94 GHZ Directional Coupler Modulator Fabrication
R- F Waveguide and Coupling Measurements
A 94 GHz Varian VRC-2113B23 klystron purchased in the late 1970s was tested, using a power supply borrowed from Prof. David Rutledge’s group. The 94 GHz tube still measured approximately 80 mW output over its 90.75 to 97.75 GHz tuning range.
The millimeter-wave coupling structure used to excite the antennas on the modulator utilizes a tapered, low dielectric constant dielectric slab waveguide “expansion fan” to increase the width
of the slab waveguide from the 0.100 inch width (2.54 mm) of WR-10 waveguide out to the length of the antenna array on the modulator, approximately 10 mm. The wide end of the fan is butt-coupled to a lithium niobate slab waveguide (εr = 28) through a “quarter-wave”
section of intermediate dielectric constant to minimize reflections. The lithium niobate waveguide is cut in a wedge of the correct angle for velocity matching, and is glued to the backside of the modulator chip. This coupling scheme is shown schematically in Figure 6 - 10.
It was used successfully by Sheehy in Refs. [1.2] and [1.3], and by Cummings in Refs. [6.1] and [6.2], but it was not truly optimized for those measurements.
Figure 6 - 10: Slab dielectric waveguide coupling scheme for millimeter-wave modulators.
To optimize the coupling of the millimeter-wave modulation into the modulator, reflections at the junctions between the various slab waveguide sections must be minimized. This must be done by trial and error, since no accurate theory exists for the metal-waveguide-to-slab wedge junction, or for slab-to-slab junctions using a “quarter-wave” matching section. To carry out
this optimization, transmission measurements of the two such structures, coupled “back- to-back” were made with variously sized matching layers. It can be assumed that the transmission loss from the WR-10 waveguide to the modulator would be approximately half the loss (in dB) of the overall transmission. A photograph of a back-to-back slab waveguide arrangement is shown in Figure 6 - 11. Two polypropylene tapered slab waveguides are coupled to a uniform section of lithium niobate through “quarter-wave” thicknesses of an intermediate dielectric constant material, Stycast.®
Figure 6 - 11: Photograph of a “back-to-back” coupling structure.
In the measurement setup, the fanned-out sections of slab waveguide were inserted into W- band horns. The overall transmission was measured and compared to the signal measured with the metal waveguide connected “flange-to-flange.” To remove the effects of detector non-linearity, a precision attenuator was used to keep the detector signal level the same for both the transmission through the entire structure and the transmission through just flange-to- flange WR-10.
Many combinations of fan dimensions, and matching section dielectric constants and thicknesses were evaluated. Polypropylene (εr = 2.2) 1 mm thick was originally used for the expansion fans. The 1 mm thickness is a good match for the 1.25 mm height of WR-10 waveguide and the 0.656 mm width of the dipoles on the lithium niobate substrate. It also
gives a reasonably well-confined mode on the slab. In the case of infinite plane-wave transmission through a dielectric interface, a “quarter-wave” matching layer should have a dielectric constant equal to the geometric mean of polypropylene and lithium niobate, (2.2 x 28)1/2 = 7.8, and should have a thickness of 0.25x (3.2 mm/√7.8) = 0.28 mm (or an odd multiple thereof). Of course, in the slab waveguide coupling structure, the fields are not fully confined to the dielectric material. The effective dielectric constant of the guide will be reduced in all cases. Simple slab waveguide theory, such as in Ref. [6.5] for example, shows how to calculate the change in effective dielectric constant. For the polypropylene guide 1 mm thick at 94 GHz, the effective dielectric constant is 0.60 x 2.2 = 1.32. For the lithium niobate guide 1 mm thick at 94 GHz, it is 0.916 x 28 = 25.6. For the intermediate dielectric constant
Figure 6 - 12: Plot of dielectric constant correction factor as a function of dielectric constant for a 1 mm thick slab waveguide at 94 GHz.
material in the vicinity of 8, the correction factor is about 0.72. These factors are for TM0 propagation in the slab, as is correct for this setup. For TE0 propagation, the correction values are somewhat larger. Figure 6 - 12 shows the dielectric constant correction factor for both TE0 and TM0 modes as a function of the slab dielectric constant for 1 mm thick slab waveguides at 94 GHz.
One might think that knowing these correction factors for the effective dielectric constant, the
“quarter-wave” matching formula could be recalculated for an ideal match. Unfortunately, in addition to the change in propagation velocity and wave impedance, there will be a mismatch in the spatial distribution of the modes in the three regions, so that there will be a
“discontinuity” reflection, even if the mode velocities and wave impedances are correctly arranged for “quarter-wave” matching. At the time of this work, no reasonable theory exists for these discontinuities. For these reasons, a trial and error approach was followed, using the materials at hand rather than ordering special values of dielectric constant.
An additional problem arose as the back-to-back measurements proceeded, that of mechanical instability. Polypropylene is a flexible plastic material, and it proved difficult to maintain a flat, rigid structure while making the measurements. Sheehy also had this problem, but decided to simply “live with it.” This time, in the interest of using a more rigid material, fused silica (1 mm thick) was chosen for the expansion fans. Fused silica has a dielectric constant of εr =4.0 at millimeter-wave frequencies, so that the optimum (infinite plane wave approximation) matching dielectric constant would be (4 x 28)1/2 = 10.6, and a quarter wave would be 0.25x (3.2 mm/√10.6) = 0.25 mm thick. The correction factor for a 1 mm thick slab at 94 GHz is 0.572, so the effective dielectric constant is 2.3. For a matching slab 1 mm thick at 94 GHz with dielectric constant about 10, the correction factor is 0.765 for the TM0 mode. However, the transmission losses were a few dB higher then in the guides based on polypropylene, so the fused silica slab was abandoned for the flexible but low loss polypropylene.
It is difficult to make actual quarter-wave layers because they are so thin. The dielectric material was Emerson and Cuming Stycast® artificial dielectric. This material is made from a high dielectric constant powder suspended in a low loss plastic matrix. The dielectric constant
is controlled by the fraction of the powder used. It is not a strong material, and thin sections break easily. The most successful method found to make thin layers was to cut as thin a piece as possible with a saw, then glue it to the dielectric fan and lap it to the desired thickness with sandpaper on glass. Even so, the material would generally break off during attempts to make to make sections actually one quarter wavelength in thickness. Typically, odd numbers of quarter wavelengths were used to gain some material strength. However, the absolute accuracy required is the same.