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User Manual
110 of 562
V 1.0
2021-08-25
XDPP1100 technical reference manual
Digital power controller
Compensator
K
D
_index
K
D
K
D
_real
94
28672
14.000
95
30720
15.000
96
32768
16.0
97
36864
18.0
98
40960
20.0
99
45056
22.0
100
49152
24.0
101
53248
26.0
102
57344
28.0
103
61440
30.0
104
65536
32.0
105
73728
36.0
106
81920
40.0
107
90112
44.0
108
98304
48.0
109
106496
52.0
110
114688
56.0
111
122880
60.0
112
131072
64.0
113
147456
72.0
114
163840
80.0
115
180224
88.0
116
196608
96.0
117
212992
104.0
118
229376
112.0
119
245760
120.0
The PID creates two mid-band zeros, f
z1
and f
z2
, in the compensator transfer function. Based on the real number
representation of the PID coefficients, the location of the zeros can be obtained according to Equations (6.19)
to (6.20), where T
SAMPLE
equals
1
50𝑀𝐻𝑧
.
𝑓
𝑧1
= (
1
2𝜋𝑇
𝑆𝐴𝑀𝑃𝐿𝐸
) (𝐾
𝑃
_𝑟𝑒𝑎𝑙 − √𝐾
𝑃
_𝑟𝑒𝑎𝑙
2
− 4𝐾
𝐷
_𝑟𝑒𝑎𝑙 ∗ 𝐾
𝐼
_𝑟𝑒𝑎𝑙)/2𝐾
𝐷
_𝑟𝑒𝑎𝑙
(6.19)
𝑓
𝑧2
= (
1
2𝜋𝑇
𝑆𝐴𝑀𝑃𝐿𝐸
) (𝐾
𝑃
_𝑟𝑒𝑎𝑙 + √𝐾
𝑃
_𝑟𝑒𝑎𝑙
2
− 4𝐾
𝐷
_𝑟𝑒𝑎𝑙 ∗ 𝐾
𝐼
_𝑟𝑒𝑎𝑙)/2𝐾
𝐷
_𝑟𝑒𝑎𝑙
(6.20)
6.1.3
Post-filter and summation
The post-filter is a single-pole low-pass filter, and it receives its input, pd_term, from the PID filter. The integral
term has negligible gain compared to the proportional and derivative terms at high frequency, so no additional
filtering is needed.
The compensator duty cycle output is created by adding the post-filtered output to: