Question

Design a circuit which removes the entire audio frequency range (approximately 20 Hz to 20 kHz, for human hearing), but amplifies the signal voltage of all other frequencies by a factor of 15.

Answer 1

Solution;- The required circuit is a band stop filter that stops frequencies from 20 Hz to 20kHZ and amplifies all other frequencies by factor 15. » One way to achieve such a design in using a Low pass filter with a gain of 15 dB and a cutoff frequency "We of Wi (20 Hz) In parallel with a high pass filter with a gain of 15 dB and a catoff frequency wc at WH (20 kHz), both begin fed to an adder. > The design can be classified to two stages, Low pass and high pass filter stages, the Low pass op amp filter stage is shown in Figure 1. R2 V+ M + RI M Vo Rf 4 M с Figure I The capacitor is represented in the s-domain as Zc = ㅗ SC Perform KCL at vt Vi-V+ V+ Vi -V+ =(V+)sc I Rz R2 R2 Se (

solve for Vt; t = V1 1 © HSR2C + Golf +1 • Perform Kc L at v- Vo-V. V- Vo V- Rf RI Rg Ri V-(RS Ri Bit V-= Vt for an Ideal op amp, therefore substitute by (I) to get 고 1 + I RG IHSR₂C = Vi that (1+RE) - selor Its R₂C From a it is observed that the transfer function of the Law pass filter is the product of the transfer function of the general Low pass filter. Circuit topology & the gain of the non-doverting amplifier, From (3 It is evident that the gain is the second It Rg :), 15dB Rf 10 It Ri 20 =

ec Let Ri= 1 kr, then Re is given by ... Rf 30.62 kr And the corner frequeny of the filter is given by Wc = R2 C Let R₂ = 5ks and the frequency wc (W2 of the band stop ) is given by 21* 20 rad/s, then the capacitor is, 5X103 X2T X 20 C = 1.59 MF The high pass op amp stage is shown sh Fg 2. VA Ca с V. of V R2 3 Ri M Vo Rf

V+ HVAC "Rz The capacitor is represented on the s-domain as Zc = 466 Perform kcl at V+, Vi-Vt - Vt sc R2 => Visc = R2 solve for Vt SC V+ = Vi étsc E Vi SR2 C 1+ SR2C Perform kcL at V., Votv-v. RF Ri Vo Vo Rg Rf RI RE Ri But V-= Vt for an ideal op ampe therefore substitute 13 we get vo = Vi SR2C Rg Its R2C Vat V- 1) V- (+) t b) Rf RI

Vo SR2C Vi + 1 +SR2C -> (4) RI From 4 it is observed that the transfer function of the filter is the product of the transfer function of the general high pass filter circuit topology and the gain of the non- Inveating amplifier Fromc4, ) it is evident that the gain is the second factor (i+ R$ ) RI 150 B lo R Let Ri=1kh, then Rf is given by Rfa And the corner frequency of the filter i is given by We = R2C Let R2=5ke and the frequency wc is given by 25 X 20X103 hadis, then 20 lt Rf 30.62 kor the Capacitor is 5X103 x 27T *20 * 103 1.59 nF

Design the filter circuit with the obtained Values to create a bandstop filter with a Low frequency cutott of 20 Hz, and a high frequency cutoff of 20kHz as shown in Figure (3) 5 kr V+ R + VA + Ika 30.62K4 VoH M 1.594C F Adder 1.59nF V+ HD + С V- + Vo Iks M 30.62 km VOL V I Figure 3