Page 61 - Understanding Automotive Electronics

2735 | CH 2 Page 48 Tuesday, March 10, 1998 10:55 AM

2 THE SYSTEMS APPROACH TO CONTROL AND INSTRUMENTATION

Systematic loading errors are due to the energy extracted by an instrument
when making a measurement. Whenever the energy extracted from a system
under measurement is not negligible, the extracted energy causes a change in
the quantity being measured. Wherever possible, an instrument is designed to
minimize such loading effects. The idea of loading error can be illustrated by
the simple example of an electrical measurement, as illustrated in Figure 2.13.
A voltmeter M having resistance R measures the voltage across resistance R.
m
The correct voltage (v ) is given by
c
R

v = V --------------- 1 
c

R 
R +
However, the measured voltage v is given by
m
R p 

v = V -----------------
m  R + R 
p
1
where R is the parallel combination of R and R :
m
p
RR m
R = ----------------
p
R + R m
Loading is minimized by increasing the meter resistance R to the largest
m
possible value. For conditions where R approaches infinite resistance, R
m p
approaches resistance R, and v approaches the correct voltage. Loading is
m
similarly minimized in measurement of any quantity by minimizing extracted
energy. Normally, loading is negligible in modern instrumentation.
Another significant systematic error source is the dynamic response of the
instrument. Any instrument has a limited response rate to very rapidly
changing input, as illustrated in Figure 2.14. In this illustration, an input
quantity to the instrument changes abruptly at some time. The instrument

Figure 2.13
Illustration of
Loading Error

FPO

48 UNDERSTANDING AUTOMOTIVE ELECTRONICS