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DMC-2X00 Chapter 10 Theory of Operation y 139
DAC
The DAC or D-to-A converter converts a 16-bit number to an analog voltage. The input range of the
numbers is 65536 and the output voltage range is +/-10V or 20V. Therefore, the effective gain of the
DAC is
K= 20/65536 = 0.0003 [V/count]
Digital Filter
The digital filter has three elements in series: PID, low-pass and a notch filter. The transfer function of
the filter. The transfer function of the filter elements are:
PID D(z) =
KZ A
Z
CZ
Z
()
−
+
− 1
Low-pass L(z) =
1
−
−
B
ZB
Notch N(z) =
()()
()()
ZzZz
ZpZp
−−
−−
The filter parameters, K, A, C and B are selected by the instructions KP, KD, KI and PL, respectively.
The relationship between the filter coefficients and the instructions are:
K = (KP + KD) ⋅ 4
A = KD/(KP + KD)
C = KI/2
B = PL
The PID and low-pass elements are equivalent to the continuous transfer function G(s).
G(s) = (P + sD + I/s) ∗ a/(S+a)
P = 4KP
D = 4T
⋅ KD
I = KI/2T
a = 1/T ln (1/B)
where T is the sampling period.