AWR Application Notes

Design and Implementation of a Miniature X-Band Edge-Coupled Microstrip BPF Using AWR Software 2 www.cadence.com/go/awr Bandpass Filter Construction A BPF can be constructed from resonant structures, such as a waveguide cavity or open-circuit transmission lines (i.e., stubs). An important parameter in filter design considerations is the fractional bandwidth, which is defined as the ratio of the passband bandwidth to the geometric center frequency. The inverse of this quantity is called the Q-factor. If ω1 and ω2 are the frequencies of the passband edges, then bandwidth ∆ = 2− 1Δ = 2− 1 geometric center frequency 0= √ 1. 2 and = -. /- Parallel-coupled line are another popular topology for PCB filters. While these resonant structures can be based on shorted or open-circuited parallel lines, open-circuit lines are the simplest to implement since the manufacturing does not require making a connection to the ground plane, often achieved through the use of vias. The design consists of a row of parallel λ/2 resonators that couple to each of the neighboring resonators, forming the topology shown in Figure 1. Wider fractional bandwidths are possible with this type of filter than with the capacitive gap filter implementation, which is formed with an in-line row of transmission lines separated by a small gap between line segments. Figure 1: Filter with parallel edge-coupled lines. Conventional Chebyshev design equations were used as follows: J-inverters 3 J-Inverters: ) 3 ( * 2 * ) 2 ( 1 1 * 2 * ) 1 ( * 2 * 1 0 1 , 1 0 1 , 1 0 0 01 + + + + = - = = = n n n n j j j j g g FBW Y J n to j g g FBW Y J g g FBW Y J p p p ) 4 ( 0 1 2 w w w - = FBW where ) 6 ( 0 1 1 ) ( ) 5 ( 0 1 1 ) ( 2 0 1 , 0 1 , 0 1 , 0 2 0 1 , 0 1 , 0 1 , 0 n to j Y J Y J Y Z n to j Y J Y J Y Z j j j j j j o j j j j j j e = ú ú û ù ê ê ë é ÷ ÷ ø ö ç ç è æ + - = = ú ú û ù ê ê ë é ÷ ÷ ø ö ç ç è æ + + = + + + + + + Even- and odd- impedances of the coupled lines where 3 J-Inverters: ) 3 ( * 2 * ) 2 ( 1 1 * 2 * ) 1 ( * 2 * 1 0 1 , 1 0 1 , 1 0 0 01 + + + + = - = = = n n n n j j j j g g FBW Y J n to j g g FBW Y J g g FBW Y J p p p ) 4 ( 0 1 2 w w w - = FBW where ) 6 ( 0 1 1 ) ( ) 5 ( 0 1 1 ) ( 2 0 1 , 0 1 , 0 1 , 0 2 0 1 , 0 1 , 0 1 , 0 n to j Y J Y J Y Z n to j Y J Y J Y Z j j j j j j o j j j j j j e = ú ú û ù ê ê ë é ÷ ÷ ø ö ç ç è æ + - = = ú ú û ù ê ê ë é ÷ ÷ ø ö ç ç è æ + + = + + + + + + Even- and odd- impedances of the coupled lines Equations used for the even and odd impedance of the coupled lines were: 3 J-Inverters: ) 3 ( * 2 * ) 2 ( 1 1 * 2 * ) 1 ( * 2 * 1 0 1 , 1 0 1 , 1 0 0 01 + + + + = - = = = n n n n j j j j g g FBW Y J n to j g g FBW Y J g g FBW Y J p p p ) 4 ( 0 1 2 w w w - = FBW where ) 6 ( 0 1 1 ) ( ) 5 ( 0 1 1 ) ( 2 0 1 , 0 1 , 0 1 , 0 2 0 1 , 0 1 , 0 1 , 0 n to j Y J Y J Y Z n to j Y J Y J Y Z j j j j j j o j j j j j j e = ú ú û ù ê ê ë é ÷ ÷ ø ö ç ç è æ + - = = ú ú û ù ê ê ë é ÷ ÷ ø ö ç ç è æ + + = + + + + + + Even- and odd- impedances of the coupled lines

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