High-Pass Filters

• Figure shows some common implementations of high-pass filters.  
• Note that in each of the high-pass filters shown above, the inductors are in shunt with the input while the capacitors are in series with the input.  
• This is because the reactance XL of an inductor increases with the signal frequency, i.e., XL = 2πfL, while the reactance XC of a capacitor decreases with the signal frequency, i.e., XC = 1 / 2πfC.  
• Thus in these high-pass filters, the capacitors resist the passing of an ac signal as the frequency decreases, while the inductors shunt them towards the ground as the frequency decreases.  
• Either way,  the effect is to attenuate the signal as frequency decreases.

 

The following equations apply to the high-pass filters in Figure above:

1)  L = Zo / 4πf 

2)  C = 1 / (4πf Zo) 

3)  Zo = sqrt(L/C)

4)  f = 1 / (4π sqrt(LC))

where Zo is the line impedance and f is the cut-off frequency of the filter.