A(s) = L(s) G(s)
then it follows that G(s) must have magnitude of
|G(j500)| = |A(j500)/L(j500)| = 160
and a phase
arg [G(j500)] = arg [A(j500)] - arg [L(j500)] = -135
°
+ 194
°
= 59
°
In other words, we need to select a filter function G(s) of the form
G(s) = P + sD
so that at the frequency
ω
c =500, the function would have a magnitude of 160 and a phase lead of
59 degrees.
These requirements may be expressed as:
|G(j500)| = |P + (j500D)| = 160
and
arg [G(j500)] = tan-1[500D/P] = 59
°
The solution of these equations leads to:
P = 160cos 59
°
= 82.4
500D = 160sin 59
°
= 137
Therefore,
D
=
0.274
and
G = 82.4 + 0.2744s
The function G is equivalent to a digital filter of the form:
D(z) = 4KP + 4KD(1-z-1)
where
P
=
4
∗
KP
D
=
4
∗
KD
∗
T
and
4
∗
KD = D/T
Assuming a sampling period of T=1ms, the parameters of the digital filter are:
KP = 20.6
KD
=
68.6
The DMC-1600 can be programmed with the instruction:
KP
20.6
KD
68.6
In a similar manner, other filters can be programmed. The procedure is simplified by the
following table, which summarizes the relationship between the various filters.
176
•
Chapter 10 Theory of Operation
DMC-1600
