Twin notch filter working
The correct answer is \$ T=RC/2 \$ only if using: {R,R/2 and C,2C}

Of course, using: {R,2R and C,2C} then it is \$T=RC/4\$ so both are true.


  Can someone please explain to me in depth as to how this twin notch circuit is working?


It works by superposition of attenuated LPF and HPF causing exact same reduced amplitude and opposite phase cancelling the combined signal.  The output impedance of the HPF also loads the output of LPF and visa-versa and contributes to the response of each.

The notch phase response starts at 0 deg at DC rising to +135' neaR notch then 0 at centre then dropping to -135' ( =-90'-45') with +/-45' shift for each midpoint.

The depth in dB of the notch depends on the external load to be high and the worst case tolerance error of each part.  A worst case random part tolerance of 1%  might reduce the notch to -40 dB and shift the frequency according to T=RC/2 tolerance stackup.

e.g. 60Hz  The depth is limited by the resolution of the step frequency plot with an offset of 0.01 Hz at 60.01 Hz for a 60Hz notch.


Using a 50 Ohm generator would work except above the notch attenuation occurs based on R ratios.