Parent Category: 2019 HFE

*By Jeff Kahler*

**Introduction**

Diplexer, duplexer, triplexer, and N-plexer designs may include electrical and physical design requirements that are not only difficult and cumbersome, but at times may seem to be mutually exclusive. This is especially true at high frequencies, typically above ~100MHz and into the multi GHz range, where substrate and interconnect parasitic effects can significantly degrade performance and must be optimized without overburdening the designer or lengthening development time.

This article presents an accurate and efficient flow for the design of these components employing a combination of Nuhertz Technologies filter solutions (FS), NI AWR software, specifically Microwave Office circuit design software, and Modelithics RF and microwave simulation models. This flow has been shown to overcome numerous physical/electrical design challenges of these devices at high frequencies.

Design success is accomplished using the optimization capabilities in Microwave Office software, combined with the extremely accurate and flexible vendor component models available from Modelithics, and the efficient, user-friendly design automation from Nuhertz. Seasoned design engineers can generally meet the device requirements with ease using this accurate and efficient software design flow that quickly achieves high-frequency diplexer, duplexer, and triplexer designs that meet both the electrical and physical design requirements. N-plexer designs can be derived in Microwave Office software from duplexer and triplexer building blocks using simple copy/paste functions. The AXIEM planar or Analyst™ 3D finite-element method (FEM) electromagnetic (EM) simulators can be used for further analysis/optimization of multi-GHz designs.

**Filter Design Challenges**

Ideal diplexer designs are inherently problematic even at low frequencies due to the finite source resistance and interactions of the low-pass and high-pass legs. Duplexers (two bandpass legs), triplexers (low-pass, bandpass, and high-pass legs), and N-plexers (multiple legs), are similarly problematic for the same fundamental reasons. Undesired input reflections (S11) and droopy output frequency responses (S1,2, S1,3, …S1,N) at cutoff frequencies become difficult to manage. Ideal contiguous diplexers (those with no 3-dB frequency gaps between adjacent passbands) tend to interact right between the legs so as to mitigate, but not eliminate, undesired frequency input reflections and output responses.

Noncontiguous diplexers (those with frequency gaps between adjacent passbands) exhibit worse frequency response degradation but can be mitigated with the use of shunt LC-series resonator reflection compensators that force the undesired reflections into the frequency gap between the passbands and away from the passband frequencies. Duplexers and N-plexers with outer bandpass legs exhibit similar frequency response degradation at the outer bandpass cutoff frequencies and can be compensated for in a similar manner at the outer edge frequencies.

The frequency response mitigating effect of noncontiguous diplexer design reflection compensators can be offset by element values that exceed the desired range, or whose physical size may be outside the physical design requirements. Adjusting for elements of more desired values can bring the elements sizes back inside the physical design requirements, and if the designer is lucky, may still meet electrical design requirements. In some cases, it may come down to a choice between meeting the physical design requirements or meeting the electrical design requirements. This is, of course, an unacceptable solution that can be resolved with the advanced design techniques presented in this article.

The reflection compensation elements are computed using algorithms based on identical diplexer high pass and low pass leg topologies, orders, pass band attenuation, and stop band attenuation. Some applications require that the high pass and low pass legs be designed with differing topologies, orders and/or attenuation requirements. This compounds the reflection compensation problem in that the reflection compensation elements will not compensate as well, and worsen the frequency response further.

In addition to the inherent frequency response degradation of ideal diplexers, real-world diplexer frequency responses suffer from the non-optimum values of available discrete components and finite inductor Q, even at lower frequencies. At higher frequencies, additional parasitic effects of interconnects and pad geometries will degrade the frequency response even further, possibly to the point it is no longer recognizable. Since high-frequency diplexer designs also include low-frequency and ideal-frequency degradation problems, it is practical to optimize all of them at the same time in order to produce a final design that meets all electrical and physical design requirements.

**Diplexer Design**

The design process starts with a simple Nuhertz FS synthesized filter design for an eight-pole noncontiguous (a gap exists between low-pass and high-pass 3-dB frequencies) elliptic diplexer with a 500-MHz center frequency and a 200-MHz gap. An even order is chosen to minimize the inductor count and a reflection compensator is used to force the reflections into the gap and away from the upper and lower passbands. The center frequency of 500 MHz is well into the frequency range where substrate and interconnect parasitics can have an impact. The Nuhertz ideal filter and Microwave Office S-parameter frequency response and optimization goals are shown in Figure 1. The “Export” drop-down control is used to export the design into Microwave Office software for further analysis.

It can be seen in Figure 1 that the ideal diplexer easily meets the frequency response requirements. However, once real (manufactured) components, interconnects, and substrates are incorporated, the frequency response will most likely decay significantly at these design frequencies.

Figure 1 • Simple ideal diplexer with Microwave Office S-parameter frequency response.

Modelithics Murata 06031QW18A inductor models and Modelithics AVX 0603 ACCUP capacitor models are chosen for the real-world design implementation. Inductor and capacitor families were carefully selected based on their good performance at high frequencies and to provide numerous candidate components for selection by the Microwave Office discrete optimizer. The family element size range extends to include the compensation element ideal values, assuring that the compensation element physical sizes will be as acceptable as the rest of the diplexer element physical sizes. It is also possible to select multiple inductor and capacitor families to account for large differences in element sizes. Each family should be selected to meet the frequency and physical size requirements of the particular elements for which it is selected.

The substrate chosen is a 20-mil Modelithics Rogers 4003C1. The interconnect geometry will be defined as a substrate height ratio for simplicity, but the option does exist for the designer to define interconnect geometries with the substate’s physical height dimension specified. The Nuhertz FS export panel with the selections for this design is shown in Figure 2. The Parts Library and Interconnects options are set to “Modelithics COMPLETE” and “Include Interconnects”.

Figure 2 • Nuhertz FS export page with Modelithics definitions.

Modelithics parts families and substrate selections are very simple. A drop-down menu contains all the families and substrates available and the designer can simply select the desired family, families, or substrate. Multiple families can be selected by checking the appropriate checkbox (Figure 3).

Figure 3 • Modelithics part family selection process.

Now that the ideal design is available and-world parts and the substrate has been selected, the next step is to export again into Microwave Office software to obtain the schematic, layout, and frequency response of the design using the Modelithic’s parts and substrate model. Part selection and interconnect insertion is 100% automated, however, manual adjustments to the interconnect layout can be made, if desired, by adding and adjusting layout elements in the Microwave Office schematic. The exported design with all the components is shown in Figure 4 and reveals the S-parameters in the real simulation have degraded significantly from the ideal design.

Figure 4 • Real diplexer exported into Microwave Office software.

Looking closely at the Microwave Office schematic, the Modelithics parts assignments are made using discrete equations that are compatible with the Microwave Office discrete optimizer. Furthermore, the interconnect geometries are all defined with equations that are optimizable, as seen in Figure 5. For the first optimization pass, only the Modelithics parts are optimized. The optimizable equations are displayed in blue and non-optimizable equations are displayed in black in the Microwave Office schematic.

Figure 5 • Modelithics part selection with Microwave Office discrete optimizer.

The discrete optimizer will attempt to select the best Modelithics parts that most closely fit the design optimization goals. Once a suitable parts selection process is complete, a second optional optimization pass that includes the interconnect geometry will be executed for this example.

The first optimization pass has interconnect geometry disabled by deselecting the appropriate check box in the Microwave Office export panel, as shown in Figure 6.

Figure 6 • Deselect interconnect geometry optimization.

To run the discrete optimizer, select “Discrete Local Search” in the optimizer window and select “Start” in the lower left of the optimizer window. The optimization constant reduces in size as the optimization process completes and will stop when it can optimize no further. It is advisable to make more than one discrete optimization run and use the run that reduces to the smallest number. The best results out of three optimization runs in this example is shown in Figure7, along with the circled locations of the relevant controls and displays. An optimization constant is seen to be 27 in the optimization window, which is a significant improvement from the original 630. A significant improvement can also be seen in the simulated S-parameters that now more closely match the optimization goals.

Figure 7 • Best Modelithics parts selection from the Microwave Office Discrete optimization pass.

In many cases, the Modelithics part discrete optimization pass is sufficient to meet design requirements, and the design is essentially finished, leaving only the task of moving parts and layouts around to meet footprint size and board space limitations. If the frequency response does not yet meet design requirements, the interconnect geometry must be optimized. To optimize the interconnects, select the appropriate check box in the Microwave Office export panel, as shown in Figure 8, and select “Update.”

Figure 8 • Select interconnect geometry optimization.

This will update all the relevant interconnect geometry equations to enable tuning and optimizing. The optimizable equation is shown in blue in the Microwave Office schematic in Figure 9. The “S” and “W” equations control the interconnect geometry and are now ready to optimize.

Figure 9 • Interconnect geometry variable equations set to optimize.

The Microwave Office optimizer will be run again, with both Modelithics part selection and interconnect geometry set for optimization. “Discrete Local Search” will be selected, followed by “Pointer Gradient,” which fine tunes the optimization. The results, shown in Figure 10, indicate a near-perfect S-parameter response and a very small residual optimization constant of 1.4. It should be noted that if it is desirable to move the layout around to meet footprint and board space requirements, that movement should be performed prior to optimizing the Modelithics elements and interconnect geometry.

Figure 10 • Final diplexer design with optimized Modelithics parts and interconnect geometry.

At frequencies nearing 1 GHz, it is advisable to verify the frequency response using the AXIEM 3D EM planar simulator. This is easily done for the final design by right clicking on the Microwave Office schematic extraction block and selecting “Enable,” then “Add Extraction,” as shown in Figure 11.

Figure 11: Microwave Office schematic extraction block showing “Enable” and “Add Extraction” selections.

The AXIEM EM frequency response in Figure 12 shows a very close match to the Microwave Office circuit simulation S-parameter frequency response.

Figure 12 • Frequency Response of the AXIEM EM simulation.

As the results of the AXIEM frequency response shows slight degradation from the circuit simulation response, it may be desirable to perform EM extraction optimizations to further improve the frequency response of the diplexer. Extraction optimizations can be computationally intensive, thus increasing computer simulation time. Designers should use their best judgement to know if the additional compute time is justified. In this case, further extraction optimization was justified, and the constant is reduced from 4.5 before extraction optimizations to 1.8 afterwards. The final AXIEM frequency response is shown in Figure 13.

Figure 13 • Final AXIEM diplexer S-parameter frequency response.

**Duplexer Design**

Duplexers are like diplexers, except that duplexers have two bandpass legs instead of a low-pass and high-pass leg. The center frequency reflection compensator for noncontiguous duplexers remain identical to that of diplexers. Duplexers have an additional design problem in that the outside edges of the bandpass legs’ cutoff frequencies tend to droop for the same reasons that the noncontiguous diplexer cutoff frequencies tend to droop. This outer edge drooping can be mitigated by the addition of outer edge reflection compensators, just like the center frequency reflection compensation of noncontiguous diplexers.

Figure 14 shows a simple ideal 6-pole elliptic FS duplexer design centered at 200 MHz with an outer edge bandwidth of 200 MHz. An “equal legs” topology was chosen to minimize the shunt inductor spread and to more easily optimize the two passbands. Three shunt LC resonators serve as reflection compensators; one for the center frequency and one for each of the bandpass outer edges.

Figure 14: Part 1: Ideal 6-pole elliptic FS duplexer with Microwave Office S-parameter frequency response.

Figure 14 • Part 2: Ideal 6-pole elliptic FS duplexer with Microwave Office S-parameter frequency response.

The same design steps for finalizing the duplexer design can be followed that were used for the diplexer design: optimize for the best Modelithics parts, optimize the interconnects, and then perform EM extraction optimizations with the AXIEM software if necessary. Figure 15 shows the parts and optimized layout design of the duplexer.

Figure 15 • Modelithics parts and layout optimized duplexer in Microwave Office software.

**Triplexer Design**

Triplexers are similar to diplexers, but with a bandpass section between the low-pass and high-pass legs. Two reflection compensators are needed for noncontiguous triplexers, one between the low-pass and bandpass section and one between the bandpass and high-pass section. Triplexers employ the same design as diplexers, but the junction at the split point is more complex, resulting in more interconnect parasitics, which in turn may lessen the maximum frequency performance or ability to meet design goals. Figure 16 is an optimized interconnect triplexer with some manual length adjustments at the split junction. Note the final optimization constant is 14, which is somewhat higher than that achieved in the diplexer and duplexer designs described above.

Figure 16 • Modelithics parts and layout optimized triplexer in Microwave Office software.

**N-Plexer Design**

N-plexers consist of a series of bandpass sections with an optional low-pass and/or high-pass section at each end. FS will not design N-plexers directly, but they can be developed in parts by designing duplexers and triplexers individually, exporting into Microwave Office software, and then copy/pasting the desired sections into the Microwave Office N-plexer design. It should be noted that the additional complexity of the N-plexer junction point microstrip layout may limit the frequency range of an LC lumped-element N-plexer design. Figure 17 depicts an N-plexer design in Microwave Office software. Note that the reflection compensators have been located on the input of the individual N-plexer legs in all cases. This can be done at the discretion of the designer.

Figure 17 • N-plexer schematic and layout in Microwave Office software.

**Conclusion**

This article described a straightforward methodology for designing high-frequency lumped-element diplexers, duplexers, triplexers, and N-plexers using the Nuhertz FS, NI AWR Design Environment platform (inclusive of Microwave Office circuit simulator and AXIEM 3D EM planar simulator), and Modelithics RF/microwave component models. The final designs have been shown to be valid, accurate, and usable. The bulk of the design process is automated, saving design and development time and enabling faster time to market.

**About the Author**

Jeff Kahler is the President and Technical Director of Nuhertz Technologies.

### April 2022

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