E1C06 09/14/2010
11:55:5 Page 229
The loading error, e I ¼ I m À I
0 , is
e I ¼ E 1
ÀZ m
Z
2
1 þ Z 1 Z m
ð6:42Þ
From Equation 6.42 or Equations 6.40 and 6.41, it is clear that to reduce current-driven loading
error, then Z m ( Z 1 , such that e I ! 0.
Example 6.5
For the Wheatstone bridge shown in Figure 6.18, find the open circuit output voltage (when
R m ! 1) if the four resistances change by
dR 1 ¼ þ40 V dR 2 ¼ À40 V dR 3 ¼ þ40 V dR 4 ¼ À40 V
KNOWN Measurement device resistance given by R m
ASSUMPTIONS R m ! 1
Negligible source impedance
FIND E o
Z 1
Z 1
Z m
E 1
I m
Device 1
Device 2
I'
(a)
(b)
Equivalent circuit
Z m
Figure 6.17 Instruments in series with signal path.
B
C
D
A
R 2 = 5000
R 1 = 5000
R 3 =
8000
R 4 =
8000
I 2
I 3
I 1
I 4
E i = 50 V
E o
R m
Figure 6.18 Bridge circuit for Example 6.5.
6.5 Loading Errors and Impedance Matching 229
11:55:5 Page 229
The loading error, e I ¼ I m À I
0 , is
e I ¼ E 1
ÀZ m
Z
2
1 þ Z 1 Z m
ð6:42Þ
From Equation 6.42 or Equations 6.40 and 6.41, it is clear that to reduce current-driven loading
error, then Z m ( Z 1 , such that e I ! 0.
Example 6.5
For the Wheatstone bridge shown in Figure 6.18, find the open circuit output voltage (when
R m ! 1) if the four resistances change by
dR 1 ¼ þ40 V dR 2 ¼ À40 V dR 3 ¼ þ40 V dR 4 ¼ À40 V
KNOWN Measurement device resistance given by R m
ASSUMPTIONS R m ! 1
Negligible source impedance
FIND E o
Z 1
Z 1
Z m
E 1
I m
Device 1
Device 2
I'
(a)
(b)
Equivalent circuit
Z m
Figure 6.17 Instruments in series with signal path.
B
C
D
A
R 2 = 5000
R 1 = 5000
R 3 =
8000
R 4 =
8000
I 2
I 3
I 1
I 4
E i = 50 V
E o
R m
Figure 6.18 Bridge circuit for Example 6.5.
6.5 Loading Errors and Impedance Matching 229