I am working on an assignment about Passive, second order low-pass filters. Cool little things if you get to know them.
We are given the placements of the passive components (Inductor(L1), Resistor(R1) and Capacitor(C1)) without their values.
The only given specification is that the cut-off frequency (fc) is 78 kHz.
The circuit is shown below.
If the Photo is unclear here's the Schematic:
My questions are:
1.How to make the predicted low-pass filter Transfer function for this specific circuit?
(In other words...the expression for the Output Voltage Phasor to Input Voltage Phasor? ) (Using sinusoidal steady-state analysis and answer in modulus argument form)
2.Secondly how do I calculate or choose the component values for the filter? ...
The components must work out so that:
2.1) the Phase Angle between the output voltage and input voltage is -90 degrees at the cut-off frequency (78 kHz).
(A suggestion given to me was to choose a Inductor value and a Capacitor value that is at my disposal and to calculate the required Resistor value to build the circuit after calculations ).
2.2) that the Ratio of the amplitudes of the Output Voltage to the amplitude of the Input Voltage is 0.7079 at the cut-off frequency(fc).
PS: I have a 1mH Inductor at my disposal,- thats why it is the only value I entered on the circuit for now :) - And the Capacitors at my disposal is 1uF, 10uF, 22uF, 100uF or 470uF ).
I can't wait to here from you!