Appendix 2

Tapered Transmission Line Test Fixture Construction

This appendix describes a type of test fixture for use when measuring high impedance balanced transmission lines. This type of fixture can provide a broader frequency range of impedance transformation for coupling to and measuring high impedance transmission line than a conventional lumped transformer like those described in Appendix 1 can alone.

Two variations of type are described here. Each of these use a Klopfenstein taper1 design to provide impedance transformation over a relatively large usable frequency range and to some degree a better modal transformation than is available with the lumped transformer approach. The first version is depicted in Figure 1 and describes the version used in Experiment 5 and elsewhere. A related tapered fixture for use with a single wire transmission line was previously published2

At this point it might be well to note that a Klopfenstein taper is perhaps not the ideal taper for best transformation between TEM and TM modes. While in TEM regions it provides an appropriate impedance transformation profile to create low reflection along its length, it does not include the effects of modal changes that are present and most significant in the region between TEM and TM mode transmission lines. This is particularly in the region where similar e-field is present for each mode and where that ratio is changing most rapidly. Generally speaking changes in taper should be “slowed down” there while more toward the high impedance end where the line is becoming predominantly TM the taper has less importance because the impedance is moving asymptotically to 377 ohms. Because of this, a better taper should be possible, however, it is not being provided with the designs shown here which use a strict Klopfenstein taper.

Although the Klopfenstein taper can be applied to situations having high transformation ratios, generally high ratios are more demanding in terms of dimension and can be more restrictive in achievable bandwidth. For this reason the versions being presented here, while being used as part of a fixture for converting from a 50 ohm, single ended and TEM environment to a 754 ohm balanced TM line were designed to only provides impedance conversion from about 200 ohms to 754 ohms between balanced lines.

The remaining portion of the impedance conversion is in a TEM context and done with a lumped transformer/balun as described in Appendix 1. This shows construction of a 1:2 voltage ratio toroidal transformer that can be used along with a tapered line to provide both 50 to 200 ohm impedance conversion but also to operate as a balun to convert from single-ended to balanced environment.

The combination of the lumped and tapered transformations provides conversion from the 50 ohm coaxial environment of a VNA to that of a high impedance 1m spaced balanced LUT shown in the Experiments. The tapered line can connect directly to 1m spaced open-wire LUT. Together they can operate over a broad bandwidth providing balance, impedance and modal conversion without excessive reflection or radiation.

is fabricated from 3/32” diameter, copper plated steel welding rod. This rod is stiff enough that when held in position by 3D-printed plastic and 1/4” PVC tubing spacers can have approximately the correct shape to produce the desired Klopfenstein impedance taper required along its length. Those spacings are calculated from a spread sheet which uses the Klopfenstein/ equations.

Starting from the closely spaced end, which at .500” spacing has a TEM balanced impedance of about 200 ohms, the spacing increases smoothly to a maximum of 1 meter at the wide end, over an entire length of 96”.

The taper largely follows the Klopfenstein solution to create wide bandwidth match between lines of different impedance. However, at wide spacing and the high impedance end, this adherence is dropped in an attempt to reduce tight bends. This is on the presumption that the dominant mode in this region is TM and that reducing bends by increasing the radius of curvature is more important than adhering to the equation followed in the lower impedance portion. This adjustment is empirical and practical rather than analytic.

Table 1: 3/32” (D)iameter conductor spacing vs distance from 200 ohm (narrow) end.

3/4" PVC pipe and 4-way box is used as a supporting framework. The final (S)pacing has been reduced below the TEM value but since the mode is almost entirely TM this has little negative consequence.

Tapered Fixture Fabrication

Keeping with the use of inexpensive materials, a Klopfenstein tapered transmission line for adapting 200 ohm TEM mode balanced drive to a high impedance TWA was fabricated in the same manner as the TWA from CAT5 conductor, 3D-printed PLA and drinking straw spacers.

Figure 6 provides approximate TEM impedance, position and spacing along the fixture’s length for suitable adapters made from 3/32” or AWG24 conductor. These characteristics create a 200 ohm TEM to 754 ohm TM adapter with characteristics similar to those shown in Appendix 2.

Figure 6: Spacing for two Klopfenstein taper transmission line transformers using either 3/32” rod or CAT5 conductor and having an approximately 120 MHz low frequency cutoff. Narrow spacing is provided using 3D-printed PLA parts while for two different versions, wider spacing is created with PVC tubing or with drinking straws and plugs in the same way as for the TWA. The total length is the same for each design.

 Suitable spacers for the narrow portion of the adapters are 3D printed from PLA. For the 1 m line, the wider spacings are created by ¼” PVC tubing and 3D-printed plugs while for the CAT5 version, used with a traveling wave antenna connection with 3” spacing, trimming straws are cut to length and secured to the conductor in the same way as for the TWA itself. This use is described elsewhere.

 Once the tapered transformer portion is complete only a 50:200 ohm coax to balanced transformer is needed to complete the entire fixture For low power or receive only use and testing, the lumped T-130 4:8 turn fixture shown in Appendix 1 can be used. But for narrow band use or for higher power transmitting a standard half wave coax balun is more suitable. For this simply cut a section of 50 or 90 ohm coax to a half wavelength and connect center conductors to the tapered line, the grounds together and a 50 ohm cable or connector to one side. These are described in amateur radio handbooks.

1A Transmission Line Taper of Improved Design, R. Klopfenstein, Proceedings of the IRE, pp 31-35, January 1956

2 A Surface Wave Transmission Line, Elmore & Watrous, QEX May/June 2012, ARRL Newington, Connecticut