Low-Pass
4-Pole
Appendix A
Butterworth
Theoretical Transfer Characteristics
1
Frequency Response
0
-20
-40
-60
-80
-100
f/fc
Amp
(dB)
Phase
(deg)
Delay
(sec)
(Hz)
0.00
0.10
0.20
0.30
0.40
0.50
0.00
0.00
0.00
-15.0
-30.1
-45.5
-61.4
-78.0
.416
.418
.423
.433
.449
.474
0.00
-0.00
-0.003
-0.017
0.60
0.70
0.80
0.85
0.90
-0.072
-0.243
-0.674
-1.047
-1.555
-95.7
-115
-136
-147
-158
.511
.558
.604
.619
.622
2
2
3 4 5 6 7
0.1
3 4 5 6 781.0
10.0
Normalized Frequency(f/fc)
0.95
1.00
1.10
1.20
1.30
-2.21
-3.01
-4.97
-7.24
-9.62
-169
-180
-200
-217
-231
.612
.588
.513
.427
.350
Delay (Normalized)
2.0
1.0
0.0
1.40
1.50
1.60
1.70
1.80
-12.0
-14.3
-16.4
-18.5
-20.5
-242
-252
-260
-266
-272
.289
.241
.204
.175
.152
1.90
2.00
2.25
2.50
2.75
-22.3
-24.1
-28.2
-31.8
-35.1
-277
-282
-291
-299
-304
.134
.119
.091
.072
.059
2
3
4
5 6 7 8 91.0
0.15
1.5
0.1
3.00
3.25
3.50
4.00
5.00
-38.2
-41.0
-43.5
-48.2
-55.9
-309
-313
-317
-322
-330
.049
.041
.035
.027
.017
Normalized Frequency(f/fc)
Step Response
6.00
7.00
8.00
9.00
10.0
-62.3
-67.6
-72.2
-76.3
-80.0
-335
-339
-341
-343
-345
.012
.009
.007
.005
.004
1.2
1.0
0.8
0.6
0.4
0.2
-0.0
1.Normalized Group Delay:
The above delay data is normalized to a corner frequency
of 1.0Hz.The actual delay is the normalized delay divided
by the actual corner frequency (fc).
0
1
2
3
4
5
Normalized Time (1/f sec)
Normalized Delay
Actual Delay =
Actual Corner Frequency (fc) in Hz
7
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