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Bessel Filter Prototype Element Values

A Gaussian filter is a filter whose impulse response is a Gaussian function. Gaussian filters are designed to give no overshoot to a step function input while minimizing the rise and fall time. This behavior is closely connected to the fact that the Gaussian filter has the minimum possible group delay. Mathematically, a Gaussian filter modifies the input signal by convolution with a Gaussian function; this transformation is also known as the Weierstrass transform. - Wikipedia

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 the equations here.




Prototype filter schematic - capacitor input - RF Cafe
Capacitor Input
Prototype filter schematic - inductor input - RF Cafe
Inductor Input

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
Order L1 C2 L3 C4 L5 C6 L7 C8 L9 C10

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