E1C06 09/14/2010
11:55:5 Page 228
Interstage Loading Errors
Consider the common situation of Figure 6.16, in which the output voltage signal from one
measurement system device provides the input to the following device. The open circuit potential E 1
is present at the output terminal of device 1 with output impedance Z 1 . However, the output signal
from device 1 provides the input to a second device, which, at its input terminals, has an input
impedance Z m . As shown, the Th evenin equivalent circuit of device 1 consists of a voltage generator,
of open circuit voltage E 1 , with internal series impedance Z 1 . Connecting device 2 to the output
terminals of device 1 is equivalent to placing Z m across the Th evenin equivalent circuit. The finite
impedance of the second device causes a current, I, to flow in the loop formed by the two terminals,
and Z m acts as a load on the first device. The potential sensed by device 2 is
E m ¼ IZ m ¼ E 1
1
1 þ Z 1 =Z m
ð6:38Þ
The original potential has been changed due to the interstage connection that has caused a loading
error, e I ¼ E m À E 1 ,
e I ¼ E 1
1
1 þ Z 1 =Z m
À 1
ð6:39Þ
For a maximum in the voltage potential between stages, it is required that Z m ) Z 1 such that
e I ! 0. As a practical matter, this can be a challenge to achieve at reasonable cost and some design
compromise is inevitable.
When the signal is current driven, the maximum current transfer between devices 1 and 2 is
desirable. Consider the circuit shown in Figure 6.17 in which device 2 is current sensitive, such
as with a current-sensing galvanometer. The current through the loop indicated by the device 2 is
given by
I m ¼
E 1
Z 1 þ Z m
ð6:40Þ
However, if the measurement device is removed from the circuit, the current is given by the shortcircuit value
I
0
¼
E 1
Z 1
ð6:41Þ
Z th
I
Z 1
Z m
E 1
Device 1
Device 2
(a)
(b)
Equivalent circuit
E 1
E m
E 1
Figure 6.16 Equivalent circuit formed by interstage (parallel) connections.
228 Chapter 6 Analog Electrical Devices and Measurements
11:55:5 Page 228
Interstage Loading Errors
Consider the common situation of Figure 6.16, in which the output voltage signal from one
measurement system device provides the input to the following device. The open circuit potential E 1
is present at the output terminal of device 1 with output impedance Z 1 . However, the output signal
from device 1 provides the input to a second device, which, at its input terminals, has an input
impedance Z m . As shown, the Th evenin equivalent circuit of device 1 consists of a voltage generator,
of open circuit voltage E 1 , with internal series impedance Z 1 . Connecting device 2 to the output
terminals of device 1 is equivalent to placing Z m across the Th evenin equivalent circuit. The finite
impedance of the second device causes a current, I, to flow in the loop formed by the two terminals,
and Z m acts as a load on the first device. The potential sensed by device 2 is
E m ¼ IZ m ¼ E 1
1
1 þ Z 1 =Z m
ð6:38Þ
The original potential has been changed due to the interstage connection that has caused a loading
error, e I ¼ E m À E 1 ,
e I ¼ E 1
1
1 þ Z 1 =Z m
À 1
ð6:39Þ
For a maximum in the voltage potential between stages, it is required that Z m ) Z 1 such that
e I ! 0. As a practical matter, this can be a challenge to achieve at reasonable cost and some design
compromise is inevitable.
When the signal is current driven, the maximum current transfer between devices 1 and 2 is
desirable. Consider the circuit shown in Figure 6.17 in which device 2 is current sensitive, such
as with a current-sensing galvanometer. The current through the loop indicated by the device 2 is
given by
I m ¼
E 1
Z 1 þ Z m
ð6:40Þ
However, if the measurement device is removed from the circuit, the current is given by the shortcircuit value
I
0
¼
E 1
Z 1
ð6:41Þ
Z th
I
Z 1
Z m
E 1
Device 1
Device 2
(a)
(b)
Equivalent circuit
E 1
E m
E 1
Figure 6.16 Equivalent circuit formed by interstage (parallel) connections.
228 Chapter 6 Analog Electrical Devices and Measurements