Our topic today is designing a Microstrip Lowpass Chebyshev filter using NuHertz and HFSS. A Chebyshev has ripples in the passband and smooth response 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 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. The rectangular stubs with a single side are narrower in width. The stepped impedance is the narrowest.

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

Min Stubs |
83.51 |
9.13 |
-0.58 |
-13.50 |
-24.63 |

Min Segments |
83.51 |
9.13 |
-0.64 |
-11.52 |
-24.33 |

Split Stubs |
76.33 |
15.16 |
-0.64 |
-11.26 |
-25.02 |

Spaced Stubs |
176.81 |
15.18 |
-0.43 |
-13.00 |
Fails before 2GHz |

Radial Stubs |
76.57 |
13.57 |
-0.65 |
-11.35 |
-27.42 |

Butterfly Stubs |
75.28 |
10.03 |
-0.64 |
-13.50 |
-24.00 |

Stepped Impedance |
85.54 |
5.08 |
-0.64 |
-12.50 |
-21.34 |

Table 1: LPF topologies

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

Implementation |
Why using it? |

Min Stubs |
Select the ladder sequence that produces the fewest stubs. |

Min Segments |
Select the ladder sequence that produces the fewest series segments. |

Split Stubs |
Useful when the single side stubs are too wide. |

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

Radial Stubs |
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. |

Butterfly Stubs |
Useful when the single radial stub is too wide. |

Stepped Impedance |
Useful to minimize the physical length of the filter. |

With the exception of stepped impedance, all options have smooth curves. Even so, it has the highest average insertion and sharpest drop. After the passband, the stepped impedance is more stable and drops quickly.

Figure 8: Return loss

Figure 9: Return loss

Figure 10: Insertion Flat up to 1 GHz

Figure 11: Insertion

October 24, 2024