a design of the novel coupled-line bandpass filter using defected ...

182.5 Chebyshev lowpass filter prototypeThe Chebyshev response that exhibits the equal-ripple passband and maximallyflat stopband is depicted in Figure 2-8. The amplitude-squared transfer function thatdescribes this type of response is [6]SΩ = 1(2-35)+ Ω( j )221 2 21 ε Tnwhere the ripple constant ε is related to a given passband ripple L Ar in dB and n isnumber of filter order by( )L Ar1010 1ε = − (2-36)FIGURE 2-8 Chebyshev lowpass responseT n (Ω) is a Chebyshev function of the first kind of order n, which is defined asTn( )( n−1)( n−1Ω)⎧⎪cos cos Ω Ω≤1Ω =⎨⎪⎩cosh cosh Ω≥1(2-37)Hence, the filters realized from (2-35) are commonly known as Chebyshev filters.Able to derived a general formula of the rational transfer function from (2-35)for the Chebyshev filter, that isS21ni=1( iπn)2 2Π ⎡ηsin /i=1 ⎣ +( p)=nΠ +( p p )i⎤⎦1/2(2-38)