Click here for the
Analog Devices (Fig. 10) document containing the graph.
A Gaussian filter is a filter whose impulse response is a Gaussian function.
Gaussian filters are designed to give no overshoot to a step function input while
minimizing the rise and fall time. This behavior is closely connected to the fact
that the Gaussian filter has the minimum possible group delay. Mathematically, a
Gaussian filter modifies the input signal by convolution with a Gaussian function;
this transformation is also known as the Weierstrass transform.
- Wikipedia
Here are the lowpass prototype poles for a Gaussian filter to 6 dB and to 12
dB. Lowpass prototype inductor
and capacitor values are here.
 Note*: The values given in the two tables below
have been edited to agree with those in Table XI and Table XII in "AN-649:
Using the Analog Devices Active Filter Design Tool." Even it contains an extraneous
number in the 3rd-order Gaussian to 12 dB table.
The values given in
Chapter 8 of Analog Device's Design Handbook for both the Gaussian to 6 dB and Gaussian
to 12 dB appear to be wrong (they are what I originally used). Always
be sure to verify critical references.
| 3 |
0.9622 0.9776 |
1.2214 |
| 4 |
0.7940 0.6304 |
0.5029 1.5407 |
| 5 |
0.6190 0.3559 0.6650 |
0.8254 1.5688 |
| 6 |
0.5433 0.4672 0.2204 |
0.3431 0.9991 1.5067 |
| 7 |
0.4580 0.3649 0.1522 0.4828 |
0.5932 1.1286 1.4938 |
| 8 |
0.4222 0.3833 0.2878 0.1122 |
0.2640 0.7716 1.2066 1.4798 |
| 9 |
0.3700 0.3230 0.2309 0.08604 0.3842 |
0.4704 0.9068 1.2634 1.4740 |
| 10 |
0.3384 0.3164 0.2677 0.1849 0.06706 |
0.2101 0.6180 0.9852 1.2745 1.4389 |
|
| 3 |
0.9360 0.9360 |
1.2168 |
| 4 |
0.9278 0.9192 |
1.6995 0.5560 |
| 5 |
0.8075 0.7153 0.8131 |
0.9973 2.0532 |
| 6 |
0.7019 0.6667 0.4479 |
0.4322 1.2931 2.1363 |
| 7 |
0.6155 0.5486 0.2905 0.6291 |
0.7703 1.5154 2.1468 |
| 8 |
0.5441 0.5175 0.4328 0.1978 |
0.3358 0.9962 1.6100 2.0703 |
| 9 |
0.4961 0.4568 0.3592 0.1489 0.5065 |
0.6192 1.2145 1.7429 2.1003 |
| 10 |
0.4535 0.4352 0.3886 0.2908 0.1136 |
0.2794 0.8289 1.3448 1.7837 2.0599 |
|
* Thanks to RF Cafe visitor Tim C. for pointing out the errors.
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