For this example, the required filter order is five, to theoretically meet the specifications. This then equates to the required susceptances as:

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2 For this example, the required filter order is five, to theoretically meet the specifications. This then equates to the required susceptances as: = = = Likewise, the electrical lengths of the cavities at f 0 (in rad) are: θ 1 =θ 5 = θ 2 =θ 4 = θ 3 =2.654 The physical lengths are easily determined by the known formula of the wavelength in a rectangular waveguide: Here λ 0 is the free space wavelength and f c is the cutoff frequency of the guide. As for the propagation constant, it is available directly as a measurement inside the Microwave Office software. The measurement K_Port is there as well and found under the Electromagnetic measurement category. Working through the necessary formulas, the physical lengths are determined to be: =18 mm =20.4 mm =20.96 mm The next step is to determine the iris opening. This must be mapped to a susceptance at f 0. For this, one iris is considered and the opening is parameterized.

3 Determination of Susceptance Referring to Figure 3, Port 1 is de-embedded to the plane of the iris. Port 2 is terminated with Z 0 of the waveguide, so there is no reflection from Port 2. Thus, S 11 is due to iris susceptance alone. Figure 3: Determination of susceptance. A pure susceptance, or shunt inductance, draws a trajectory on the constant conductance circle on a Smith chart, as shown in Figure 4. It is expected to see such behavior at f 0 as a function of the iris opening. Figure 4: A pure susceptance draws a trajectory on the constant conductance circle on a Smith chart, indicated by the red arrow. Single Parameterized Iris Analyst allows geometry parameterization such that the parameters are exposed and controlled from within Microwave Office circuit design framework. Figure 5 shows that the local variables in Microwave Office on the left side are used as parameters of the 3D model in the middle, which accordingly generates the geometry on the right. Figure 5: Parameters for geometry parameterization are exposed and controlled by the 3D editor from within Microwave Office.

4 When looking at the S 11, it is important to use the generalized S (GS) measurement under the Electromagnetic category because the ports are terminated by the dispersive characteristic impedance of the WG rather than 50 ohms. The susceptances can then be evaluated at f 0 using output equations as depicted in Figure 6. Figure 6: The susceptance at f 0 can be evaluated using output equations. Figure 7 shows the nearly perfect result of the susceptance versus the iris opening. =1.0402=3.87 mm =2.7404=5.52 mm =3.7714=6.01 mm Figure 7: The nearly perfect results of the susceptance versus the iris opening. Final Model and Fine Tuning Having determined the dimensions of the filter, the full filter model can now be constructed. has been parameterized to and W 1 to W 3, simplifying the implementation of the design equations (Figure 8). Figure 8: Implementation of the design equations with parameterized to and W 1 parameterized to W 3.

5 The results of the first attempt, shown in Figure 9, are very good. However, the irises are not ideal they have finite thickness, so the cavities are not ideal either. Figure 9: Results of first attempt at parameterization. The bandwidth is 926 MHz with the center at 8871 MHz, so a nominal redesign (optimization/tuning) is necessary at 1080 MHz centered at 9129 MHz. With the new f 0 at GHz, the results of the first redesign iteration, as shown in Figure 10, are: =17.37 mm =19.68 mm =20.24 mm =1.007=3.87 mm Figure 10: First redesign of filter. =2.63=5.50 mm =3.623=6.00 mm This iteration produces a band of GHz to GHz. The BW is then squeezed 34 MHz and the frequency is moved up 60 MHz for the second design iteration, resulting in the following, as shown in Figure 11. =17.31 mm =19.59 mm =20.13 mm Figure 11: The second redesign. =1.061=3.98 mm =2.811=5.64 mm =3.866=6.12 mm The second iteration produces a band of GHz to GHz and RL better than 19.5 db over the band. Using design equations, the frequency can be shifted 5 MHz and the RL improved to meet the passband specification exactly (Figure 12). =17.28 mm =19.58 mm =20.13 mm Figure 12: The second correction. = 3.95 mm = 5.62 mm = 6.10 mm

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7 Optimizing the nominal values with a resolution of 10 um, the yield can be improved to 41.5% with ±20 um tolerance. This is not good enough the tolerance has to be reduced. The yield sensitivity histograms in Figure 15 suggest a minimum tolerance: if the dimensions to ±5 um can be controlled, 100% yield can be achieved. Figure 15: Yield sensitivity histograms suggest a minimum tolerance. Having identified good nominal values, a corner analysis EM sweep can now be run where all parameters are varied at their extremes. Figure 16 shows that the RK is acceptable. Figure 16: The filter response shows that the return loss is acceptable. For the last modification, design equations are used to expand frequency limits a bit to provide a safe margin. Conclusion This application note has showcased a design example for an iris-coupled waveguide (WG) bandpass filter designed using Microwave Office circuit design software and the Analyst 3D FEM EM simulator. The passband specifications are met with =17.175, =19.515, =20.07, W 1 =3.915, W 2 =5.59, and W 3 =6.07, as shown in Figure 17. The yield is 100%, if the dimensions can be controlled to ±5 um precision. At 8 GHz and 10.5 GHz the rejection is better than db and db, respectively. References Ian Hunter: Theory and Design of Microwave Filters, Institution of Engineering and Technology, London, UK Figure 17: The passband specifications are met with L1=17.175, L2=19.515, L3=20.07, W1=3.915, W2=5.59 and W3= National Instruments. All rights reserved. A National Instruments Company, AWR, Microwave Office, National Instruments, NI, and ni.com are trademarks of National Instruments. Other product and company names listed are trademarks or trade names of their respective companies. AN-MWCMP