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Band-Rejection Filter Design

The document describes the transformation from a low-pass filter to a band-rejection filter. The corner frequency of the low-pass filter becomes the lower and upper -3 dB frequencies of the band-rejection filter. The difference between these frequencies is the normalized bandwidth. The quality of the filter rejection is defined as the center frequency divided by the bandwidth. Replacing the normalized bandwidth term yields the transfer function for a band-rejection filter. An active twin-T filter is also described which uses an op-amp to increase the quality factor of the original passive twin-T RC network filter.

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23 views1 page

Band-Rejection Filter Design

The document describes the transformation from a low-pass filter to a band-rejection filter. The corner frequency of the low-pass filter becomes the lower and upper -3 dB frequencies of the band-rejection filter. The difference between these frequencies is the normalized bandwidth. The quality of the filter rejection is defined as the center frequency divided by the bandwidth. Replacing the normalized bandwidth term yields the transfer function for a band-rejection filter. An active twin-T filter is also described which uses an op-amp to increase the quality factor of the original passive twin-T RC network filter.

Uploaded by

lecuellarq85gmailcom
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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|A| [dB] |A| [dB]

0 0 ∆Ω
–3 –3

0 1 Ω 0 Ω1 1 Ω2 Ω

Figure 16–36. Low-Pass to Band-Rejection Transition

The corner frequency of the low-pass transforms to the lower and upper –3-dB frequen-
cies of the band-rejection filter Ω1 and Ω2. The difference between both frequencies is the
normalized bandwidth ∆Ω:
DW + W max * W min

Identical to the selectivity of a band-pass filter, the quality of the filter rejection is defined
as:
fm
Q+ + 1
B DW
Therefore, replacing ∆Ω in Equation 16–19 with 1/Q yields:
A 0ǒ1 ) s 2Ǔ
A(s) + (16–20)
1 ) Q1 ·s ) s 2

16.6.1 Active Twin-T Filter


The original twin-T filter, shown in Figure 16–37, is a passive RC-network with a quality
factor of Q = 0.25. To increase Q, the passive filter is implemented into the feedback loop
of an amplifier, thus turning into an active band-rejection filter, shown in Figure 16–38.
C C

R/2
VIN VOUT

R R

2C

Figure 16–37. Passive Twin-T Filter

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