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I'm told "ripple bandwidth" is different from a "-3dB bandwidth" or corner frequency. How is this commonly defined, and how do I derive it?

My application:

There seems to be a discrepancy in the way Elsie (a filter design package, mine v2.75, fully registered version) defines corner frequency, \$f_c\$ , at least for an LPF.

Normally \$f_c\$ defined as -3dB \$S_{21}\$ point.

In Elsie, If I set \$f_c\$ at 30MHz, \$S_{21}\$(30MHz) = -0.5dB, but \$S_{21}\$ = -3dB point at about 38 MHz, VSWR = 1.1 at 30MHz, for a 0.01dB ripple, 5-pole Chebyshev capacitor-input LPF.

If I set \$S_{21}\$ = -3dB at 30MHz, I get \$f_c\$ = 23.686MHz, VSWR(30MHz) =4.1

I'm told that Elsie is defining \$f_c\$ in a different way, based on the "ripple bandwidth".

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    \$\begingroup\$ Do you have a link to where ripple bandwidth is mentioned anywhere? It's probably the passband ripple width in Hz. \$\endgroup\$
    – Andy aka
    Commented Jan 9, 2016 at 11:58
  • \$\begingroup\$ @Andyaka, No links. I've looked at various combinations of Google and IEEE Xplore searches over the last 2 months but could find nothing substantive. My source (who told me) was Jim Tonne himself, the author of Elsie, but I didn't want to push the relationship by asking him "newbie" questions. I also asked on the Linked In "RF/uWave Filters" group, but got no response. \$\endgroup\$ Commented Jan 9, 2016 at 12:20
  • \$\begingroup\$ Now's the time to ask him - I couldn't substantiate my belief on google either. \$\endgroup\$
    – Andy aka
    Commented Jan 9, 2016 at 12:26

1 Answer 1

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For a Butterworth filter, the 'bandwidth' is always the frequency at which the response is -3dB of its maximum value.

For a Cheby filter, where you choose the depth of ripple for your application, most filter design packages (I've not used Elsie, but it seems the same as others) define the bandwidth of a lowpass filter as the highest frequency at which the response is the ripple depth below its maximum value.

This makes a lot of sense, as if you specify a passband ripple, this definition of bandwidth is the range of frequencies for which the passband response is in specification. You can always find out what the -3dB bandwidth is by analysis of the response.

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    \$\begingroup\$ the max gain corresponds to the poles, the min ripple gain to the gap between poles, and the slope into attenuation as it leaves the last pole behind \$\endgroup\$
    – Neil_UK
    Commented Jan 9, 2016 at 14:01

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