Question

Design a Delyiannis-Friend filter to satisfy the following specifications: Mid-band frequency fo = 100 kHz Mid-band voltage gain = 10 Pole Q = 4 Both capacitors should be 1 pF. Analyze your circuit for an ideal opamp, and with an opamp gain of 50 dB.

Answer 1

Delgiannis - Friend Filted to satisfy Here we need to design a the following Specifications: fo= 100kHz Mid-band voltage gain = 90 Pole, Q = 4 Cq , C₂ = 1 pF Opamp-Gain = 50db HH = Vet Ra/vus) This is the simplified One - hade circuit With this fimflifuation we may opply Kirlhoff's Corrent Law at nader Semning the currents into nedal equation gives? 1 (Vx - Vy) + C₂ S V x + (rx - V2 C,S = 0 If we climinate the voltage Ve and folre for Velv, we obtain: V = T($) = (-1/R,C,)s 52+(!) (%6n + Y Js+ YR,R.C7C2 Let C, = C₂ = 0 , equation has a simplified form of a T(s) = (-/Rp c)s - 3²+ ( ^/R. C)'s + / R, Race Confaring this equation with standard Bandpass filter response, T($) = -(,1@)s 3²+ (Wola)s + use (ii) Equeting coefficients of equation (i) a lic); 40,- ENRIRE , Q = even , BW ac

Now the Delyiannis Feriend Filled circuit (on be specified on the value of a alone. Let w set the volece of 2 with the Toonifer Funition of the friend circuit, V = -2Qs - Ciei) Va S²+ (%) s tt Comparing this equation with the standard form of eq? Cic); with us 1 T 52+ (1/Qls th e y fox which I V₂ (1) 1 = 1 1/22 th Putting this value in eqr Ciei); gives like (02) = 222 ST for &= 4 and fo = 100 kHz We design the circuit.

The normalized element values are determined by a olone and then frequently scaling is required from w=1 to f = 100x10 Hz , requiring Kg = 20 x 100x 103. Using the scaling equation for Capacitous Cow = 1 Cold - 1012 = 1 km = 6 - Kf Km us 20 X 100x103 km 100 0.7854F copsakas 200.96ke awal 1.032 2 0.785ef $ 6.48 kr (normalized values) (values after frequency sealing) Find Axsulle