#### Jonathan56

- Jan 3, 2017

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- Jan 3, 2017

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I have a question regarding corner frequency for second order filter.

I don't understand how I can have two roots in the denominator which will indicate two corner frequencies each of them at different frequency and with 20db/decade and the same transfer function express in standard normalized form (express with the quality factor) indicate only one corner frequency (power of two <=> 40db/decade).

2 corner frequency or one?

Example with an LCR filter - two-pole low-pass filter

s = jw and w = 2 x pi x F

G(s) = 1 / (1 + sL/R + s²LC) = 1 / (1 + sA + s²B) with A = L/R and B = LC

__Quadratic formula__

G(s) = 1 / [ ( 1 - s/s1 ) (1 - s/s2) ]

with s1/2 = -A/(2B) x [1 -/+ rsqt(1 - 4B/A)]

==> This indicates that there is

**two corner frequencies**

standard normalized form

G(s) = 1 / [1 + s(Qw0) + (s/w0)²]

==> This indicates that there is

**only one corner frequency**

The example above is taken from the book:

Fundamentals of Power Electronics SECOND EDITION

Robert W. Erickson and Dragan Maksimovic

page 282

Thank you for your help.

Jonathan