# Second order filter - quadratic formula and standard normalized form

#### jonathan56

Joined Jan 4, 2017
1
Hi,

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
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