This paper presents a new property of maximally-at 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-at 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.
2. Tsai, C.-M. and H.-M. Lee, "The effect of component Q distribution on microwave filters," IEEE Trans. Microw. Theory Tech., Vol. 54, No. 4, 1545-1553, 2006.
3. Dishal, M., "Design of dissipative band-pass filters producing desired exact amplitude-frequency characteristics," Proc. of the IRE, Vol. 37, No. 9, 1050-1069, 1949.
4. Bode, H. W., Network Analysis and Feedback Amplifier Design, Van Nostrand, New York, NY, 1945.
5. Matthaei, G. L., L. Young, and E. M. Jones, Microwave Filters, Impedance Matching Networks and Coupling Structures, McGraw-Hill, New York, NY, 1964.
6. Cameron, R. J., C. M. Kudsia, and R. R. Mansour, Microwave Filters for Communication Systems: Fundamentals, Design, and Applications, Wiley-Interscience, Hoboken, NJ, 2007.
7. Hunter, I. C., Theory and Design of Microwave Filters, IET Press, London, U.K., 2001.
8. Gradshteyn, I. S. and I. M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, Burlington, MA, 2007.
9. Saeedi, S., J. Lee, and H. H. Sigmarsson, "Novel coupling matrix synthesis for single-layer substrate-integrated evanescent-mode cavity tunable bandstop filter design," IEEE Trans. Microw. Theory Tech., Vol. 63, No. 12, 3929-3938, Dec. 2015.