Electronic Design

Pi filter has notch just outside passband

Some applications such as antialiasing could benefit from a lowpass filter with a notch just outside the passband. The filter in Fig. 1 is a Cauer or Elliptic type, but with a source impedance of zero. Typically, these filters as given in texts have a normalized source impedance that results in a −6 dB voltage gain. Through trial and error, I arrived at the coefficients as shown, which is why I chose to call it a π filter.

The filter has some useful properties (Fig. 2). For instance, dc gain is exactly 0 dB with no offset, and is independent of component tolerances. The passband is flat with a 1-dB peak at about 0.8 × fref. The corner frequency fref is at −0 dB and the notch frequency is exactly 2 × fref.

The “T” configuration was chosen to accommodate conversion to an opamp active filter. The filter is first transformed by multiplying all components by 1/s (Fig. 3). Inductors become resistors, resistors become capacitors, and capacitors become frequency-dependent negative resistors (FDNRs). An FDNR is easily implemented with two op amps. The final filter schematic has its component values and corner frequency scaled in the normal fashion (Fig. 4).

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