Microwave filters conventionally reflect electromagnetic (EM) waves from the load back to the source. In some cases, however, it is desirable to separate the reflected wave from the input, to protect the source from excessive power levels, for example. For this reason, absorptive filters have been developed to minimize reflections.¹

Figure 1 shows the basic configuration of an absorptive filter. This type of filter is useful not only as an absorption filter, but also works as power combiner or diplexer. When there is only one signal input (port 1), port 2 is an absorption port and port 3 is an isolated port. Port 4 is the output port. When different input signals are applied at port 1 and port 3, the configuration can also work as a signal combiner. Recently, the substrate-integrated-waveguide (SIW) technique^2,3 has been proposed in waveguide applications for microwave and millimeter-wave systems. SIW is made of various metallic via arrays in the substrate. Standard printed-circuit boards (PCBs) or low-temperature-cofired-ceramic (LTCC) substrates have been used to fabricate SIW devices. SIW technology has some advantages, such as high quality factor (Q), low insertion loss, reduced size, low cost, and easy integration with planar circuits. As a result, SIW technology is widely applied to all kinds of different filters^4-6 and diplexer designs.⁷

In this article, a new class of cross-coupled absorption filter has been developed based on the SIW technique. It has sharp selectivity and high Q, and is easily integrated with planar circuits. The 3-dB hybrid coupler with two steps developed in this report differs from work published earlier.⁸ This 3-dB hybrid coupler exhibits good performance of power distribution. An absorption filter was fabricated with standard PCB boards, and a comparison of measured data with simulation results shows close agreement. It is apparent that SIW to air-filled waveguide transitions could be adopted to improve the power capacity and reduce the insertion loss compared to SIW-microstrip transitions.

Absorption filters are often used to separate reflected EM waves from an input signal port to protect the port from signal overload, for example. The structure of an absorption filter (Fig. 1) can also be used in other applications. The two filters in Fig.1 are identical.

In principle, when an EM wave is applied to port I (Fig. 2), only output signals result at port III. Ports II and IV are isolated from port I. When signals are reflected by the filters, they are all collected at Port II (Fig. 3) while the input and reflection signals are isolated at Port I.

Atia and Williams⁹ first developed the coupling matrix synthesis methods of generalized Chebyshev filters for symmetric filter responses. Amari^10,11 developed gradient-based optimization methods to synthesize the coupling matrix of a generalized Chebyshev filter. The coupling matrix of the filter presented here was extracted by means of gradient-based methods. The third-order filter has a center frequency of 11900 MHz and return loss of 22 dB. The bandwidth is 220 MHz. A finite transmission zero is positioned at 11800 MHz. The coupling matrix and frequency responses are shown in Fig. 4. In some cases, negative coupling occurs for the coupling matrix. Rosenberg¹² proposed that the negative coupling could be accomplished by using the transformation properties of higher-order cavity modes (e.g., TE₁₀₂) with H-plane coupling windows.

The dimensions of the coupling windows were obtained by simulations according to the normalized coupling matrix shown in the matrix of Eq. 1. Note that the resonating frequencies are not the same because of asymmetric frequency responses. Computation equations for the coupling coefficients by simulation are given by Eq. 2¹³:

where:
f_0i = the resonating frequency of a resonator without coupling windows and
f_pi = the resonating frequency of a resonator with coupling windows, and i = 1, 2.

Simulation software was used to determine the initial dimensions of the filter, and the size of the SIW cavity was determined by the corresponding resonance frequency from ref. 14 for the TE₁₀₁ dominant mode:

where:
w_eff = the equivalent width of the SIW cavity and l_eff = the equivalent length of the SIW cavity. They are expressed by^15,16:

where:
w = the actual width of the SIW cavity,
l = the actual length of the SIW cavity,
d = the diameter of the metallic via holes,
p = the distance between adjacent metallic via holes,
c = the speed of light in free space,
m_r = the relative permeability of the substrate, and
e_r = the relative permittivity of the substrate.

For the TE₁₀₂ mode, the length of cavity is double of that of TE₁₀₁ mode. The equation (4) is also applied to determine the equivalent length and width of TE₁₀₂ mode cavities.

The absorption filter was designed by a combination of two identical filters and two identical 3-dB hybrid couplers. Figure 5 shows the frequency response of one of the 3-dB hybrid couplers. The return losses of port 1 and port 2 are better than 22 dB from 10.8 to 11.8 GHz.

Figure 6 shows the dimensions of one of the 3-dB hybrid couplers. An optimization procedure was needed for direct integration of the individual filters and hybrid couplers to achieve good performance.

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