At 8:48 you introduce Actual 2-pole low pass filter response. How can a passive filter output a postive gain at the cutoff frequency. For me is does not make sense passive components are able to deliver positive gain?
The large voltage gain which you have noticed near the pole frequency does not imply amplification or power gain, and as soon as you attach a resistive load to the circuit this would become clear. In the low pass and high pass filters, the load as plotted is purely reactive, so zero real power is actually delivered even though the voltage can be very high. In the bandpass filter, you might notice that the load as plotted is resistive and the gain peaks at exactly 1.
