The response from voltage to current in the inductive branch is the first order low pass function and the same in the capacitive branch is the first order high pass function.
So we can make the input impedance independent of the frequency if the input current is also independent of frequency (already the voltage applied is independent of frequency).
Which can be made by just adding those two currents, Under below two conditions.
1. The rate of fall and rise(to a step input) equal. i.e. The time constant of both branches equal.
i.e; Rc * C = L / Rl.
2. The initial and final current values in capacitive and inductive branch respectively are the same; there by no transition.
i.e; Rc = Rl. 😃🤗
