I'm designing an active bandpass filter (using only BJTs, voltage sources, resistors and capacitors) with the following properties:
Corner frequencies \$8 ~ \text{kHz}\$ and \$800 ~ \text{kHz}\$ (bandwidth of about \$790 ~ \text{kHz}\$)
\$40 ~ \mathrm{dB/dec}\$ roll-off of the LPF (second order filter)
\$20 ~ \mathrm{dB/dec}\$ roll-off of the HPF (first order filter)
Gain of about \$42 ~ \text{dB}\$
Low input impedance: \$\sim 60 ~ \Omega\$ (over a wide range of frequencies \$80 ~ \text{Hz} - 80 ~ \text{MHz}\$)
High output impedance: \$\sim 50 ~ \text{k}\Omega\$ (over a wide range of frequencies \$80 ~ \text{Hz} - 80 ~ \text{MHz}\$)
I thought about the following simple input stage: let the input be applied across a resistor (\$R'\$) with the desired input impedance followed by a unity-gain buffer (which has a high impedance and therefore wouldn't affect much the input impedance). Then, take the output of the buffer and process it through an HPF filter (and later through LPF). However when I tried to implement the buffer using emitter-follower I quickly ran into some problems.
In order to establish a proper biasing of the transistor we have to have the resistors \$R_1\$ and \$R_2\$. Crucially, a coupling capacitor \$C_{in}\$ is required (otherwise the circuit just does't work properly - SPICE simulation yields extreme attenuation in the frequency response). But the introduction of this capacitor creates two serious problems:
It affects the input impedance. The input impedance now changes with frequency, and it's hard to maintain a constant low input impedance over such a wide range of frequencies
It acts as an HPF filter and therefore adds another pole. In other words, if I want to have \$20 ~ \mathrm{dB/dec}\$ roll-off I must remove the HPF filtering of the buffer output (which in turn completely changes the design of the circuit).
What are some possible ways to alleviate these issues without over-complicating the circuit?