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

13The even- and odd-mode characteristic impedances given by the following closedformexpressions are accurate to within 0.6% over the ranges 0.1 ≤ u ≤ 10, 0.1 ≤ g≤ 10 and 1 ≤ ε ≤ 18.rQ = 0.8685u10.194Q = 1+ 0.7519g+0.189g22.31QQ6−0.387⎡ ⎤ ⎡10⎛8.4 ⎞ 1 g= 0.1975 + ⎢16.6 + ⎜ ⎟ ⎥ + ln ⎢g 241⎣⎢ ⎝ ⎠ ⎦⎥ ⎢⎣1 + /3.4( g )3 102Q1= ⋅⎣14 Q3 −Q3Q2u exp( − g) + ⎡2 −exp( −g)⎤u⎦⎤⎥⎥⎦Q⎡ 0.638= 1.794 + 1.14ln ⎢1+⎣ g+0.517g5 2.43⎤⎥⎦Q61= 0.2305 + ln281.3 ⎢⎣1 + g /5.8⎡ 10g ⎤⎢10 ⎥++( )⎥⎦1 ln 1 0.5985.11.154( g )Q10 + 190g1 82.3g7 32= + ( ) ( )Q8= exp ⎡−6.5 −0.95ln g − g/ 0.15⎣5⎤⎦( ) ( )Q = ln Q ⋅ Q + 1/16.59 7 856Q10 Q4exp Q2 u( u)Q ⎡Qln ⎤= − ⎢ Q ⎥9⎣ ⎦thenZceeZc εre / εre= (2-31)1 − Q ε . Z / 3774rec