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input signal by responding with very small amplitudes, which is seen by the small MðvÞ, and by
large time delays, as evidenced by increasingly nonzero b 1 .
Any combination of v and t produces the same results. If we wanted to measure signals with
high-frequency content, then we would need a system having a small t. On the other hand, systems
of large t may be adequate to measure signals of low-frequency content. Often the trade-offs
compete available technology against cost.
The dynamic error, dðvÞ, of a system is defined as d v
ð Þ ¼ MðvÞ À 1. It is a measure of the
inability of a system to adequately reconstruct the amplitude of the input signal for a particular input
frequency. We normally want measurement systems to have a magnitude ratio at or near unity over
the anticipated frequency band of the input signal to minimize dðvÞ. Perfect reproduction of the
input signal is not possible, so some dynamic error is inevitable. We need some way to state this.
For a first-order system, we define a frequency bandwidth as the frequency band over which
MðvÞ ! 0:707; in terms of the decibel (plotted in Figure 3.12) defined as
dB ¼ 20 log M v
ð Þ
ð3:11Þ
this is the band of frequencies within which M(v) remains above À3 dB.
0.01
Decibels (dB)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
0.10
1.00
10.00
100.00
–20
–10
–8
–6
–4
–2
0
Magnitude ratio
M( )
Figure 3.12 First-order system
frequency response: magnitude
ratio.
0.01
–90
–80
–70
–60
–50
–40
–30
–20
–10
0
0.1
1.0
10.0
100.0
Phase shift, ( )[°]
Figure 3.13 First-order system
frequency response: phase shift.
94 Chapter 3 Measurement System Behavior
15:24:53 Page 94
input signal by responding with very small amplitudes, which is seen by the small MðvÞ, and by
large time delays, as evidenced by increasingly nonzero b 1 .
Any combination of v and t produces the same results. If we wanted to measure signals with
high-frequency content, then we would need a system having a small t. On the other hand, systems
of large t may be adequate to measure signals of low-frequency content. Often the trade-offs
compete available technology against cost.
The dynamic error, dðvÞ, of a system is defined as d v
ð Þ ¼ MðvÞ À 1. It is a measure of the
inability of a system to adequately reconstruct the amplitude of the input signal for a particular input
frequency. We normally want measurement systems to have a magnitude ratio at or near unity over
the anticipated frequency band of the input signal to minimize dðvÞ. Perfect reproduction of the
input signal is not possible, so some dynamic error is inevitable. We need some way to state this.
For a first-order system, we define a frequency bandwidth as the frequency band over which
MðvÞ ! 0:707; in terms of the decibel (plotted in Figure 3.12) defined as
dB ¼ 20 log M v
ð Þ
ð3:11Þ
this is the band of frequencies within which M(v) remains above À3 dB.
0.01
Decibels (dB)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
0.10
1.00
10.00
100.00
–20
–10
–8
–6
–4
–2
0
Magnitude ratio
M( )
Figure 3.12 First-order system
frequency response: magnitude
ratio.
0.01
–90
–80
–70
–60
–50
–40
–30
–20
–10
0
0.1
1.0
10.0
100.0
Phase shift, ( )[°]
Figure 3.13 First-order system
frequency response: phase shift.
94 Chapter 3 Measurement System Behavior