# Transformation from Normalized Low-Pass Filter to Denormalized High-Pass Filter

I would like to ask a question about the a method (method number 2) to go from a normalized LPF to a HPF: Note: normalized refers to frequency normalization for the mentioned filters.

1- One method allows to go from normalized LPF to denormalized HPF by using the transformation (refer to Figure below)

This then allows to get for example an inductor L' in the denormalized HPF by using the capacitor value C in the normalized LPF: L'= $$\ \frac{1}{C\omega_{p}}\$$

2- Another method allows to go from a normalized LPF to a HPF. However, I am not sure if it leads to a normalized or denormalized HPF. Here is the transformation (Figure below):

And an inductor L' in the HPF is obtained by L'= $$\ \frac{1}{C\omega_{0}^{2}}\$$ where C is the capacitor in the normalized LPF.

Would this L' represent the inductor in a normalized HPF or denormalized HPF in the case where we start from a normalized LPF?

Thank you

• It does depend on L or C unless you choose that. it could depend on if R load is series or parallel load swapped with C for attenuation. – Tony Stewart EE75 Dec 31 '20 at 16:36
• Just to make sure I got your point: Do you believe this means that using the second method, if the LPF is normalized, the HPF obtained would be as well? – Martin Delaverge Douce Dec 31 '20 at 17:40
• Both methods are valid. The first one is normalized, the second isn't. You can easily verify this, numerically. Happy New Year. – a concerned citizen Dec 31 '20 at 18:06