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 element 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)
=
K Z
A
Z
CZ
Z
(
)
−
+
−
1
Low-pass L(z)
=
1
−
−
B
Z
B
Notch
N(z)
=
(
)(
)
(
)(
)
Z
z Z
z
Z
p Z
p
−
−
−
−
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.
For example, if the filter parameters of the DMC-1600 are
KP = 4
KD
=
36
KI = 2
PL
=
0.75
T = 0.001 s
the digital filter coefficients are
K
=
160
A
=
0.9
DMC-1600
Chapter 10 Theory of Operation
•
171
