase
balance depends on the remaining two inductive
arms.
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5.6.2 INDUCTANCE COMPARISON BRIDGE
G
Z1
Z4 Z3
Z2
RS
LS
L1
R1
R4
R3
This bridge circuit is used for medium inductances and can be arranged
to yield results of considerable precision.
In the given bridge, the unknown inductance represented by it’s
equivalent series inductance LS and resistance RS.
L1 is the standard inductance and R1 is a variable resistor to balance RS.
R3 or R4 used to balance the bridge.
442
33111
;
;
RZjwLRZ
RZjwLRZ
SS
The load impedances are:
3411
3241
).().(
RjwLRRjwLR
ZZZZ
ss
When the bridge is balanced:
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Then , the equation is simplified as:
334141 .. RjwLRRRjwLRR ss
After equating the real terms in both sides, we get:
341 . RRRR s3
4 1
R
R R R s
After equating the Imaginary terms in both sides:
3
4 1
R
R L L s
341 . RjwLRjwL s
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(ii) Maxwell-Wein Bridge The positive phase angle of an inductive impedance may be compensated by the
negative phase angle of a capacitive impedance put in the opposite arm. The
unknown inductance then becomes known in terms of this capacitance.
This bridge is found to be most suitable for measuring coils with a low Q-
factor (1 < Q < 10 ) (LS is not much larger than RS).
SS jwLRZRZ
RZCjwR
RZjwC
RZ
433
22
11
111
11
;
; 1
11
The load impedances are:
32
11
1
3241
1
RRjwLRCjwR
R
ZZZZ
SS
When the bridge is balanced:
After equating the real & Imaginary terms:
G
R2
R3
RS
LS
R1
C1 Z2
Z4
Z1
Z3
321
1
32 and RRCLR
RRR SS
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EXAMPLE 10
A Maxwell-Wien bridge as shown in below operates at a supply
frequency of 100Hz used to measure inductive impedance. The
bridge
balanced at the following values:
1 1 2 30.01 F, 470 , 2.2 and 100C R R k R
Find the series resistance and inductance and determine its Q-factor.
Z1
Z2
Z4
C1
Z3
R1
R2
R3
RS
G
LS
SOLUTION 10
2 3
1
2.2k 100468.1
470S
R RR
R
1 2 3 0.01 2.2 100 2.2SL C R R k mH
32 100 2.2 100.00295
468.1
s
s
wLQ
R
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5.8 HAY BRIDGE (ALSO KNOWN AS OPPOSITE-ANGLE BRIDGE)
This bridge is a modification of the Maxwell-Wien bridge.
It is useful for measuring the resistance and inductance of coils with
high Q-factor. (R1 very low value)
SS jwLRZRZ
RZwC
jRZ
433
22
1
11
;
; -
The load impedances are:
32
1
13241 RRjwLRwC
jRZZZZ SS
When the bridge is balanced:
After equating the real & Imaginary terms:
2
1
2
1
2
321
2
1
2
1
2
321
2
1
2
1 and
1 CRw
RRCL
CRw
RRRCwR SS
Z1 Z2
Z4Z3
R2
R3
RS
G
LS
C1
R1
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EXAMPLE 11
Z1 Z2
Z4Z3
R2
R3
RS
G
LS
C1
R1
Calculate the inductance and resistance of the network that causes a
Hay bridge as shown in figure below to null with the following
component values: w=3000rad/s, C1=0.1nF, R1=20k, R2=10k
and R3=1k.
SOLUTION 11
To find the series resistance and
inductance, we use the above equations as:
1 2 3
2 2 2 2 2 2
1 1
0.1 10 11
1 1 (3000) (20 ) (0.1 )S
C R R n k kL mH
w R C k n
2 2 2 2
1 1 2 3
2 2 2 2 2 2
1 1
(3000) (0.1 ) 20 10 10.018
1 1 (3000) (20 ) (0.1 )S
w C R R R n k k kR
w R C k n
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5.9 SCHERING BRIDGE
C1 and R1 are made adjustable while C4 and R4 are the unknown
impedance, then we have a Schering bridge.
Schering bridge is used for measuring unknown capacitance
and dissipation factor.
2
3
4
4
11
13241
1
wC
jR
wC
jR
CjwR
RZZZZ
When the bridge is balanced:
After equating the real & Imaginary terms:
3
214
2
134 and
R
CRC
C
CRR
4
4433
2
2
11
111
11
; ;
; 1
11
wC
jRZRZ
wC
jZ
CjwR
RZjwC
RZ
The load impedances are:
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Dr. Wael Salah
5.9 SCHERING BRIDGE
X
XwC
X1
3
21
2
13 and R
CRC
C
CRR XX
Subs. Rx and Cx
Giving
13
5.11 WIEN BRIDGE
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Dr. Wael Salah
The generally accepted standard range
of audible frequencies is 20 to 20,000 Hz