by endolith
Last Updated July 25, 2018 14:25 PM

For calculating the equivalent noise bandwidth of a non-brickwall filter, I can find two different sets of numbers, both of which claim they are similar things:

```
Order EqNBW
1 1.5708
2 1.1107
3 1.0472
4 1.0262
5 1.0166
6 1.0115
7 1.0084
8 1.0065
9 1.0051
10 1.0041
```

- RF Cafe Filter Equivalent Noise Bandwidth "Butterworth (fco = 3 dB)")
- ADC Noise Figure by Walt Kester
- Figure 2: Relationship Between Noise Bandwidth and 3-dB Bandwidth for a Butterworth Filter
- "will pass the same noise power as the non-ideal filter"

- Linear Circuit Design Handbook by Hank Zumbahlen
- Figure 6-147 : "Relationship between noise bandwidth and 3 dB bandwidth for Butterworth filter"

- The Concepts of Noise Bandwidth and Cumulative Noise

```
1 1.57
2 1.22
3 1.16
4 1.13
5 1.12
```

- Equivalent Noise Bandwidth by Radio Geek
- "have same integrated noise power"

- Equivalent Noise Bandwidth by Tim J. Sobering
- "a noise power equivalent to the original transfer function"

- PGA309 Noise Filtering
- Operational Amplifier Noise by Art Kay
- "brick wall correction filter"

Which is correct?

Or are they both correct; just used in different calculations?

After figuring this out, I made a chart of the different factors and the types of filters they work for: ENBW Filter correction factors vs order

The effective noise bandwidth depends on the shape of transfer function. It's easy to calculate it numerically.

See my Matlab script below that calculates the ENBW for a Butterworth lowpass filter. You can adapt it to your needs.

```
for N=1:10
[b,a] = butter(N, 1, 's');
f = @(x) (abs(freqs(b,a,x)).^2);
bw = integral(f, 0, 1e6);
fprintf('Order: %d, ENBW: %g\n',N, bw);
end
```

In case you don't have Matlab, the output is given below

```
Order: 1, ENBW: 1.5708
Order: 2, ENBW: 1.11072
Order: 3, ENBW: 1.0472
Order: 4, ENBW: 1.02617
Order: 5, ENBW: 1.01664
Order: 6, ENBW: 1.01152
Order: 7, ENBW: 1.00844
Order: 8, ENBW: 1.00645
Order: 9, ENBW: 1.0051
Order: 10, ENBW: 1.00412
```

- ServerfaultXchanger
- SuperuserXchanger
- UbuntuXchanger
- WebappsXchanger
- WebmastersXchanger
- ProgrammersXchanger
- DbaXchanger
- DrupalXchanger
- WordpressXchanger
- MagentoXchanger
- JoomlaXchanger
- AndroidXchanger
- AppleXchanger
- GameXchanger
- GamingXchanger
- BlenderXchanger
- UxXchanger
- CookingXchanger
- PhotoXchanger
- StatsXchanger
- MathXchanger
- DiyXchanger
- GisXchanger
- TexXchanger
- MetaXchanger
- ElectronicsXchanger
- StackoverflowXchanger
- BitcoinXchanger
- EthereumXcanger