Galil DMC-13X8 user manual Theory of Operation

However, since

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 ωc =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-13X8 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.

USER MANUAL Chapter 10 Theory of Operation • 169