Cross-connected Waveguide Lines as Standards for Millimeter- and Submillimeter-wave Vector Network Analyzers N M Ridler and M J Salter National Physical Laboratory, Teddington, TW11 0LW, UK, nick.ridler@npl.co.uk Abstract — This paper describes some investigations into establishing primary standards of loss for waveguide Vector Network Analyzers (VNAs) operating at millimeter- and submillimeter-wave frequencies. The standards comprise straight sections of waveguide, where the waveguide line is orientated such that the waveguide aperture is at right-angles to the waveguide apertures on the VNA test ports. This ‘crossconnected’ waveguide forms a section of waveguide that is effectively below cut-off. The mechanical discontinuity between the cross-connected waveguide and the VNA test ports also generates significant reflection. The combined effect due to these two loss mechanisms – cut-off attenuation and discontinuity reflection loss – can be predicted from electromagnetic theory and so can be used to establish sections of cross-connected waveguide, of various lengths, as primary standards of loss. The paper describes these standards in detail and compares experimental results, obtained using a VNA operating in the 50 GHz to 75 GHz band, with values predicted by electromagnetic modeling software. Index Terms — Attenuation measurement, Electromagnetic modeling, Measurement standards, Millimeter wave measurements, Submillimeter wave measurements, Waveguide junctions I. INTRODUCTION In recent years, there has been a significant increase in the available upper operating frequency of Vector Network Analyzers (VNAs). This has enabled VNAs to be used at millimeter and submillimeter wavelengths. With this increase in frequency comes a need for verifying the performance of these VNAs at these operational frequencies. Traditionally, this has been done in waveguide at lower frequencies using VNA waveguide verification kits containing devices such as sections of precision waveguide (with close to zero reflection and transmission loss) and sections of reduced-height waveguide (with significant reflection and transmission loss) [1] – [3]. However, at high millimeter- and submillimeter-wave frequencies, reduced-height waveguide becomes difficult to manufacture reliably and to the necessary degree of accuracy. This is because the height of conventional waveguide, with an aperture width-to-height ratio of 2:1, is already very small. For example, waveguide used at 1 THz has nominal dimensions of (250 x 125) µm. To further reduce the height of such waveguide, in a controlled manner, is mechanically challenging in the extreme. New methods are therefore required to realise waveguide verification devices that exhibit significant reflection and transmission loss. It is further desirable if the characteristics of these devices can be predicted from first principles, or, using electromagnetic modeling software, thus making them ‘calculable’ devices suitable for primary standards applications. This paper describes an investigation into one type of device – referred to here as “cross-connected” waveguide (or “cross-guide”, for short). This device is simply a section of precision waveguide that is connected so that the waveguide aperture is at right-angles to the usual connection orientation of the waveguide. The cross-guide is aligned using the alignment dowels found on the conventional UG-387 waveguide interfaces on the VNA test ports. This paper presents experimental results obtained on some cross-guide lines in the WR-15 waveguide size at frequencies from 50 GHz to 75 GHz, this being the conventional operating band for this waveguide size [4]. These results are compared with electrical performance predicted using electromagnetic modeling software – in particular, CST Microwave Studio [5]. Finally, the paper contains recommendations on how these devices can be improved for use in all other waveguide sizes used at millimeter and submillimeter wavelengths [6]. II. CROSS-GUIDE REALIZATION A cross-guide device can be realized by connecting a short section of conventional waveguide (i.e. a line) so that its aperture is at right-angles to the apertures of two conventionally-oriented waveguides. For example, in a test/measurement configuration, these conventionally-oriented waveguides could be the test port reference planes of a VNA. A diagram illustrating this connection strategy for the waveguide apertures is shown in Fig. 1. For the investigations described in this paper, the crossguide line sections were aligned using the dowel pins on a conventional MIL-DTL-3922/67D (often called UG-387) type interface [7] – see Fig. 2. The sections of waveguide that were used to establish the cross-guide lines were relatively short and did not contain the dowel pins shown on the interface in Fig. 2. (These short lengths of waveguide, when connected in the conventional manner, can be used as Line standards during VNA calibration techniques such as TRL [8], LRL [9], etc.) One of these lines is shown in Fig. 3 – where Fig. 3a shows the waveguide line with its aperture orientated in the usual way for connection to the interface in Fig. 2. Dowel pins Fig. 1 Diagram to illustrate a section of cross-guide inserted between two conventionally-oriented waveguides A key feature with the UG-387 interface is that the dowel pins and dowel holes are equally spaced and positioned symmetrically around the connecting face of the interface. This means that the waveguide line shown in Fig. 3a can also be connected to the interface in Fig. 2 after the line has been rotated through 90°, so that the aperture of the line is at rightangles with respect to the aperture shown in Fig. 2. This orientation of the waveguide line section is shown in Fig. 3b, which shows the same waveguide line from Fig. 3a except with the aperture orientated at right-angles to the interface in Fig. 2. The alignment accuracy of waveguides connected using UG-387 interfaces is governed solely by the accuracy of the diameter and position of the dowel pins and dowel holes found on UG-387 interfaces used to make the connection. Since both the conventional connection and the cross-guide connection of the line shown in Fig. 3 uses essentially the same dowel pin/hole alignment process (i.e. two dowel pins on each VNA test port fitting into the four dowel holes on the waveguide line), the expected alignment accuracy for both the conventional and cross-guide connections will be the same. This indicates that the quality of connection (in terms of alignment and repeatability) for a cross-guide line will be comparable with that of a conventionally-connected line (e.g. when used during a VNA calibration process). Fig. 2 Conventional MIL-DTL-3922/67D (UG-387) waveguide interface, showing the two dowel pins Outer dowel holes Fig. 3a A short waveguide line, showing the four outer dowel holes that are used for aligning the waveguide during connection to UG387 interfaces. Note that the conventional waveguide aperture widthto-height ratio is 2:1 Aperture width-toheight ratio is now 1:2 III. MEASUREMENTS AND MODELING A. Measurements A series of measurements were made on some candidate cross-guide lines using NPL’s Primary Impedance Measurement System (PIMMS) [10]. A millimeter-wave VNA was configured with WR-15 waveguide test ports. These test ports were established as reference planes by performing a ‘Thru-Reflect-Line’ (TRL) calibration [8] using: a “¼-wave” line (as the Line standard); a flush short-circuit connected, in turn, to both test ports (as the Reflect standard); and, joining the test ports together (as the Thru standard). Fig. 3b The same waveguide line shown in Fig. 3a, except rotated through 90° so that the ratio of the waveguide aperture width-toheight is now 1:2. The outer dowel holes remain in the same location, due to their symmetrical positioning around the face of the interface Three relatively short waveguide lines, with approximate lengths 1.6 mm, 2.0 mm and 3.6 mm, were connected as cross-guide lines to the VNA test port reference planes. In addition, a relatively long cross-guide line (of approximately 50 mm) was also measured by the VNA in order to investigate if signals in a section of cross-guide line could propagate along relatively long lengths of line. B. Modeling The S-parameters of three different lengths of WR-15 crossguide line were simulated using the time domain solver in CST Microwave Studio [5]. The cross-guide line lengths simulated were 1.6 mm, 2.0 mm, and 3.6 mm corresponding to the three shortest measured cross-guide lines. The longest measured cross-guide line of length 50 mm was not simulated. In the simulations, the background material in the computational domain was set to perfectly electrical conductor (PEC) and vacuum bricks were defined to represent two aligned sections of WR-15 waveguide, corresponding to the two VNA test ports with an orthogonally oriented section of WR-15 waveguide connected between them, corresponding to the cross-guide. The frequency range of the simulation was set as 50 GHz to 75 GHz. Energy was fed into and extracted from the computational domain by means of waveguide ports at the inputs to the two aligned waveguide sections. The computational domain was discretized using a hexahedral mesh. The S-parameters of the cross-guide alone were deembedded by shifting the reference planes from the waveguide ports to the cross-guide ports. Since all the waveguides in the simulation were assumed to be lossless, the de-embedding only affected the phase of the S-parameters. Because of symmetry and reciprocity the simulated S-parameters S11, S22, S21 and S12 satisfied the following conditions: S11 = S22 and S21 = S12. Fig. 4 Transmission for the 1.6 mm cross-guide line: measured (PIMMS); modeled (CST MWS) Fig. 5 Transmission for the 2.0 mm cross-guide line: measured (PIMMS); modeled (CST MWS) IV. RESULTS Figs. 4, 5 and 6 show plots of the measured transmission magnitude, as a function of frequency, for the three short lengths of cross-guide line (i.e. 1.6 mm, 2.0 mm and 3.6 mm). These plots show that, for all three cross-guide lines, the transmission magnitude varies smoothly with frequency. The plots also show that each cross-guide line produces a different amount of attenuation – the longer the cross-guide line, the greater the amount of attenuation. This suggests that short lengths of cross-guide line can be used to realize standards of attenuation – the value of attenuation being related to the length of the cross-guide line. Fig. 6 Transmission for the 3.6 mm cross-guide line: measured (PIMMS); modeled (CST MWS) Figs. 4, 5 and 6 also show the modeled transmission magnitude, for the same three cross-guide lines. The modeled transmission values show the same type of variation with frequency and with length of cross-guide line. Any discrepancy between the measured and modeled electrical performance should be accountable by the uncertainties in both the measured and modeled values. Fig. 7 shows a plot of the measured transmission magnitude for the 50 mm long cross-guide line. This Fig. also shows a plot of the measured transmission between the two VNA test port reference planes when both ports are terminated with short-circuits. The measurement of the two short-circuits provides an indication of the level of isolation between the two VNA test port reference planes, since effectively no signal should be transmitted under these conditions. Since the measured transmission for the 50 mm cross-guide line and the two short-circuits is very similar (at around –80 dB), this indicates that no detectable amount of signal propagates along the full length of the 50 mm cross-guide line. This suggests that the electromagnetic wave in the cross-guide line is not able to propagate in the usual fundamental TE10 mode but instead decays evanescently as the wave enters the cross-guide section of the line – i.e. the cross-guide section of line acts as a waveguide below cut-off [11]. band1 and upper frequencies for this waveguide band (i.e. 50 GHz, 62 GHz and 75 GHz). TABLE I MEASURED ATTENUATION FOR THE THREE CROSS-GUIDE LINES AT 50 GHZ, 62 GHZ AND 75 GHZ. Attenuation (dB) Cross-guide length (mm) 50 GHz 62 GHz 75 GHz 1.6 24.29 17.63 11.39 2.0 28.96 21.36 13.55 3.6 47.40 36.05 21.70 These attenuation values are also plotted in Fig. 8, where it is clear that the attenuation values for the three cross-guide lines, at each frequency, lie on a straight line. This indicates that it is feasible to design cross-guide attenuation standards, choosing the length of the cross-guide line to give the required value of attenuation. A series of such devices could then be used as verification standards for VNA transmission measurements by providing a wide range of known values of attenuation. Fig. 8: Attenuation versus cross-guide line length at 50 GHz, 62 GHz and 75 GHz Fig. 7 Transmission for the 50 mm cross-guide line and the isolation measurement A straight-line fit to the values at 62 GHz has the following equation: α = 9.335 L + 2.662 V. DISCUSSION In the previous section, it was suggested that short lengths of cross-guide line could be used to realize standards of attenuation. To investigate this further, selected attenuation values for the three short cross-guide lines measured previously are shown in Table I, below – at the lower, mid- (1) where L is the length of the cross-guide line and α is the associated attenuation (dB). This equation can be re-arranged to show what length of cross-guide line needs to be used to achieve a required value of attenuation: L = (α - 2.662)/9.335 1 (2) The mid-band frequency value used here is the approximate geometric mean frequency of the recommended lower and upper frequencies for this waveguide size. For example, Table II gives calculated values of cross-guide line length, using (2), to give 10 dB steps of attenuation in WR-15 at 62 GHz. Table II shows that changing the length of the cross-guide line section by approximately 1.07 mm produces a change in attenuation of 10 dB at 62 GHz. TABLE II CALCULATED VALUES OF CROSS-GUIDE LINE LENGTH TO PROVIDE KNOWN STEPS OF ATTENUATION AT 62 GHZ Attenuation (dB) 10 20 30 40 50 60 Required crossguide length (mm) 0.79 1.86 2.93 4.00 5.07 6.14 the phase varies smoothly across the full waveguide band. However, the phase at any given frequency does not vary appreciably with the length of the line. For the transmission phase, this further suggests that the wave in the cross-guide line section is not propagating using a conventional waveguide mode but is instead decaying evanescently with no appreciable phase change associated with the wave. It is also interesting to note that there is an almost constant 90° phase difference, across the full band, between the reflection and the transmission coefficient phases. VI. OTHER S-PARAMETERS Although the main focus of this paper has been the use of cross-guide lines to develop primary standards of attenuation, it is also informative to examine the reflection properties of these lines, and also to look at the phase behavior of both the reflection and transmission coefficients. Fig. 9 shows a plot of the measured linear reflection coefficient magnitude of the three short lengths of cross-guide line measured in the previous sections. This Fig. shows that all lines exhibit very high reflection across the full waveguide band. The amount of reflection is only mildly dependent on the length of the line – the longer the line, the higher the reflection coefficient. This can be seen clearly at 75 GHz – i.e. the maximum recommended operating frequency for this waveguide size. Fig. 10 lines Reflection coefficient phase for the three short cross-guide Fig. 11 Transmission coefficient phase for the three short crossguide lines VII. IMPROVING CROSS-GUIDE ALIGNMENT Fig 9 Linear reflection coefficient magnitude for the three short cross-guide lines Figs. 10 and 11 show plots of the phase of the reflection and transmission coefficients, respectively. Both Figs. show that The mechanism used for aligning the cross-guide lines investigated in this paper has been the dowel pins and dowel holes as specified for the conventional UG-387 interface [7]. However, it is well known that this interface does not provide good alignment accuracy for waveguides used for precision measurements at higher millimeter- and submillimeter-wave frequencies. This has led some manufacturers to introduce a ‘precision’ version of the UG-387 interface (see, for example [12]) which contains two additional alignment holes above and below the waveguide aperture (at ‘north’ and ‘south’ positions). Fig. 12 shows a photo of a ‘precision’ UG-387 interface that contains these two additional inner dowel holes. Inner dowel holes decay (i.e. attenuation) and path length (i.e. cross-guide line length). In this respect, the cross-guide line acts like a waveguide below cut-off (WBCO) [11]. Such a line can therefore be considered as a primary standard of attenuation in any waveguide size that can be realized to a suitable degree of accuracy. However, cross-guide lines are considered to be most applicable in small waveguide sizes where other devices (such as reduced-height waveguide) become difficult to realize reliably. For any given waveguide size, a series of cross-guide lines of different but known lengths will provide a series of ‘known’ values of attenuation. These devices could be used to construct waveguide VNA verification kits in any waveguide size. Similarly, such devices could also be used to verify the linearity of a VNA – for example, during a measurement uncertainty evaluation process. Addendum Fig. 12 ‘Precision’ UG-387 waveguide interface, showing the two inner dowel holes at ‘north’ and ‘south’ of the waveguide aperture During connection, two precision dowel pins are inserted into these holes, and into similar holes on the device under test (assuming the device is also fitted with the precision version of the UG-387 interface). In fact, the waveguide line shown in Fig. 3 already contains these inner dowel holes. However, when this line is rotated through 90° to form a cross-guide line, these inner dowel holes are now positioned at ‘east’ and ‘west’ positions (see Fig. 3b), rather than ‘north’ and ‘south’ positions (as in Fig. 3a), and so these holes no longer align with the inner dowel holes found on the ‘precision’ UG-387 interfaces. Therefore, a method of improving the alignment of cross-guide lines used with ‘precision’ UG-387 interfaces would be to include an extra pair of precision inner dowel holes (situated at ‘east’ and ‘west’ with respect to the conventionally-aligned aperture) so that these additional holes can be used to align the waveguide, with respect to ‘precision’ UG-387 VNA test ports, when the waveguide is configured as a cross-guide line. This alignment process will enable cross-guide lines to be aligned with the same degree of accuracy as conventionally-orientated waveguides connected using ‘precision’ UG-387 interfaces. This will facilitate the use of cross-guide lines as accurate primary standards at all millimeter- and submillimeter-wave frequencies. VIII. SUMMARY The cross-guide lines investigated in this paper have exhibited some interesting properties. Firstly, it appears that the wave in the cross-guide line does not propagate in a conventional manner (e.g. using the TE10 mode) – instead, the wave becomes evanescent and decays exponentially. This suggests that there is a direct relationship between signal Since having this paper accepted for publication, the authors have become aware of another published paper that has already described the use of cross-connected waveguide for verifying scattering parameter measurements [13]. In [13], the term “90° shim” is used to describe the type of device that is called “crossconnected” waveguide in this paper. It is clear that [13] was responsible for introducing this type of device for the purpose of verifying scattering parameter measurements. The authors of this current paper apologize to the authors of [13] for not referring to their work in the version of this paper that was distributed at the ARFTG conference. ACKNOWLEDGEMENT The work described in this paper was funded by the National Measurement Office of the UK government’s Department for Business, Innovation and Skills, UK. REFERENCES [1] R W Beatty, "Calculated and Measured S11, S21 and Group Delay for Simple Types of Coaxial and Rectangular Waveguide 2-port Standards" NBS Technical Note 657, December 1974. [2] Maury Microwave, “Two-port Standard Sets”, Technical Data Sheet 3A-322A, April 1998. http://maurymw.com/pdf/datasheets/3A-322A.pdf. [3] Agilent Technologies, “11645A R, Q, U, V, W Waveguide Verification Kits User's and Service Guide”, Part Number 11645-90013, November 2004. [4] MIL-DTL-85/3C, “Waveguides, Rigid, Rectangular (Millimeter Wavelength)”, October 2005. [5] www.cst.com. (Computer Simulation Technology company web-site.) [6] N M Ridler and R A Ginley, “IEEE P1785: A New Standard for Waveguide Above 110 GHz”, Microwave Journal, Vol 54, No 3, Cables & Connectors Supplement, pp 20-24, March 2011. 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