Figure 1 illustrates some details of the geometry of the proposed structure. As shown in Fig. 1, the structure consists of a microstrip line on the left, followed by a traditional tapered microstrip transition, a dielectric-filled waveguide, an air-filled matching cavity, an ultra-thin cavity filter. The structure is symmetrical around the center of the ultra-thin cavity filter.

Figure 2 displays the design parameters of the structure from both a top and side view. The microstrip lines are printed on the Rogers RT/Duroid 5880 with a dielectric constant of 2.2 and a loss tangent of 0.0009. The substrate has a thickness of 0.127mm, while the upper layer metal copper has a thickness of 0.018mm. And the substrate of the dielectric-filled waveguide is also the Rogers RT/Duroid 5880. To simulate the thickness of the silver paste used to adhere the substrate to the cavity during physical assembly, the lower layer metal thickness is set to 0.035mm. The dimensions of the structure are listed in Table 1.

Table 1

Dimensions of the proposed structure (dimensions in mm).

WS1 | WS2 | W1 | W2 | W3 |

0.38 | 2 | 0.945 | 1.045 | 1.45 |

L1 | L2 | L3 | L4 | LC |

1.78 | 1.74 | 1.45 | 1.05 | 0.33 |

TAP | SUBL | a | b | airL |

0.72 | 0.6 | 2.54 | 0.18 | 3.42 |

The microstrip line operates in a quasi-TEM mode, as shown in Fig. 3(a), while the dominant mode of transmission in the dielectric-filled waveguide is TE10, depicted in Fig. 3(b). Figure 3 shows that the electromagnetic field transmitted by the microstrip line is suitable for exciting the electromagnetic field of the rectangular waveguide in its dominant mode. To prevent discontinuities in the electromagnetic field, a tapered microstrip line structure is used to connect the 50-Ohm microstrip line to the dielectric-filled waveguide. This structure has been established through theoretical analysis [10–12].

For a rectangular waveguide operating in the dominant TE10 mode, its transmission characteristics depend solely on its width and are independent of its height. To integrate the dielectric-filled waveguide into the substrate, the height of the waveguide can be made identical to the thickness of the microstrip line. Figure 4 shows the simulation results for the electric field intensity of the microstrip-to-dielectric-filled waveguide transition at 94 GHz, which is simulated by using Ansys HFSS.

The design of an ultra-thin cavity filter starts with creating a standard-sized filter centered at 94 GHz with a 5 GHz bandwidth. The filter uses an H-plane magnetic coupling approach, and it is constructed by cascading inductive irises with resonant cavities. The iris discontinuity generates higher modes of the electromagnetic field nearby, which cannot propagate in the waveguide. As a result, the magnetic energy near the iris is greater than the electric energy, allowing the iris to function as an inductive structure. Consequently, the inductive iris and its adjacent resonant cavity are treated as an impedance inverter, while the resonant cavity can be modeled as a series resonant circuit. Together, they form the bandpass filter structure of the impedance inverter. Reference [13] shows the design theory for the corresponding coupling matrix, which enables the creation of a filter with standard dimensions.

Conventionally, the three sides of a rectangular resonant cavity are denoted as *a*, *b*, and *l*, with *l* > *b* > *a*. The resonant wavelength and electromagnetic field equations of the resonant cavity are given in formulas (1), indicating that the resonant characteristics of the cavity are independent of its height, *b*. In waveguide cavity filters, the resonant mode within the cavity is TE101, which can be easily excited by TE10 mode. Therefore, the height of the filter can be reduced to match the height of the dielectric-filled waveguide, enabling connection to the waveguide through an air-filled matching cavity.

\(\begin{gathered} \lambda =\frac{2}{{\sqrt {{{(\frac{1}{a})}^2}+{{(\frac{1}{l})}^2}} }} \hfill \\ \left\{ \begin{gathered} {E_y}= - \frac{{2\omega {\mu _0}a}}{\pi }{H_0}\sin (\frac{\pi }{a}x)\sin (\frac{\pi }{l}z) \hfill \\ {H_x}=j2\frac{a}{l}{H_0}\sin (\frac{\pi }{a}x)\cos (\frac{\pi }{l}z) \hfill \\ {H_z}= - j2{H_0}\cos (\frac{\pi }{a}x)\sin (\frac{\pi }{l}z) \hfill \\ {E_x}={E_z}={H_y}=0 \hfill \\ \end{gathered} \right. \hfill \\ \end{gathered}\) . (1)

Figure 5 shows the simulation results of the same cavity filters with and without the proposed microstrip to ultra-thin cavity filter transition structure. The 5th order cavity filter without transition structure has an insertion loss of less than 0.5 dB and a return loss better than − 26 dB in the 91.5–96.5 GHz passband. However, the ultra-thin cavity filter with the proposed transition structure has an insertion loss of less than 1.5 dB and a return loss better than − 20 dB. Therefore, only 1 dB deterioration because of the added transition structure.

Figure 6 illustrates the impact of varying the length of the air-filled matching cavity (*L4*) on the structure. It can be observed that the air-filled matching cavity plays important roles in the whole structure. when the variations of *L4* are within ± 0.05 mm during simulation, the return loss of the structure changes substantially.