A second-order active band pass filter (BPF), known as a band pass Sallen-Key circuit, is shown in Figure 2.37.
(a) Show that the frequency response function of this filter is given by 

where

ω₀ = ˆš2(RC) ^-1

Q = ˆš2 / 4 - k

K = 1 + R_a / R_b

(b) Plot |H (f)|.

(c) Show that the 3-dB bandwidth of the filter can be expressed as B = f₀ / Q, where f₀ = ω₀ / 2Ï€.

(d) Design a BPF using this circuit with center frequency f₀ = 1000 Hz and 3-dB bandwidth of 300 Hz. Find values of R_a, R_b, R, and C will give these desired specifications.

/V2) jo) -0 + (/0) (jo) + ; %3D 2f jo) 3D R V; R Output 3R Input Ra Rp Figure 2.37