The second-order section is a simple circuit that can generate a sinusoidal response. The circuit is shown in Figure 1. It contains two cascaded amplifiers, A1 and A2 with the same transconductance G1=G2=G, and a feedback amplifier A3 with transconductance G3. The capacitance C is the same for both stages. The feedback amplifier has its output proportional to the difference between V2 and V3. The sign of the feedback of positive. The A4 and A5 are differentiator.
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The figure 2 shows the transfer function of Hs(s) and Hd(s). Hs(s) is transfer function of Vin and Vout. Hd(s) is transfer fuction of Vdif-Vref and Vin, where Vref is constant. The cut-off frequency is depending on tou-value. The gain is depending on Q value.
The figure 3 shows the frequency response of Hs(s) with Q = 0.7(blue), 0.8(red), 0.9(green).We can see that it is a low pass filter. The figure 4 shows the frequency response of Hd(s) with Q = 0.7(blue), 0.8(red), 0.9(green).we can see that it is a band pass filter with very sharp tuning.