A new property of maximally-flat lowpass filter prototype coefficients with application in dissipative loss calculations

This paper presents a new property of maximally-flat filter prototype coefficients. The property can be used to relate the summation of all the coefficients to an elegant expression which only includes the first coefficient. This property is then used to calculate the increase in insertion loss of this type of filters in the presence of dissipative losses due to elements/resonators finite quality factors. This presented equation for the excess loss is very convenient and does not require referring to the prototype element value table. The property is also used to show that the group delay of a maximally-flat lowpass filter at ω = 0 rad/sec is only a function of the first element value of the prototype filter. Finally, a commercial circuit simulation tool is used to generate examples to verify the accuracy of the presented analytical equations. Additionally, the results are compared to expressions found in classical literature.