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# Bessel Filter Lowpass Prototype Element Values

Simulations of Normalized and Denormalized LP, HP, BP, and BS Filters

Lowpass Filters

(above)

Highpass Filters

(above)

Bandpass and Bandstop Filters

(above)

A Bessel filter is a filter whose impulse response is a Bessel function. Bessel filters are designed to give maximally flat group delay and maximally linear phase change across the band and into the transition region. They are very close to Gaussian type filters.

The table below lists prototype element values for the normalized lowpass function, which assumes a cutoff frequency of 1 rad/sec and source and load impedances of 1 Ω. Either an input capacitor (top reference line in table) or an input inductor (bottom line in table) can be used.

Convert values to other cutoff frequencies, impedances, and to highpass, bandpass or bandstop using denormalization equations.

 Capacitor Input Inductor Input
 Capacitor Input, RS=RL=1 Ω, f=1 rad/sec Order C1 L2 C3 L4 C5 L6 C7 L8 C9 L10 1 2.000 2 0.576 2.148 3 0.3374 0.9705 2.2034 4 0.2334 0.6725 1.0815 2.2404 5 0.1743 0.5072 0.804 1.111 2.2582 6 0.1365 0.4002 0.6392 0.8538 1.1126 2.2645 7 0.1106 0.3259 0.5249 0.702 0.869 1.1052 2.2659 8 0.0919 0.2719 0.4409 0.5936 0.7303 0.8695 1.0956 2.2656 9 0.078 0.2313 0.377 0.5108 0.6306 0.7407 0.8639 1.0863 2.2649 10 0.0672 0.1998 0.327 0.4454 0.5528 0.6493 0.742 0.8561 1.0781 2.2641 L1 C2 L3 C4 L5 C6 L7 C8 L9 C10 Inductor Input, RS=RL=1 Ω, f=1 rad/sec