Our topic today is designing a Microstrip Lowpass Chebyshev-Type2 filter using NuHertz and HFSS. A Chebyshev type 2 has a flat response in the passband and ripples in the stopband. We'll compare the different options in NuHertz.

Lowpass filters are made from lumped L and C components. Such an approach is hard to implement for high-frequency applications. Distributed elements are needed for high-frequency filters. This process uses RF lines and RF stubs.

It's possible to replace the capacitors with open lambda/4 stubs using Richard's transformation. Inductors have a problem, so they can only be replaced with lambda/4 stubs or lambda/2 stubs.

Figure 1. Richards Transformation

Lowpass can't be done with short stubs, and long stubs aren't practical either. Kuroda's identities let you replace the inductor with a short transmission line and a capacitor. Therefore, the filter is just a bunch of open stubs connected by short transmission lines.

Figure 2. Kuroda's identity

LPF can be implemented using smaller sections of transmission lines, each with a specific impedance, like low, high, low, high, etc.

Knowing what can be done, we go back to NuHertz. Lowpass and Chebyshev-type 2 are chosen. The requirements, the passband, the stopband, the stopband insertion, and others need to be specified. Use distributed elements. NuHertz gives you a lot of options by doing this. Which one should I pick? All of them will be implemented in HFSS and compared for performance, dimensions, sensitivity, etc.

Figure 3. NuHertz setup for LPF Chebyshev-II Planar Filter

Select any one of the options and export to AEDT.

Figure 4. Exporting the design to AEDT

In AEDT, we solve all the options. You will notice that the filter is fully parameterized. Consequently, one can perform optimization.

Figure 5: All implementations in NuHertz

Here are the NuHertz predictions compared to the HFSS calculations. Because HFSS is a 3D EM solver, it's more accurate. You can use the optimizer to make the designs identical or to improve the response.

Figure 6: HFSS versus NuHertz Insertion (Green HFSS, Blue NuHertz)

Figure 7: HFSS versus NuHertz Return Loss (Green HFSS, Blue NuHertz)

Below is a table summarizing the differences between the topologies. Dimensions are in millimeters. All approaches are the same length, except for the spaced stubs, which are quite long. Same observation for the width of the filter,

Implementation |
Length |
Height |
Insertion @0.8GHz |
Return Loss @0.8GHz |
Insertion @2GHz |

Stepped Stub Resonators |
53.38 |
17.66 |
-1.49 |
-6.20 |
-50.00 |

Stepped Stub Resonators Split |
54.05 |
18.56 |
-1.72 |
-5.54 |
-19.27 |

Single Stub Resonators |
60.40 |
14.83 |
-2.04 |
-4.81 |
-27.13 |

Spaced Stubs |
147.07 |
40.86 |
-0.9 |
-9.00 |
-9.00 |

Radial Resonators |
55.92 |
16.70 |
-1.81 |
-5.38 |
-20.30 |

Radial Resonators Split |
55.53 |
16.05 |
-2.02 |
-4.89 |
-19.27 |

Table 1: LPF topologies

In Nuhertz, the following comments are added for each type:

Implementation |
Why using it? |

Stepped Stub Resonators |
Nominal one to realize transmission zeros |

Stepped Stub Resonators Split |
Similar to the top one, but used when the resonator are too big |

Single Stub Resonators |
Useful when the single side stubs are too wide. |

Spaced Stubs |
Useful for maintaining realizable geometry and low frequency response accuracy. |

Radial Resonators |
Useful when rectangular stubs would be too wide in that it minimizes the width of the T-joint and reducing physical size when long fat sections would otherwise be required. |

Radial Resonators Split |
Useful when the single radial resonators is too wide. |

All options have smooth curves, except for the spaced stubs, which have ripples. Even so, it has the highest average insertion and sharpest drop. Similarly, after the passband, the spaced stubs are more stable and quickly drop.

Figure 8: Return loss

Figure 9: Return loss up to 1 GHz

Figure 10: Insertion Flat up to 1 GHz

Figure 11: Insertion up to 1 GHz

October 29, 2024