Dual Mode Broadband Hybrids: Theory and Experiment

Technical Feature

Dual Mode Broadband Hybrids: Theory and Experiment

Alex D. Lapidus
Microwave Communications Company International Inc.
Valencia, CA

A theoretical approach to both side and top wall (hybrid) couplers based on strong experimental work is developed. Broadband operation, related to dual mode propagation through the coupling section, is established. The experimental data demonstrate an operating bandwidth greater than 20 percent with an amplitude imbalance less than 0.6 dB. The means of control and optimization over the major parameters of the hybrid coupler such as amplitude and phase balance, return losses and isolation are presented.

The Basic Theory of Operation

The coupling section of either side or top wall hybrid couplers allows a simultaneous propagation of two independent modes TE₁₀ and TE₂₀ for the side and TE₁₀ and TEM for the top wall hybrid couplers. Generally speaking, it offers an opportunity for an arbitrary power split at the output ports while keeping two input ports isolated. Since the major use of the hybrid device is a 90° (quadrature), 3 dB signal division at the outputs, the formation of this type of response and the necessary conditions to be held in order to meet these requirements will be discussed.

The operation of the side wall couplers (Riblet short-slot coupler) has been described in previous literature.^1-5 Figure 1 shows the electric field distribution inside the side wall hybrid coupling section. The TE₁₀ mode launched in port 1 results in both TE₁₀ and TE₂₀ mode propagation inside the coupling section.^2,5 The negative electric field part of the TE₂₀ mode nulls a part of the TE₁₀ mode at port 2 providing port-to-port isolation. To understand the output power and phase split formation, an even- and odd-mode approach can be applied.⁵ Consider two coherent signals of one-half amplitude and in-phase are applied to ports 1 and 2. An E-field maximum occurs at the center plane of the coupling section, which can be replaced with a magnetic wall. This is denoted as an even-mode and associated with a TE₁₀ wave in that section. Now suppose that two coherent signals of one-half amplitude and out of phase are applied to ports 1 and 2. An E-field null occurs at the center plane that, in this case, can be replaced with an electric wall. This is denoted as an odd-mode and associated with a TE₂₀ wave formed in the coupling section. Figure 2 illustrates the combined signal formation along the coupling section. At the very beginning of the coupling section, the even- and odd-modes cancel each other at port 2 and add to each other at port 1. At an arbitrary point in the coupling section, the even-mode (TE₁₀ ) gains greater phase than the odd-mode (TE₂₀ ). The total signal of the right side (ports 1 to 4) is greater than the total signal of the left side (ports 2 to 3), and is 90° behind. At the end point of the coupling section the even- and odd-modes each have gained a sufficient phase to result in a 90° phase difference between them. The output at ports 3 and 4 allocated in this spot couple out an equal amount of power (3 dB split) with port 3 output signal (coupled) 90° ahead of port 4. It should be noted that an equal power division maintained between even and odd (TE₁₀ /TE₂₀ ) modes not only provides a maximum input port (1-2) isolation, but also assures a 90° output port (3-4) phase shift upon an arbitrary coupling opening length.

A top wall hybrid junction has the same function and application as a side wall, yet is slightly more compact and broader band.⁶

The electric field distribution inside the top wall hybrid coupling section is shown in Figure 3 . The TE₁₀ fundamental waveguide mode applied to port 1 results in both TE₁₀ and TEM modes propagating through the coupling section. The electric field of the suspended stripline inside the coupling section (TEM) is concentrated mainly above and below the line, so it nulls part of TE₁₀ in the proximity of port 2, providing the necessary isolation. Figure 4 illustrates all stages of the combined signal formation at the areas above and below the stripline. The argument in the case of the side wall hybrid is also valid here, with the only difference being that the output signal at port 4 is 90° ahead of port 3 (coupled).

Broadband Operation

Broadband operation of the 3 dB dual mode hybrid coupler implies an equal input signal split between two propagating modes as well as near 90° phase difference between modes maintained at the end of the coupling section over wide frequency range. It also requires a phase slope (df/df) equalization for both modes across the band.

As previously mentioned, the TE₂₀ mode of the side wall hybrid coupler originates inside and propagates through the coupling section converting back to the fundamental TE₁₀ mode as if the coupling section was partitioned by an electric wall. At the same time, the TE₁₀ mode is experiencing double waveguide width discontinuities passing through the coupling section that imposes a resonant type response to this mode. The phase response can be written as

where

first term = phase gained over coupling section electrical length
second term = resonance related phase shift
x = l_10r /l₁₀ - l₁₀ /l_10r is a waveguide resonator variable expressed in terms of wavelength

l_10r = TE₁₀ mode wavelength inside the coupling section

Expressed in term of frequency, Equation 1 can be written as

where

l_10r » (1.05-1.1)l = TE₁₀ resonance wavelength
l = coupling section length (the resonator is said to employ a full length waveguide cavity formed by the input and output inductive susceptances)
f_10co = TE₁₀ cut-off frequency in the coupling section
c = free space speed of light

Analogously, the phase response of the TE₂₀ mode is found as

The theoretical phase responses for the coupling section of specified dimensions are presented in Figure 5 . Because of the resonant condition imposed, the TE₁₀ mode phase remains quasi-linear yet gains an increased slope (df/df), making it approach the TE₂₀ phase response. Two 90° phase difference points (they will later be defined as cross-over points of ideal 3 dB power split) occur at approximately 18 and 21 GHz, which determines the hybrid coupler operational bandwidth. The phase difference between the two cross-over points is slightly less than 90° (about 88°), which results in a minimal pass band imbalance. The actual coupling value at port 3 can be found from S₃₁ (dB) = 20 log (sin W/2), where W is the phase difference between the two modes.⁵ It should be noted that the loaded Q_e of the TE₁₀ mode resonator formed by the coupling section structure is rather low (»1.2), which provides a flat amplitude response over the operational band or, in other words, does not affect an equal power split, the importance of which was stressed above.

Dual mode propagation in the top wall hybrid coupler is similar to the side wall configuration, except for the fact that the fundamental TE₁₀ mode experiences no noticeable resonant impact, while the excited TEM mode is resonating inside the coupling structure. The phase response of both modes can be determined as

where

f_10co = TE₁₀ cut-off frequency in the coupling structure

Based on Equations 4 and 5, the phase vs. frequency curves are very similar to those of the side wall coupler, except that the TE₁₀ mode is represented by the upper and the TEM mode by the lower graphs with two 90° difference points of ideal 3 dB split, which theoretically proves that broadband operation of the top wall coupler is feasible. It was found that the TEM resonant wavelength is approximately 0.94 to 0.95 the coupling section length (full length resonator with capacitive input/output susceptances) and the loaded Q_e is approximately 1.8.

Experimental Results

A number of units for the waveguide bands WR-28, 42, 51 and 75 were developed and tested. Figure 6 shows typical side and top wall couplers used for prototyping. Figure 7 shows a WR-75 side wall hybrid amplitude balance and return loss response. The two points of equal power split (signal paths of ports 1-4 and 1-3), which determine the operational bandwidth and maximum imbalance, are called cross-over points. The location of the cross-over points and the frequency gap separating them are adjustable by slight changes of length and width of the coupling section. The operational bandwidth is usually determined by the return loss and maximum imbalance limitation, and is related to the quasi-resonant type of reflection response of the TE₁₀ mode and is achievable for up to 20 to 22 percent by widening the distance between the cross-over points. The maximum imbalance in this case is approximately 0.6 to 0.7 dB and the return loss is better than 20 dB. Experimental adjustment of the hybrid is necessary to optimize the cross-over point locations as well as the return loss in the operational band. For example, a slight shrinking of the coupling section reduces the minimum phase difference between two modes located inside the operational band. At the same time, the two 90° points for the ideal 3 dB split are moving away from each other, broadening the band at a certain expense of amplitude balance in the center. Further shortening results in a more significant port 3 coupling value reduction in the frequency range between the two cross-over points. Lengthening of the coupling section causes a reverse effect and eventually results in greater power coupled out from port 3 than port 4. Since the coupling section width sets a cut-off frequency, its adjustment specifically affects the TE₂₀ and TE₁₀ modes wavelength of the side and top wall hybrid couplers, respectively, and has a similar effect on the cross-over point locations and operational band correction. Figure 8 shows the same WR-75 side wall hybrid with adjusted cross-over point locations. The width of the side wall hybrid is narrower than double the waveguide in order to provide higher mode (TE₃₀ ) free operation. A tuning screw of about 1/3 the junction width diameter, having a radial bottom and placed in the exact center of the side wall hybrid junction, is an efficient tool for fine balance and return loss adjustments. When introduced deeper inside the unit, it is increasing the current path for the TE10 mode that is equivalent to a slight lengthening of the coupling section and results in the same narrowing of the frequency gap between the two cross-over points. Visually, it looks like it pushes down the amplitude response of the straight signal path between ports 1 and 4 and brings up that of the coupled path of ports 1 to 3. It was found that the electrical lengths of both the TE₂₀ and TE₁₀ paths in the side wall hybrid junction, at the first and second cross-over point frequencies, computed as a function of junction length and width only, are approximately 180°/270° and 270°/340°. The tuning screw contributes to the TE10 current path and makes the actual electrical length at the second cross-over point around 360°. The TE₁₀ resonant frequency is slightly below the second cross-over point.

Not related to amplitude balance, a separate adjustment of all above mentioned means may be necessary for an experimental return loss optimization. The feeding waveguide bends contribute to the overall mismatch, so trimming of either side walls or the partition between two waveguides and tuning screw adjusting, all affect the coupling opening resonant frequency, and may significantly compensate the input and output mismatch and result in the performance shown previously. In any case, in order to achieve a return loss greater than 26 dB over a relatively wide band covering at least the frequencies falling between the two cross-over points, the input and output waveguide bends by themselves should be optimized with respect to available space. An experimental development of the high performance side wall hybrid is based on the simultaneous use of all three mutually complementing tuning tools. The finite thickness of the partition separating the input and output waveguides of the side wall hybrid coupler contributes to the higher mode excitation at the edges of the coupling opening. Thinning of the partition would improve both return loss and isolation. A reasonable thickness should be at least less than 20 times the coupling section width.

Figure 9 demonstrates the amplitude balance and return loss performance of a WR-42 top wall hybrid. The advantage of its performance over the side wall hybrid is that an operating band of 35 to 37 percent is achievable (see return loss response) with a 1 to 1.2 dB amplitude imbalance degradation. The fact that the fundamental TE10 mode propagates through the coupling section with no resonance contributes to the broad return loss response. Considering the coupling section as a waveguide discontinuity, the excitation of a quasi-resonant TEM mode affects the average return loss over the band, making its adjustment more complicated. The length and width of the coupling section has a similar impact on the amplitude imbalance and cross-over point locations as the side wall hybrid, so the described adjustment technique is also justified. Since no tuning screw can be used for fine balance tuning or return loss adjustment, the prototyping had to be made using a split block unit with a replaceable slotted septum between the two sections. The coupling section cross dimension should provide a TE₁₁ mode free propagation. Consequently, its height should be smaller than twice the waveguide width. It was found that the TE₁₁ mode propagation starts at a frequency roughly 2 GHz higher than computed for the plain waveguide so the height of the coupling section can be adjusted to keep the theoretical f_coTE11 just slightly above the pass band. The stripline formed by the two symmetrically cut slots prevent TH₁₁ mode propagation. In order to improve the return loss, both standard waveguides, one on top of the other, should gradually transition to the quasi-square coupling section. A slight change of the length of the slots has a similar effect as the side wall hybrid, but it was observed that shorter slots improve the return loss of the top wall hybrid. A slight reduction of the length of the slots along with a narrowing of the coupling section width may result in less than 0.5 dB imbalance and a 18 to 20 dB return loss over a wide operating band. A reduction of the stripline thickness minimizes the lateral part of the TEM electric field density, which also improves the overall return loss and isolation. Nevertheless, a reasonable thickness should be at least ten times smaller than the coupling section height and five times smaller than the stripline width. Tapering the ends of the slots may further improve the return loss of the top wall hybrid.⁶

A moderate band return loss optimization (better than 26 dB) is possible by adjusting the coupling sections dimensions as well as optimizing the waveguide length input and output bends and the coupling section.

A stripline of 43 to 47 percent of the coupling section width provides a necessary 3 dB input signal split between two modes.

As was mentioned in the basic theory of operation, an equivalent input signal split between the two modes results in a perfect 90° phase difference at the outputs as well as greater channel-to-channel isolation. The actual isolation is very much a function of reflections. The prototypes developed showed broadband phase balance held within ±1°. A typical channel-to-channel isolation for a side wall hybrid coupler and its return loss are shown in Figure 10 .

Conclusion

A successful design of either side or top wall broadband hybrid junctions implies that four major electrical parameters such as equal power split, 90° phase difference, input and output return loss and channel-to-channel isolation are to be met over a given frequency range. A key factor for a broad operating band is the resonant condition the junction by itself imposes to either TE₁₀ or TEM modes by increasing their phase slopes, which results in the formation of two cross-over points for an ideal power split and quasi-flat coupling response. An experimental adjustment of the hybrid junction is necessary to locate the cross-over points at the frequency edges of the specified band.

References
1. H.J. Riblet, "The Short-slot Hybrid Junction," Proceedings of the I.R.E. , Vol. 40, February 1952, pp. 180-184.
2. David M. Pozar, Microwave Engineering , Addison-Wesley Publishing, 1993.
3. Ferril Lossee, RF Systems, Components and Circuits Handbook , Artech House Inc., Norwood, MA, September 1997.
4. Scott B. Durgin, "Ghost Cancellation in TV Switchless Combiner Systems," Passive Power Products, Technical Publications , October 27, 1997.
5. Louis W. Hendrick and Ralph Levy, "Design of Waveguide Narrow-wall Short-slot Couplers," IEEE Transactions on Microwave Theory and Techniques , Vol. 48, No. 10, October 2000.
6. Eugene Hadge, "Compact Top Wall Hybrid Junction," IRE Transactions on Microwave Theory and Techniques , Vol. MTT-1, No. 1, March 1953.

Alex D. Lapidus received his BS and MS degrees in electrical engineering from the University of Technology, Nizhny Novgorod, Russia. He has more than 20 years experience in the design and development of microwave/millimeter-wave components and subsystems. In 1991 he moved to the United States, where he joined the UCLA High Frequency Electronics Group and participated in the development of mm-wave radars and measuring techniques for plasma diagnostics. Since April 1995 he has been employed by Microwave Communications Company International Inc., where he is involved in the design and development of various filtering systems and passive microwave components. He currently holds the position of chief engineer. He has a published extensively in the field of mw/mm-wave components