*The performance of a broadband broad beam substrate integrated waveguide (SIW) cavity-backed microstrip antenna (CBMSA) is studied using the theory of characteristic modes (TCM). TCM provides insight into characteristic mode (CM) propagation in the SIW CBMSA, which helps formulate design guidelines for broad bandwidth performance. These guidelines are validated with the design of a 64-element S-Band antenna array. The array is fabricated, and the measurements agree closely with simulation. It demonstrates gain greater than 8 dBi, beamwidth greater than 90 degrees, bandwidth greater than 18 percent, cross-polarization less than -20 dB and efficiency greater than 90 percent. This compares favorably with results reported in the literature*.

TCM was first proposed by Garbacz.^{1,2} Harrington^{3} formulated it in a matrix form and applied it to scattering problems. It is shown that the CMs are orthogonal and usable as basis functions to represent the induced surface currents on any arbitrary perfect electric conductor (PEC) surface. An electric field integral equation was formulated, relating the surface currents to the tangential electric fields through a Green’s function operator assuming a lossless dielectric.^{3,4} Now, TCM is applied to numerous electromagnetic problems like antenna design,^{5-10 }antenna beam shaping,^{5} RCS reduction,^{11} antenna chassis design^{12} and antenna-platform interaction.^{5,13} Antenna bandwidth enhancement is also demonstrated successfully using TCM.^{6,7,14,15} CMs depend solely upon the shape and the size of an object and are independent of excitation. The feed decides the coupling between the modal excitation coefficients (MEC) and the CMs.^{5,6} Thus, TCM is useful in designing an antenna with desired characteristics.

Microstrip antennas (MSA) are desirable for the realization of phased array antennas for various applications such as 5G MIMO, phased array radar and direction of arrival (DoA) systems.^{7,16-18} The U-slot MSA (UMSA) has a broadband capability utilizing multiple resonances,^{14,15,19-21} and has demonstrated the broadest impedance bandwidth among the family of slotted MSAs.^{20} In MSA arrays, there is strong mutual coupling (MC) between adjacent structures due to surface wave (SW) propagation.^{17,22}

The CBMSA^{22,23} has a metallic cavity beneath the MSA that prohibits SW propagation, isolates nearby elements and reduces MC. Thus, it supports the use of a thicker microwave laminate for bandwidth enhancement.^{16,19} It also enables an overall size reduction: the radiating edge is less than λ_{g}/2, where λ_{g} is the guide wavelength.^{22} This increases the -3 dB beamwidth (HPBW) and the separation between nearby elements, assuming λ/2 inter-element separation. This, in turn, reduces MC and avoids the onset of grating lobes (GL).^{18} Thus, it helps to realize broadband and wide scanning phased array antennas.^{17,23} The CBMSA, however, is a complicated assembly requiring precise machining of cavities, making it difficult to integrate with multilayer circuit assemblies. The problem is aggravated in larger phased array antennas.

Wu^{24} introduced SIW technology, which emulates waveguide behavior in a printed form. SIW-based CBMSAs (SIW CBMSA) or slot antennas (SIW-CSA) have been demonstrated.^{25-35} SIW mimics a metallic cavity with an array of plated through holes (PTH). Thus, it eliminates the need for bulky metallic cavities and exhibits minimal radiation leakage. A broadband SIW CBMSA was proposed for 5G applications.^{25,43} A C-Band SIW-CSA with HPBW greater than 120 degrees and FBW of approximately 17.7 percent was demonstrated by Wen et al.^{26} A C-Band CBMSA with a mushroom-like EBG structure by Vilenskiy et al.^{27} demonstrated a FBW of approximately 12 percent and an 80-degree scan volume. Cai et al.^{28} demonstrated a multilayer SIW-CBSA operating from 18 to 30 GHz. A wide scan, probe-fed, X-Band SIW CBMPA has also been proposed.^{28,33} Chou et al.^{29} describe a SIW-CBSA PAA for DoA estimation. Current literature contains a comprehensive review of SIW antennas.^{30-35}

The design and optimization of SIW-CBMSAs, including probe location, is a time-consuming task using techniques like finite element method, finite difference time domain and method of moments.^{16} TCM, however, does not require probe inclusion^{7} and is computationally faster optimizing antenna performance, by providing information on various CMs propagating on the structure. This article describes a strategy for broadband and broad beam SIW CBMSA design using TCM. The CBMSA consists of a U-slot and an annular ring with a PTH array on a thick microwave laminate with low dielectric constant (ε_{r}) and dielectric loss (tanδ = td). The annular ring and UMSA have close resonances resulting in broad bandwidth.^{36,37} The PTH array creates a SIW cavity mitigating SWs, reducing MC and producing a wide scan volume. The antenna’s performance is evaluated in an active array environment. Simulations are compared with the measurements and prior literature.^{25,27,33,42,43}

**ANTENNA DESIGN**

The TCM based strategy for SIW CBMSA design with a coaxial probe feed consists of the following design steps (see **Figure 1**):

- Probe-fed MSA
- U-slot and integration with the MSA
- SIW CBMSA.

The design procedure uses analytical expressions,^{16} and the TCM module in Altair FEKO software.^{38 }The substrate is Rogers 5880 (ε_{r} = 2.2, td = 10^{-3}) with h ∼ 250 mils.

The design objective is an antenna element with broad bandwidth and broad beamwidth for wide scanning phased array applications, meeting the following specifications:

- Frequency of operation: S-Band
- FBW: 20 percent minimum with a center frequency = 3.3 GHz
- HPBW: greater than ±45 degrees
- Low MC and cross-polarization, i.e., less than -18 dB.

**Revisiting TCM**

CMs are the Eigenmodes forming a basis set for the induced surface currents scattered by PEC bodies.^{5-7} Thus, the radiation pattern is the linear combination of the respective orthogonal modal currents. The current distribution can be decomposed into mutually orthogonal characteristic currents. The surface currents, J, and scattered electric field, E^{s}, are related through an operator, L, as^{4}

Equation 1 can be re-written for the tangential field component as

In equation 2, the operator part is expressible in terms of impedance as

and

where Z is a complex impedance:

In Equation 5, R and X represent the resistive and reactive portions of the impedance. An eigenvalue (EV) equation is given as:^{4}

In Equation 6, μ_{n} are the EVs, and J_{n} are the eigenfunctions. Using Equations 5 and 6, 7 is obtained in a matrix form as:

In Equation 8, λ_{n} is referred to as the EV. Thus, λ_{n} = 0 represents the resonance condition, while λ_{n}< 0 or λ_{n}> 0 represent storage in the form of electric or magnetic energy, respectively. Another characteristic parameter is Modal Significance (MS), which is defined as

MS_{n}→1 represents resonance. Thus, the frequencies satisfying MS_{n }> 0.707, define the FBW of the structure. Another parameter, the characteristic angle (CA) α_{n}, defines the phase angle between the characteristic modal current and respective field and is given in Equation 10: