1. This layout shows the architecture of the proposed SIW dualmode filter.

Bandpass filters with narrowband responses having low insertion loss, sharp selectivity, compact size, and low cost are needed for modern microwave and millimeter wave communication systems.^{1} When small size is important, dualmode filters are often used for their compact structures and low loss. Dualmode filters include cavity filters and microstrip filters. The mental cavity dual mode filters have excellent performance owing to their higher resonator quality factor (Q) and higher powerhanding capability. However, they can not be easily integrated with microwave planar circuits.^{2} Microstrip dualmode filters take advantage of flexible structures and feeding techniques, but this type of filter suffers from the problem of lower Q and limited powerhandling capacity. Fortunately, a practical alternative exists by applying substrateintegratedwaveguide (SIW) circuit techniques to the design of a dualmode filter.
An SIW is a type of dielectricfilled waveguide; it is synthesized in a planar dielectric substrate with linear arrays of metal cylinders, so as to realize bilateral edge walls using a standard printed circuit board (PCB) or other planar processes. SIWs provide a lowcost, lowprofile, and lightweight scheme while delivering high performance. References 35 report on several dualmode filters based on SIW technology. In ref. 3, a singlecavity novel dualmode SIW filter with nonresonating node (NRN) is presented. Reference 4 details a highperformance millimeterwave planar diplexer based on SIW dualmode filters with circular and elliptic cavities. Reference 5 describes an "extended doublet" bandpass filter using a SIW cavity with a complementary split ring resonator (CSRR) etched on its top mental plane.
2. This graphic shows the coupling scheme for the proposed SIW dualmode filter.

An SIW structure employs a greater amount of conductive metal than a microstrip circuit designed for a similar frequency and function, thus lending itself to lowerloss performance, especially at millimeterwave frequencies. Although planar SIW structures have typically been proposed for fabrication on soft substrate materials, such as those based on polytetrafluoroethylene (PTFE), the technology is also suitable for lowtemperaturecofiredceramic (LTCC) substrates, and has been used to create numerous highfrequency circuit functions, including cavities, couplers, and filters. An SIW structure provides many of the desirable properties of rectangular waveguide, including high quality factor (Q) and low loss, especially at millimeterwave frequencies. But it is also easier and less expensive to fabricate than rectangular waveguide and is more suitable for integration with other planar circuits. The majority of SIW structures have been fabricated as magneticplane (Hplane) circuits, although some work has been performed on electricplane (Eplane) circuits, including SIW couplers employing micostriptoSIW transitions.
The references show the characteristics of SIW dualmode filter from different aspects. In the current report, a novel compact dualmode filter using a right angle crossed slot is investigated. The dualmode filter is based on a square patch of PCB material using an SIW, which results in low insertion loss and rapid falloff characteristics. Two degenerate modes are achieved with a right angle crossed slot perturbation loaded at the diagonal line. The right angle crossed slot perturbation is introduced to create a transmission zero. The filter was simulated and fabricated, with a bandwidth of 385 MHz at a center frequency of 9.4 GHz. The measured results for the fabricated prototype match closely with the simulations.
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3. These simulated curves show the Sparameters for different values of p.

Figure 1 shows the basic configuration of the proposed SIW dualmode filter. The filter features an orthogonal input/output (I/O) feed line fabricated on a commercial substrate with height, h, of 0.508 mm and relative dielectric constant, εr, of 2.2. The width of the feed line was chosen to be 1.55 mm, which corresponds to the characteristic impedance of 50 Ω. A rightangle crossed slot is used to disturb two degenerate modes, TE201 and TE102. The slot lines between the SIW and the 50Ω microstrip transmission line act as the transition. The center frequency of the filter is determined by choosing the proper dimensions. After determining the two degraded modes of TEmon and TEr05, the resonant frequency can be estimated by Eq. 1:
where:
aeff = the effective width of the TEmon and TEr05 dualmode cavity,
leff = the effective length of the TEmon and TEr05 dualmode cavity1,
m,n,r,s = the modes,
c0 = the velocity of the electromagnetic wave in free space,
er = the permittivity of the substrate,
d = the diameter of the metallic via, and
s1 = the space between the cylinders.
4. These simulated curves show the Sparameters for different values of ws1.

Almost no leakage exists if s1 is equal to or smaller than twice d, which should be equal to or smaller than onetenth of the wavelength of the maximum frequency in the operating frequency band.
From Eq. 1, the initial dimension ratio of the dualmode SIW cavity can be determined, as shown by Eq. 2:
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5. The small size of the proposed filter is shown by this fabricated prototype.

For a square SIW cavity, the TE201 and TE102 modes resonate at the same frequency. Figure 2 shows the coupling scheme for the experimental filter fabricated in this report, where resonators 1 and 2 offer TE201 and TE102 modes, respectively. The coupling matrix of the proposed filter is represented by Eq. 3:
where:
Ms1 = the coupling between the source and resonant mode 1,
Ms2 = the coupling between the source and resonant mode 2,
M1L = the coupling between the load and resonant mode 1,
M2L = the coupling between the load and resonant mode 2,
M12 = the coupling between resonant modes 1 and 2,
M11 = the selfcoupling for resonant mode 1, and
M22 = the selfcoupling for resonant mode 2.6
The relations between the coupling coefficients and the dimensions of the filter are given in ref. 7. The locations of asymmetrical transmission zeros can be adjusted by parameter p. Figure 3 shows the simulated Sparameters of the filter with respect to different values of p. As p increases from 0.5 to 1.5 mm, the location of the transmission zero goes up from 10.052 to 10.223 GHz. It was found that the location of the transmission zero increased slightly as parameter p increases. It was also found that as p increases from 0.5 to 1.5 mm, the center frequency correspondingly increases from 9.445 to 9.6 GHz.
6. These traces show the simulated and measured Sparameters for the experimental filter.

To demonstrate the use of an SIW structure in a practical circuit, an SIW dualmodel filter with rightangle crossed slot was fabricated and characterized. The filter has dimensions of a = 15 mm, lfeed = 5 mm, w0 = 1.55 mm, l1 = 1.6 mm, w1 = 0.45 mm, s = 1 mm, d = 0.6 mm, ss = 13 mm, ws1 = 0.4 mm, and p = 0.5 mm. Figure 4 shows the simulated Sparameters for the filter design, with different values of ws1. As the value of ws1 increased from 0.2 to 0.6 mm, the center frequency increased from 9.36 to 9.48 GHz. It was discovered from the simulations that the location of the resonant frequency increased slightly as parameter ws1 increased.
To prove the validity of the proposed SIW filter structure, the dualmode design was fabricated on a commercial PCB material with permittivity of 2.2. Figure 5 shows a photograph of the fabricated filter, while Fig. 6 compares the simulated and measured Sparameters for the SIW filter. The fractal bandwidth of the proposed passband filter is 4.1% with a center frequency of 9.4 GHz. The measured minimum insertion loss is 2.3 dB. Transmission zeros are realized at 10.04 GHz. The measured results agree closely with the simulation results, save for a slight discrepancy concerning the resonant frequency. This might be due to dielectric losses, conductor losses, and transition losses between the SMA connectors and microstrip transmission line.
In summary, the SIW circuit technique yielded a dualmode filter with 4.1% fractal bandwidth and center frequency of 9.4 GHz, in close agreement with the computeraided simulations that were run prior to filter fabrication. Asymmetrical transmission zeros were created in this filter to improve the selectivity to some extent. The filter design is well suited for applications requiring lowcost fabrication and small size in the final filter.