I suspect the 'best' one could do to at least meet the 10Hz & 10kHz -5dB requirement would be to satisfy the transfer function
\(G(s)=-K*\frac{(s+\omega_a)(s+10^4\omega_a)}{(s+100\omega_a)^2}\)
Where
\(\omega_a=2\pi f_a\)
with
\(f_a=3.162 \small{Hz}\)
& K≈0.165
This gives a 1kHz gain of 13.53dB with the peak gain at 316.2 Hz of 18.33dB
Whether this transfer function can itself be realized using just the four resistor & two capacitor values with one ideal op-amp is debatable.
\(G(s)=-K*\frac{(s+\omega_a)(s+10^4\omega_a)}{(s+100\omega_a)^2}\)
Where
\(\omega_a=2\pi f_a\)
with
\(f_a=3.162 \small{Hz}\)
& K≈0.165
This gives a 1kHz gain of 13.53dB with the peak gain at 316.2 Hz of 18.33dB
Whether this transfer function can itself be realized using just the four resistor & two capacitor values with one ideal op-amp is debatable.
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