Notch Filter

Notch filters have a band rejection characteristic. This function may be realised by a twin-T network composed of resistors and capacitors. Poles are confined to the real negative axis of the complex frequency plane, but zeros can occur on the imaginary axis. Therefore, the filter eliminates a center frequency while outside of the narrow rejection band frequencies may pass through without significant attenuation.

Applications of the notch filer are found in the field of electro-acoustics where they are inserted into the signal paths of preamplifiers to compensate for room resonances. In automatic control systems they serve for cancelling mechanical resonance in complex transfer functions.

The circuit

The input file (notch_filter.cir)

notch filter

* fo = 1 / (2 pi ((r1 + r2) r3 c1 c2)^(1 / 2))    Center Frequency
* r3 (c1 + c2) = c3 r1 r2 / (r1 + r2)             Condition

.control
ac lin 200 10Hz 100Hz
plot vdb(8) xlog xlabel f[Hz] ylabel magnitude[dB] title 'AC analysis'
.endc

v1 1 0 dc 0 ac 1

e1_amp 8 0 4 5 1meg

r1 1 3 20k
r2 3 4 22k
r3 2 7 15k
r4 5 8 100k
r5 5 7 100
r6 7 6 6.8k

c1 1 2 .175uF
c2 2 4 .175uF
c3 3 7 .45uF
c4 6 0 2.2uF

.end

The results