LC Filter

To the load resistance R_L the ripple factor is directly proportional in the inductor filter and inversely proportional to R_L in the capacitor filter. Hence if these two filters are joint as LC filter or L section filter as displayed in figure the ripple factor will be independent of R_L.

It will increase the time of conduction if the value of inductance is increased. At some vital value of inductance, one diode, either D1 or D2 will all the time conducting.

The output voltage can be expressed like below from Fourier series,

V₀ = (2V_m / π) - 4V_m / 3 π cos2 ∞ t

Then the dc output voltage,

V_dc = 2V_m/ π

∴ V_{r rms} = I_rms . X_c = √2 /3. V_dc. X_c /X_L

The ripple factor

ϒ= V_{r rms} / V_dc = √2 /3.  X_c /X_L

= √2 /3. 1/4 ∞² CL

∴ X_c = 1 /2 ∞ C & X_L 2 ∞ L