A New Technique for Broadband Matching of Open-Ended Rectangular Waveguide Radiator

Abstract

The maximum reflection at an open end of a standard rectangular waveguide is about −10 dB in its operating frequency range. It is often used without matching. For critical applications, it is desirable to further reduce the reflection coefficient. In this paper, a new technique is presented for the broadband impedance matching of an open-ended rectangular waveguide. The proposed technique employs three thin capacitive matching elements placed at proper intervals via a low-loss dielectric material. The capacitance of, and distance between, the matching elements are optimized for broadband impedance matching using a simulation tool. Based on the proposed technique, two design examples are presented for the matching of a WR75 waveguide radiator. A reflection coefficient of less than −16 dB and −20 dB has been achieved over a ratio bandwidth of 2.13:1 and 1.62:1, respectively.

1. Introduction

Since the first experiment in 1900 by Flemming [1] and the first scientific theory in 1938 [2], the rectangular waveguide open-end radiator, as one of the canonical radiating elements, has been used in a wide range of applications, including near-field antenna measurement [3,4,5,6,7,8,9], dielectric material characterization [10,11], electric field measurement [12,13], array antennas [14,15,16], electric field probe calibration [17], feeding a reflector antenna [18], non-destructive testing [19,20,21], imaging sensors [22] and the excitation of various radiating elements [23,24,25,26]. A comprehensive review of various open-ended waveguides has been presented in [27].

The aperture reflection of a rectangular waveguide open end strongly depends on the ratio of the narrow-wall height (b) to the broad-wall width (a) and weakly depends on the waveguide wall thickness (t). The smaller the b/a ratio, the larger the aperture reflection. In a standard rectangular waveguide ranging from the largest WR2300 (584.2 × 282.1 mm²; 0.32−0.49 GHz) to the smallest WR1(0.254 × 0.127 mm²; 750−1100 GHz), b/a and t/a range from 0.406 to 0.512 and from 0.0081 to 0.467, respectively. The maximum reflection is 0.313 (−10.1 dB) for b/a = 0.406 and 0.225 (−13.0 dB) for b/a = 0.512 [9].

The level of reflection in an unmatched open end of a rectangular waveguide might be acceptable in some applications. For other applications, it is desirable for an open-ended waveguide radiator to have a smaller reflection coefficient over a broad frequency range. With reduced aperture reflection, accuracy is improved in measurement applications and efficiency is increased in array antenna applications.

Broadband impedance matching of the open-ended rectangular waveguide (OEG) is of the highest importance in precision measurement applications, where it is a usual practice to use metrology-grade accessories and instruments. The OEG’s improved impedance matching would be beneficial in antenna near-field measurements, the precise generation and measurement of electromagnetic fields and material constants measurements using the free-space method. Improved matching in measurement applications reduces errors arising from imperfections in calibration.

In a large phased array employing open-ended waveguide radiating elements, impedance matching reduces the reflected power, which leads to a significant improvement in power efficiency and a resultant saving on the device’s cooling costs.

In the following, we will describe in some detail a need for better impedance matching of an OEG probe in the antenna near-field measurements. A commercial near-field waveguide probe by TTI Norte S.L. Co. uses a WR62 waveguide (15.80 × 7.90 mm²) open end [28]. The aperture walls are chamfered as shown in Figure 1a. An absorber collar is placed around the probe to reduce wave reflection and scattering from the probe fixture, as shown Figure 1b. The probe’s input VSWR at the coaxial port is shown in Figure 1c and ranges from 1.3 to 2.0, or the reflection coefficient from −17.7 dB to −9.5 dB with multiple maxima and minima caused by the reflection between the probe aperture and the coaxial-to-waveguide transition.

In near-field antenna measurements, it is important to reduce the wave reflection and scattering by the scanning probe in order to minimize the effects of multiple reflections between the probe and the antenna under test (AUT), which is complicated and difficult to calibrate out [29]. Reflection from the probe aperture caused by impedance mismatch is another contributor to the multiple-reflection effects.

The reflection coefficients of a probe and an AUT in antenna near-field measurements are accounted for in a power transfer equation via 1 − |Γ|², where Γ is the reflection coefficient. The reflection coefficient is entered into a classical formula for the probe’s boresight gain by Yaghijan [3], which reads

$$G_{02}=\frac{\pi k^{2}ab}{8{(1-|\mathsf{\Gamma }|)}^2\beta /k}{\left|\left[1+\frac{\beta }{k}+\mathsf{\Gamma }\left(1-\frac{\beta }{k}\right)\right]{\left(\frac{2}{\pi }\right)}^2+C_0\right|}^2$$

(1)

Note that the complex value of the reflection coefficient Γ is used in (1), not just the magnitude. The near-field probe typically operates in the recommended operating frequency range (1.5:1 bandwidth) of a standard rectangular waveguide. Therefore, it is desirable to reduce the reflection coefficient of a waveguide open end as much as possible over a bandwidth greater than 1.5:1.

In view of the problems discussed in the above, this paper presents a new technique for the broadband impedance matching of an open-ended rectangular waveguide. A thorough literature survey reveals that this is still an open problem. By broadband, we mean the recommended frequency range (1.5:1) of a standard rectangular waveguide and beyond. A comprehensive review of existing works on this issue is presented below.

A simple method for the impedance matching of an open-ended rectangular waveguide is to load the aperture with a dielectric plug. Ivanchenko and co-workers used a Teflon^® (dielectric constant ε_r = 2.04) plug in a WR90 waveguide aperture, with fourteen dielectric cylinders of ε_r = 3.8 embedded in the plug [30]. They obtained a reflection coefficient <−15 dB at 9.5−10.5 GHz (1.11:1 bandwidth). Zhang and co-workers used a dielectric slab (ε_r = 2.7, thickness t = 0.5 mm) inside a circular waveguide (diameter = 12 mm) and close to the aperture. The aperture was equipped with a slot and a choke that were employed for radiation pattern control. They reduced the reflection coefficient to −20 dB at 17.0−19.5 GHz (1.15:1 bandwidth) [31]. The unmatched reflection coefficient ranges from −11.5 to −7.5 dB in the same frequency band.

In a phased array application, it is necessary to obtain good impedance matching in a waveguide radiator operating over large scan angles. An inductive iris matching technique has been employed for this application [32,33]. Van Schaik used an inductive iris on a 35.0 × 11.4 mm² aperture with a polythene dielectric sheet (ε_r = 2.3, t = 5 mm) placed outside the waveguide at 5 mm distance from the aperture to obtain reflection <−10 dB at 5.4−5.9 GHz for scan angles up to 60° [32].

More recent studies on this topic have been concerned with the impedance matching of an evanescent waveguide aperture. Ludlow and Fusco placed a dielectric slab (ε_r = 6.15, t = 6.36 mm) at 0.7-mm in front of a 55.0 × 27.5 mm² waveguide (f_cTE10 = 2.73 GHz) aperture to obtain −10-dB reflection at 2.13−2.70 GHz [34]. Their radiator is more like a cavity antenna than a waveguide radiator. A coaxial probe is placed at 23 mm from a back short and at 24 mm from the aperture. The probe sets up an aperture field via proximity coupling, and the dielectric slab changes the aperture admittance so that aperture matching occurs below the waveguide cutoff. The method of placing a dielectric slab in front of an aperture has long been employed for wide-scan angle impedance matching in waveguide phased arrays [35].

Ludlow and co-workers presented an impedance matching method for an open-ended evanescent-mode rectangular waveguide, using a conducting post in the aperture which is coupled directly to a feeding coaxial probe [36], or via three conducting posts placed between a feeding probe and a conducting post in the aperture [37]. The aperture in [36] works at 4.43−4.57 GHz in a waveguide having a cutoff at 6.56 GHz. The aperture of [37] is realized in a waveguide with a cutoff at 2.72 GHz and has a reflection coefficient of less than −10 dB at 2.30−2.68 GHz.

Ludlow and co-workers presented the concept of distributed coupled resonators for the impedance matching of an evanescent-mode rectangular waveguide radiator [38]. An aperture containing a dielectric slab is excited by two dielectric plugs placed between a feeding coaxial probe and the dielectric slab in the aperture. The dielectric plugs and the waveguide section between them form two coupled resonators. They achieved a ratio bandwidth of 1.23 (2.00−2.45 GHz) for a reflection coefficient <−10 dB using a waveguide with a cutoff at 2.58 GHz.

Other impedance matching methods for a below-cutoff aperture include the use of a negative permeability material [39], an electromagnetic metamaterial [40,41,42,43], a radiator–filter combined structure [44,45,46,47]. Except for the radiator–filter combined structure, the input reflection coefficient is on the level of −10 dB, not −20 dB. These methods tend to yield a narrow-band matching.

A particular challenge in OEG impedance matching is to achieve a large matching bandwidth. In all of the previous studies, it has been difficult to obtain a good impedance matching over a large bandwidth, for example, over more than an octave bandwidth. In this paper, we present a technique for the broadband impedance matching of an open-ended rectangular waveguide radiator using capacitive elements. This is the first time that the capacitive matching technique has been applied to solve this problem. The novelty of the proposed technique is in using printed capacitive elements spaced by a low dielectric constant material for a simple, low-cost implementation of the broadband impedance matching of the rectangular waveguide open-end radiator. The following are the major contributions of this paper.

• OEG impedance matching over more than an octave bandwidth;
• Achieving −20 dB reflection in the standard waveguide band;
• OEG matching with a series of printed-circuit capacitive elements precisely placed inside a waveguide via a low-dielectric-constant material.

We will show the proposed technique using two design examples—a broadband design and a low-reflection design. The two examples have been obtained using a powerful modern electromagnetic simulation tool (CST Studio Suite^TM V2023). The authors believe that the simulation tool used in this paper is accurate enough to fully demonstrate the proposed technique. All the details—the structure, technique, simulation and dimensions—are provided, so that anyone can easily reproduce the result. In the next section, we will present the proposed technique and design examples based on it.

Firstly, the reflection coefficient of an empty OEG is analyzed. Secondly, the geometry of the proposed matching structure is presented, along with its equivalent circuit representation, followed by the analysis of the circuit property of the capacitive matching element. Thirdly, two design examples of the OEG matching using the proposed technique are presented. Finally, this study is compared with previous research, followed by conclusions.

2. Aperture Matching of the Rectangular Waveguide Open End

Figure 2a shows an open-ended WR75 waveguide with broad-wall width a = 19.05 mm, narrow-wall width b = 9.53 mm and wall thickness t = 1.27 mm. The cutoff frequency f_c and cutoff wavelength λ_c of the TE₁₀ mode in a rectangular waveguide filled with a material of dielectric constant ε_r are given by

$$f_c(\mathrm{GHz})=\frac{300}{2a\sqrt{{\epsilon }_r}};{\lambda }_c=\frac{2a}{\sqrt{{\epsilon }_r}}$$

(2)

where a is the broad-wall width in mm. In a WR75 waveguide with ε_r = 1, the fundamental TE₁₀ mode cutoff is at 7.87 GHz. Figure 2b shows the simulated aperture reflection coefficient Γ_A of a WR75 waveguide radiator. It decreases steadily from −10 dB at 8.17 GHz (≡ f₁ = 1.038 f_c) to −17.9 dB at 20 GHz (≡ f₂ = 2.54 f_c). Figure 2c shows the normalized aperture admittance y_A (= g_A + jb_A), whose real part g_A and imaginary part b_A range from 0.839 to 1.17 and from 0.253 to 0.587, respectively, at 8.17−20 GHz. The aperture has a positive susceptance b_A presenting a capacitive load to the waveguide. Chamfering the walls of the open end for scattering reduction changes the aperture admittance only slightly.

Figure 3a shows the proposed structure for the broadband matching of an open-ended rectangular waveguide radiator, whose equivalent circuit representation is shown in Figure 3b. The proposed technique utilizes three matching elements M₁, M₂ and M₃ of a shunt capacitive type. D₁ and D₂ are a dielectric material of low dielectric constant (ε_r) employed to support and to precisely position the matching elements M₁, M₂ and M₃. The same dielectric material D₃ fills the waveguide W. Without D₃, the level of impedance matching is reduced. Filling the space between the aperture and the first matching element M₁ with a dielectric material also reduces the level of impedance matching. The dielectric constant ε_r is small, so that a coaxial-to-waveguide transition can be designed using the same technique as that for an air-filled waveguide.

In Figure 3b, Y_A is the aperture admittance of the matching elements M₁ to M₃, Y₀ and Y_0d are the waveguide characteristic impedance, C₁ to C₃ are the capacitance, L₁ is the aperture-to-M₁ distance, L₂ and L₃ are the inter-element distance.

The matching elements are implemented in a thin horizontal metal strip symmetrically placed in the waveguide’s E plane. They can be constructed in a printed form on a film substrate [48] or on a thin reinforced PTFE laminate [49]. By optimizing the matching element’s capacitance and the distance between the matching elements, one can obtain a broadband impedance matching with a start frequency close to the TE₁₀ mode cutoff.

The mechanism behind the all-shunt-capacitive broadband matching of a waveguide aperture is not simple. The shunt capacitance, as well as the aperture admittance, is frequency-dependent. Thus, computer optimization is one of the efficient ways to find a desired solution for broadband matching.

Firstly, characteristics of the capacitive matching element are studied. Figure 4a shows a capacitive matching element placed inside a rectangular waveguide whose length is 2 L plus the matching element’s thickness. Figure 4b shows its equivalent circuit. When the matching element’s thickness is very small relative to the guided wavelength λ_g, it can be approximated as a purely shunt element. An E-plane-centered horizontal strip of zero thickness in a rectangular waveguide can be represented by a shunt capacitance as shown in Figure 4b. The normalized susceptance B/Y₀ obtained using the variational method is given by [50]

$$\frac{B}{Y_0}=4t\left[-\ln (\cos p)+\frac{Q^2{\sin }^{4}p}{1+Q^2{\cos }^{4}p}+{\left(\frac{t}{4}\right)}^2{\left(1-3{\cos }^{2}p\right)}^2{\sin }^{4}p\right]$$

(3)

$$p=\frac{\pi H}{2b};t=\frac{b}{{\lambda }_g};{\lambda }_g=\frac{\lambda }{\sqrt{1-{[\lambda /(2a)]}^2}};Q=\frac{1}{\sqrt{1-{(b/{\lambda }_g)}^2}}-1$$

(4)

where B is the un-normalized shunt susceptance, Y₀ is the characteristic admittance in the equivalent circuit representation of the waveguide, H is the strip height, b is the waveguide narrow-wall height, λ_g is the guided wavelength, λ is the wavelength in vacuum and a is the waveguide broad-wall width.

We calculate the scattering parameters S_11′ (=S_22′) and S_21′ (=S_12′) of the structure of Figure 4a and then move the port reference plane to the surface of the matching element to obtain the de-embedded scattering parameters S_ij, i.e.,

$$S_{ij}=S_{ij}{}^{\prime }\exp \left(j\frac{4\pi }{{\lambda }_g}L\right)(i,j=1,2)$$

(5)

where λ_g is the guided wavelength given in Equation (4). From the de-embedded scattering parameters, we calculate the normalized susceptance B/Y₀ of the capacitive element. The reflection coefficient S₁₁ at the relocated reference plane of Port 1 shown in Figure 4b is now given by

$$S_{11}=-\frac{j{b}_c}{2+j{b}_c};j{b}_c=\frac{jB}{Y_0}$$

(6)

since Port 2 is matched when calculating the scattering parameters. In Equation (6), Y₀ is the equivalent characteristic impedance of the TE₁₀-mode wave. Note that there is no need to explicitly calculate Y₀, since b_c can be obtained from S₁₁. For the capacitance calculation, however, the value of Y₀ is required. The un-normalized susceptance B is calculated using Equation (6) and the capacitance C at frequency f is now given by the following equation.

$$C=\frac{B}{2\pi f}$$

(7)

The computed capacitance will be frequency-dependent [50]. In the proposed technique, it is not necessary to calculate the capacitance of the matching elements. Figure 5 shows the loci at 8−16 GHz of the simulated reflection coefficient S₁₁ (shown in Figure 4b) of a matched load in parallel with a capacitive matching element (with width a, height H) printed on a film substrate Parylux^® TAHS124500 by DuPont^TM [48] (substrate: ε_r = 3.4, tanδ = 0.0045 at 10 GHz, h = 0.0045 mm; strip: copper, t = 0.0012) for H/b ratios 0.2, 0.4, 0.6 and 0.8.

One can identify the normalized susceptance b_c of the capacitive element directly from the admittance Smith chart in Figure 5.

Table 1. Range of the normalized admittance B/Y₀ of the capacitive element at 8−16 GHz.

H/b	Min (B/Y0)	Max (B/Y0)
0.2	0.082	0.162
0.4	0.151	0.517
0.6	0.282	1.214
0.8	0.593	2.651

shows the range of the normalized susceptance b_c versus the H/b ratio at 8−16 GHz. The range of susceptance values is large enough to cover the aperture susceptance shown in Figure 1c of the WR75 waveguide open-end radiator. We have not used the theoretical Equation (3) to verify the susceptance of the capacitive strip, since our design is not based on the theory but on the computer simulation. A capacitive element in a dielectric-filled waveguide behaves in a similar way and can be analyzed using the same method as described above.

Figure 6 shows the dimensional parameters of the proposed matching structure, whose meanings are explained in

Table 2. Meaning of the dimensional parameters in the proposed impedance matching structure.

Parameter	Meaning
a, b, t	Waveguide broad-wall width, narrow-wall height and wall thickness
εr	Dielectric constant of the material supporting the matching elements and filling the waveguide
H1, H2, H3	Strip width of the capacitive matching elements M1, M2 and M3, respectively
L1	Distance between the matching element M1 and the waveguide aperture
L2, L3	Distances between the matching elements M1 and M2, M2 and M3, respectively
P0	Plane of the aperture
P1, P2, P3	Plane right after the matching elements M1, M2 and M3, respectively

. The proposed impedance matching structure can be optimized for |S₁₁| < −20 dB over the recommended operating frequency range of a standard rectangular waveguide (b = a/2), which we call a ‘Standard-Band Design’. Alternatively, a matching structure can be designed for the widest possible bandwidth over which |S₁₁| is less than, for example, −16 dB, which we call a ‘Broadband Design’. In Figure 6, P₀ to P₃ refer to the reference planes to be used in the progressive impedance matching analysis.

Before optimization via a simulation tool, we carried out a series of parametric analyses on the reflection coefficient of the ‘Broadband Design’ of an impedance-matched WR75 waveguide radiator. The results are shown in Figure 7. The dielectric constant ε_r supporting the capacitive elements is 1.13 in the ‘Broadband Design’, so that the TE₁₀-mode cutoff is at 7.40. The reflection coefficient rises above −10 dB from 16.74 GHz onwards.

In a WR75 waveguide filled with a material of ε_r = 1.13, the first six TE modes in order of increasing cutoff frequency f_c are TE₁₀, TE₂₀, TE₀₁, TE₁₁, TE₂₁ and TE₃₀, with f_c of 7.40, 14.80, 14.80, 16.55, 20.94 and 22.21 GHz, respectively. Of these modes, the TE₂₀, TE₀₁ and TE₂₁ modes can be suppressed by using structures that are symmetric in the H-plane of the waveguide. The TE₁₁ and TE₃₀ modes, however, can be excited along with the fundamental TE₁₀ mode. Therefore, the waveguide’s operating frequency will be greater than the TE₁₀-mode cutoff (7.40 GHz) and less than the TE₁₁-mode cutoff (16.55 GHz), resulting in a ratio bandwidth of 2.24 (16.55/7.40). In Figure 7, the frequency range of the analysis is set from 6 GHz to 18 GHz.

In Figure 7, we note that the matching element heights H₁, H₂, H₃ and distances L₁, L₂, L₃ between the matching elements have a sensitive effect on the reflection coefficient. The final ‘Broadband Design’ is obtained with an optimum combination of all of these parameters.

Next, an automatic optimization process is employed to find optimum values of H₁, H₂, H₃, L₁, L₂, L₃ and ε_r. The CST Studio Suite^TM 2023 offers a set of built-in optimization algorithms, among which, the “Trust Region Framework” has been used in this study. The ranges of frequency and parameter values in the optimization have been obtained from the parametric analysis carried out in the previous step.

Figure 8 shows the reflection coefficient variation during an optimization of the ‘Broadband Design’. The curve in red is the reflection coefficient of the final design of the impedance-matched WR75 waveguide radiator, while the curves in gray are intermediate reflection coefficients. As will be shown later in the ‘Standard-Band Design’, one can find an optimum design for a specific frequency range over which the reflection coefficient is less than a specified value. With a given number of the matching elements, the bandwidth will be smaller for a smaller reflection coefficient.

Following the aforementioned procedures, we obtained a second design example—the ‘Broadband Design’ whose dimensions are listed in

Table 3. Dimensions (mm) of the proposed impedance matching structure.

Design	εr	H1	H2	H3	L1	L2	L3	Substrate
Broadband	1.13	3.81	3.41	2.12	6.75	6.14	6.49	εr = 3.4, tanδ = 0.0045, h = 0.045, t = 0.012
Standard Band	1.03	3.92	4.12	1.01	5.75	4.14	4.90	εr = 3.45, tanδ = 0.0031, h = 0.51, t = 0.018

. In Table 3, h is the substrate thickness and t is the metal-trace thickness of the capacitive matching elements.

Figure 9a shows the structure of the ‘Broadband Design’, and Figure 9b compares the reflection coefficients of an unmatched radiator and the ‘Broadband Design’. In the unmatched case, the reflection coefficient ranges from −10.0 dB at 8.17 GHz to −18.0 dB at 20 GHz. In the ‘Broadband Design’, the reflection coefficient is less than −16.0 dB at 7.53−16.01 GHz (ratio bandwidth 2.13:1). Filling the waveguide with a material of ε_r = 1.13 lowers the cutoff frequency from 7.87 GHz of the air-filled WR75 waveguide to 7.40 GHz.

To see the mechanism of the capacitive matching, the complex reflection coefficient of the ‘Broadband Design’ is calculated at 7.53−16.01 GHz in the aperture (on the plane P₀ in Figure 6) and just after each matching element M₁, M₂ and M₃ (planes P₁, P₂ and P₃ in Figure 6, respectively) and is shown in Figure 10. We observe that the range of variation in the reflection coefficient magnitude is progressively reduced after each matching element. Figure 11 shows the change in the reflection coefficient magnitude in dB with the addition of each matching element. The reduction in the reflection coefficient magnitude is not monotonic.

Following the same procedures, we obtained a ‘Standard-Band Design’ shown in Figure 12a. The reflection coefficient is shown in Figure 12b. The frequency range of optimization is set from 10 GHz to 15 GHz, which is the recommended operating frequency range of the WR75 waveguide. The target reflection coefficient is set at −20 dB. The smaller reflection coefficient can be set as a target if the required bandwidth is smaller.

Table 3 lists the dimensions of the ‘Standard-Band Design’ also. The matching elements are implemented on I-Tera MT40^® substrate by Isola Group (substrate: ε_r = 3.45, tanδ = 0.0031 @ 10 GHz, h = 0.51 mm; strip: copper, t = 0.0018) [49]. In the ‘Standard-Band Design’, the reflection coefficient is less than −20 dB at 9.89–15.99 GHz (1.62:1 bandwidth). Figure 13a shows the complex reflection coefficient loci and Figure 13b the reflection coefficient magnitude at planes P₀ to P_3, with the frequency from 9.89 GHz to 15.99 GHz. In Figure 13b, we observe that the magnitude of the reflection coefficient even increases before the addition of the final matching element M₃. After the final matching element, the reflection coefficient is significantly reduced.

In

Table 4. Comparison with previous studies.

Work	Type	Frequency Range f1−f2 (GHz)	Reflection (dB)	Ratio Bandwidth f2/f1	Complexity
[30]	Dielectric plug	9.5–10.5	−15	1.11	Low
[32]	Inductive iris	5.4–5.9	−10	1.09	Low
[34]	Dielectric slab	2.13–2.70	−10	1.27	Low
[37]	Multiple conducting posts	2.30–2.68	−10	1.17	Medium
[38]	Distributed coupled resonators	2.00−2.45	−10	1.23	Medium
This Work	Printed capacitive elements	9.89−15.99	−20	1.62	Medium
		7.53–16.01	−16	2.13

, our design is compared with previous studies. As can be seen in Table 4, the new impedance matching technique proposed in this paper delivers a 1.62:1 bandwidth (9.89−15.99 GHz), with reflection <−20 dB comfortably covering the recommended operating frequency range (10−15 GHz) of the WR75 rectangular waveguide. This enables a realization of a near-field measurement probe with improved characteristics. With reflection <−16 dB, the achieved bandwidth is 2.13:1 (7.53−16.01 GHz), offering more than an octave bandwidth which can be useful for wideband/multi-band RF applications and materials measurements.

3. Conclusions

This paper proposes, for the first time in a published work, a capacitive impedance matching technique for an open-ended rectangular waveguide radiator. The proposed technique uses a three-section capacitive matching circuit of a shunt type. For easy implementation, the capacitive elements are printed on a film or on a laminated substrate, which are supported and precisely positioned by a low-loss dielectric material. The capacitance of the matching elements is frequency-dependent, and computer-based optimization has been employed to achieve a broadband matching. For improved matching performance, it is necessary to fill the space between the aperture and the first matching element with air, and to fill the space between the matching elements and the waveguide interior with a low-dielectric-constant material. Two design examples based on the proposed method show that an open-ended rectangular waveguide radiator can be matched with a 2.13:1 bandwidth for a reflection coefficient <−16 dB and with a 1.62:1 bandwidth for a reflection coefficient <−20 dB, which is more than enough to cover the recommended operating frequency range of a standard rectangular waveguide. Areas of further improvements in the proposed technique are (1) achieving a reflection coefficient <−20 dB with a ratio bandwidth greater than 2:1 and (2) reducing the reflection coefficient to less than −30 dB in the operating frequency range of a standard rectangular waveguide. Nonetheless, considering the wide-ranging applications of the open-ended rectangular waveguide radiator, we expect that the proposed technique will significantly contribute to the art of the related engineering disciplines.