The filter was designed using CST DESIGN STUDIO™ (CST DS) with a resulting layout shown in Figure 1. This is the familiar hairpin configuration consisting of microstrip circuit RF components such as microstrip lines, TEE- sections and coupled lines.
To perform optimization runs, geometrical parameters were assigned to the individual RF-components. Figure 2 shows property tables of some components including variables.
Starting out from rough dimensions of the resonator sections, a tuning process was performed. With initially only one hairpin section the groupdelay can be computed as the derivative of the phase of S11 over frequency. The location of the groupdelay curve maximum needs to match the desired center frequency and it's value at the peak has to match the theoretical groupdelay given by e.g. a Tschebychev response. The advantage of using the method is that it keeps the number of variables to be optimized very small. For the first section the coupling bandwidth is determined by the position of the feeding microstrip along one side of the hairpin. The resonance itself is can be varied by modifying the overall length of the U-shaped hairpin. Figure 2 shows the schematic layout of the hairpin when tuning the second hairpin section....
Once the 3rd section is tuned the schematic can be mirrored and simulated for the complete filter. The performance of the whole filter will not be perfect but definitely good enough to start an overall optimization process. Figure 4 shows filter response after completion of the optimization process. Only 9 variables were used, mainly concerning the lengths and gaps of the coupled U-shaped sections. Since the starting values are close to the optimum, the variational bandwidth and the number of samples can be kept small.
As a second step, the dimensions of the filter found by CST DS after the optimization run were used to build up a three dimensional model in CST MICROWAVE STUDIO® (CST MWS). The only critical part is the MTEE-section: The lengths of three arms are zero per library definition. To take the physical length into account, the feeding point was slightly shifted along the enlarged first section arm. The model and the initial dimensions are shown in Figure 5.
The optimized filter response and the CST MWS results were compared: the bandwidth is in excellent agreement. Some further tuning needs to be performed to achieve a nicely balanced return loss. The differences are most likely due to fringing and side-wall coupling effects.