Waveguide Quadrature Hybrids for ALMA Receivers

This memo describes the design of a set of waveguide quadrature hybrids suitable for use in balanced and sideband-separating mixers, balanced amplifiers, and power combiners and dividers. The hybrids are of the branchline type, which can be machined in a split block configuration on a CNC milling machine. The prototype designs are for the WR-10 band (75–110 GHz), but the dimensions are chosen to allow scaling to any waveguide band up to ~700 GHz. The designs were optimized using a space mapping procedure, with a fast but approximate microwave circuit simulator (MMICAD) and a slower but accurate FDTD EM simulator (QuickWave). Introduction and Goals Quadrature hybrids are used in balanced mixers and amplifiers, sideband-separating mixers, and power dividers and combiners. In developing receivers for ALMA, waveguide quadrature hybrids have been proposed for power combining in the first LO system [1], and for a balanced sideband-separating SIS mixer [2]. The latter requires three RF quadrature hybrids, one for sideband separation and one for each of the component balanced mixers. A quadrature hybrid is a four-port directional coupler. In the ideal case, power incident on any port is divided equally between two other ports with a 90 phase difference, and the fourth port is isolated. The waveguide form of quadrature hybrid consists of two parallel waveguides coupled through a series of apertures or branch waveguides. The latter is commonly called a branch-line coupler and is the choice for the present design because of its ease of construction as a split block and the possibility of combining multiple hybrids in a single split block structure as proposed in [2]. In an E-plane branch-line coupler, the branch guides are between the broad walls of the main waveguides so there is a plane of symmetry through the centers of the broad walls of all the waveguides. As no currents flow across this plane of symmetry, a coupler may be split in this plane without concern that imperfect contact between the two halves might affect the performance of the circuit. The amplitude and phase imbalance at the outputs of a quadrature hybrid affect the LO noise rejection of a balanced mixer and the image rejection of a sideband-separating mixer. Fig. 1 shows contours of constant image rejection (or LO noise rejection) on the amplitude imbalance vs. phase imbalance plane. The goal of the present work was to develop two waveguide quadrature hybrids, one with amplitude imbalance 1 dB and phase imbalance 1 , and the other with amplitude imbalance 0.5 dB and phase imbalance 1 . These designs should cover as much as possible of the full waveguide band (fmax/fmin 1.5) and should have dimensions suitable for fabrication on a CNC machine, even when scaled as high in frequency as ALMA Band 9 (602-720 GHz). Analysis and Optimization A WR-10 waveguide branch-line hybrid with six branches is shown in Fig. 2(a). The lengths of the branch guides and their spacings are approximately quarter of a guide wavelength at the center frequency of operation. The number of branches, the heights and lengths of the branches, and the heights and lengths of the main waveguide sections between the branches, are parameters which can be varied in optimizing the electrical performance. In the -2present design, the heights of the waveguide sections are restricted, as described in the next section, to facilitate machining hybrids scaled for operation in the higher frequency bands. Initially, the hybrid was modeled as a number of E-plane T-junctions, interconnected by waveguides as shown in Fig. 2(b), and analyzed using the microwave circuit simulator MMICAD [3]. An equivalent circuit of an E-plane T-junction, given by Marcuvitz [4], is shown in Fig. 2(c). MMICAD allows a fast optimization of the approximate equivalent circuit of the hybrid. This circuit model does not take into account the weak coupling of evanescent modes between adjacent T-junctions, which leads to a small but significant error when the T-junctions are interconnected by short waveguide sections as in the present work. The finite-difference time-domain (FDTD) EM simulator QuickWave [5] allows an accurate but slower analysis of the hybrid, including the effects of all modes, propagating and evanescent. To verify the accuracy of the QuickWave analysis, the WR-10 hybrid shown in Fig. 2 was fabricated and measured on a vector network analyzer. Figure 3 shows the measured and simulated results. Note that the measured S21 and S31 have lower amplitudes than predicted by QuickWave; this is because of waveguide loss in the actual hybrid which was not taken into account in the FDTD analysis. However, the amplitude and phase imbalance curves agree well with the measurements, verifying the accuracy of the software. The QuickWave analysis is well converged after 6,000 iterations and takes about 22 minutes on a 933-MHz Pentium III computer when using 4-port excitation. Figure 4 shows the results (a) from MMICAD and (b) from QuickWave for the six-branch WR-10 hybrid of Fig. 2(a). The amplitude and phase imbalance are shown in Fig. 4(c). It is clear that the circuit model is not accurate enough for the present work. To optimize the design of the hybrids, the advantages of the accurate but slow EM simulator (QuickWave) can be combined with those of the fast but approximate circuit simulator (MMICAD) with its powerful optimizer through the space mapping technique [6,7]. To use space mapping, the circuit model and the physical structure must have the same variables — e.g., waveguide lengths and heights. The relationship between the parameter spaces of the circuit model and the physical structure is then determined. The fast circuit optimizer can then be used to predict the parameters of an optimum physical structure. In the present hybrid design, it takes 2-4 space mapping iterations to reach an acceptable result. Design To meet the requirement that the waveguide hybrids be suitable for fabrication by CNC machine when scaled as high in frequency as ALMA Band 9 (602-720 GHz), the height of the main waveguide sections was fixed at the full height (b = a/2), and the height of the branch guides was limited to Bn 0.12a. In the 602-720 GHz band with 0.014" x 0.007" waveguide, this corresponds to a branch height Bn 0.0017". The main guides can be machined using an end mill, and the branch guides can be made with a shaving tool. Figure 5 shows a six-branch hybrid with the independent parameters labeled. Note that it is symmetrical from end to end — it was found that no advantage was gained by allowing an asymmetrical design with six independent branch heights and five independent spacings. The design variables are: the heights of the branches (Bn), the spacing between branches (Ln), and the distance (L11) between the main waveguides. The simulation and design of the hybrids was done in the WR-10 band (75-110 GHz) to enable prototypes to be measured on a vector network analyzer. The limit on branch guide height requires Bn 0.012". The height of the main waveguide sections is fixed at the standard b = 0.050". The space mapping design procedure is demonstrated in Fig. 6 for a hybrid with amplitude imbalance 0.5 dB and phase imbalance 1 . Figure 6(a) shows the optimized MMICAD solution, which we shall refer to as the MMICAD reference solution, and the QuickWave result using the same set of dimensions. Figure 6(b) shows the MMICAD solution after it is re-optimized to match the QuickWave solution (also shown for comparison). The