#### What is in this article?:

This straightforward approach helps to reduce the design complexity of computing filter dimensions and creating low-loss waveguide diplexers and multiplexers.

## Getting Started

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The first step in the diplexer design technique is to replace filters 2 and 3 with their respective reflection coefficients, Γ_{2} and Γ_{3}, and to use the initial dimensions of the septum (as shown in **Fig. 4**, where the initial dimensions of the septum are set to zero). Values for reflection coefficients Γ_{2} and Γ_{3} are obtained beforehand by numerical simulation, using commercial simulation software such as Microwave Studio from Computer Simulation Technology, the High Frequency Structure Simulator (HFSS) electromagnetic (EM) software from Ansys, or even in-house EM computational programs. With this approach, one can avoid the mathematical manipulation of the admittance or scattering matrix of the T-junction.

The next step involves adjusting the distance L_{3} such that |S_{11}| is at its smallest value at band 2. Since, by design, the filter 2 is well matched at band 2, distance L_{2} will have a negligible effect on |S_{11}|. The distance L_{2} is determined in the same way for minimum value of |S_{11}| at band 3. Lengths L_{2} and L_{3} should be large enough so that higher-order modes generated at the T-junction discontinuity and the septum are sufficiently attenuated after propagating over the distances L_{2} and L_{3}. With the values for L_{2} and L_{3} determined, typical values for |S_{11}| would be around -10 dB at each filter’s passband.

At this point in the design process, a septum with suitable height H and width W is added to reduce the value of |S_{11}|. It has been found that |S_{11}| is not sensitive to septum width W ranging from 0.05a to 0.30a. A septum width W equal to 0.30a is a good choice since it results in a mechanically stronger structure than when using a thin septum. With septum width W fixed at 0.30a, the septum height H can be adjusted until |S_{11}| is at its smallest value for both bands. With a properly designed septum, |S_{11}| is now decreased to less than -20 dB at both bands. If necessary, simultaneously adjustments can be made in L_{2}, L_{3}, and H for further improvements in |S_{11}|.

This design technique can be extended to creating general junction-type multiplexers. In the first stage, each bandpass filter is replaced with its precomputed reflection coefficient, and the dimensions of the impedance-matching elements in the multiplexing junction are set to their initial values, which may all be zero. For impedance matching the multiplexer’s kth channel, the distances from all other filters to the junction reference plane are adjusted for the lowest reflection at the kth band. This process is then repeated for all channels. This completes one design cycle of the filter distance optimization. The filter distances will be changed in each step of a design cycle. Many cycles of the filter distance optimization is carried out until a convergence is obtained.

Next, the matching elements of the multiplexer junction are adjusted for good impedance matching at all bands. If desired performance is not obtained in the second stage, the first and second stages can be repeated or combined and simultaneously adjustments made to the filter distances and impedance-matching elements of the junction.

To demonstrate the effectiveness of this design approach, a waveguide diplexer was designed and fabricated. It is a diplexer fabricated with WR-51 waveguide, with a = 12.95 mm and b = 6.48 mm and with passbands of 17.7 to 18.1 GHz (band 2) and 18.7 to 19.1 GHz (band 3). Microwave Studio was employed in the numerical simulation. Waveguide filters of order 8 with thin metal strips along the waveguide center line were designed using the Rhodes method.^{11,12} **Figure 5** shows the structure of this experimental filter, with its dimensions shown in the **table**. The filter's order determines the rolloff rate.

When two channel filters are combined in the H-plane T-junction without a septum and with filter distances L_{2} and L_{3} optimized, the resultant reflection coefficient shown in **Figure 6** is only at a level of -10 dB. Using the septum in the T-junction, the reflection coefficient was reduced to a -20-dB level. The diplexer junction's final dimensions were L_{2} = 8.15 mm, L_{3} = 6.80 mm, W = 4.00 mm, and H = 2.10 mm.

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