[Links to individual experiments and discussion are found at the bottom of this page.]
The content of these pages is intended to provide description of some experiments which produce results contrary to what might be expected from standing theory. It is intentionally not providing teaching, interpretation or claim of better theory. Rather it is intended to provide evidence which generates questions and curiosity from interested readers that might result in their replication, verification, and new experiments by those readers and so contribute to new and better understanding for all.
Definitions:
TEM Transverse Electric-Magnetic, A mode where both electric and magnetic fields are orthogonal to the direction of propagation of a wave.
TM Transverse Magnetic, A mode where only the magnetic field is orthogonal to the direction of propagation of a wave. Electric field lines may terminate longitudinally.
DUT, LUT Device or Line Under Test. SWTL A transmission line where the dominant mode is TM, normally a line that is at least one half-wavelength or longer.
VNA Vector Network Analyzer, a measuring instrument used to gather information obtained through stimulus and response from one or more ports of a DUT.
SOLT short-open-load-thru calibration, normally a VNA calibration using four measurements of three different calibration devices.
These experiments arise from previous recognition of the nature of coaxial and balanced transmission lines1,2 and that real lines of these types simultaneously propagate energy in both TEM and TM3 modes even when one or the other may be dominant. Although some overall method to the order of their presentation may be obvious they are presented in the order originally performed. Some results from one experiment may reasonably lead to questions and configuration changes that might be addressed in the next but it is intended that interpretation be left to the reader. The experiments are detailed with information included in Appendixes intended to make accurate measurements of transmission lines of this sort easy to replicate using commonly available materials and measurement tools. In particular, inexpensive and readily available modern VNA tools and analysis methods are used along with commonly available materials in order to make further experimentation by a reader easily accessible.
These goals are not easy to meet either physically or analytically because the targets of the measurements are generally high impedance transmission lines which may behave quite differently when compared to other lower impedance line measurements more commonly made. Not only can high impedance LUTs be physically large but a different interpretation, really a different theory, is necessary to gain understanding of the results when measuring with a conventional VNA.
Generally speaking, for these VNA measurements, an adapter, a kind of test fixture, must be used to convert between the VNA environment and that of the LUT. This kind of adaptation is often provided for conventional error corrected S-parameter VNA measurements and may be as basic as adapting between two connector types having the same impedance or may be to a very different DUT type, geometry and impedance. A goal of fixturing is to provide a measurement context that is similar to that of an intended application so that meaningful and useful information can be obtained. It is often one for which suitable calibration devices are available within the DUT environment.
While a VNA, per se, simply gathers stimulus/response measurement information from a directional device, when used with calibration and error correction to return S-Parameters there is an implicit understanding that the results apply to a measurement plane, the location of a planar surface along a transmission line and at right angles to it where a calibration may have previously been performed.
Usually prior to DUT measurement, calibration measurements using SOLT or other calibration standards are used to produce values that provide definition for an “error adapter” which represents the implicit imperfect fixturing of the raw VNA hardware. Mathematical operations involving this error adapter are performed on raw measurement data to provide the error correction – for removal of the imperfections of the VNA itself as well as any effects of additional fixturing hardware between the VNA and the measurement plane. A helpful video is available to describe this4.
After the calibration process has been performed, additional measurements then produce results which can be interpreted as what an error-free VNA having measurement planes located at the ports of a DUT would measure. Thus there is an implicit expectation that the calibrated measurement of a DUT being examined can be suitably interpreted using TEM theory as describing conditions at the orthogonal measurement plane.
For common 1-port or 2-port DUT measurements, either single or two port calibration and measurement techniques are used. Stimulus may be applied to only one port while response is initially measured as signal returned from one or both ports of the DUT. Stimulus applied to only one port is called a 1-path measurement or to both ports, creating a 2-path measurement.
The first subscript of an S-parameter indicates the port where return is being measured while the second indicates which port is being stimulated. 1-port 1-path measurements produce a single S-Parameter, S11 or S22 depending on the port being measured while 2-port, 2-path DUT measurement can provide up to four S-parameters. For 1-path 2-port measurement S11 & S21 are returned when stimulus is applies to Port 1. When Port 2 of the DUT is stimulated for a 2-path measurement, S22 & S12 can also be measured as well .
A large class of common 2-port DUT types are symmetric and reciprocal. These include passive devices having no magnetic materials or active stages such as filters and transmission lines. These devices are considered to be reciprocal soand applying stimulus from only one of the ports while taking two response measurements but then duplicating these to produce a total of four can be much simpler and still very useful. This 1-path measurement is commonly done with inexpensive VNAs currently available. Even these inexpensive VNAs can produce full 2-port measurement data if the DUT is physically reversed and a 1-path measurement repeated.
To achieve error corrected 2-port DUT measurements in a 1-path environment, SOLT calibration can be used to provide 6 error adapter terms. To do this, stimulus is applied from VNA Port 1 while responses are measured at Ports 1 and 2 while special SOLT calibration devices are measured. Measurement of these calibration devices provides the six required error terms so that future DUT measurements can produce fully corrected reflection and transmission S-Parameters S11 and S21, referenced to two defined measurement planes where the calibration device standards were located. For future measurements these planes are considered as DUT Ports 1 and 2, respectively. For a 2-path measurement the DUT must be turned around such that calibration is performed while stimulus is applied to Port 2 and response is measured at both ports as before. The 2-path measurement not only requires hardware changes to accomplish the stimulus change but also an additional 6 error terms to produce a total of 12 for the calibration process. Two additional S-Parameters, S22 and S12 can then be obtained as well and the resulting S-parameters are not limited to describing reciprocal, non-magnetic DUTs as they are in the 1-path case.
In these experiments not only is transmission line type quite different from the 50 ohm coaxial environment of the VNA, being generally much larger physically it may also be differential rather than single ended. This difference must be accommodated by suitable unbalanced-balanced conversion within a test fixture.
Generally speaking, short, lower impedance lines tend to dominantly support TEM00 mode so that conventional VNA measurement and theory suffice. However for very high impedance lines it is previously known that the mode of propagation may include significant or even dominant TM. In TM00 mode propagation the e-field is not transverse but longitudinal. Creating a test fixture that not only adjusts for physical connection, dimension and impedance difference but also for these modal differences is a complex problem. Analyzing measured results also becomes more of a problem since the error correcting algorithms used for lower impedance measurement no longer apply.
All together these differences make it difficult to create an ideal environment in which to measure the characteristics of a high impedance transmission line using a conventional VNA. TEM-to-TM mode adaptation is particularly difficult. In balanced line the TEM mode tends to by dominated by electric field lines concentrated between the conductors that are not radially symmetric around a conductor. In the TM mode field lines tend to have radial symmetry and require significant line length, on the order of a half wavelength or more, in order to become well established and dominant,. While the test fixtures and the experiments that follow attempt to address some of these difficulties they do not do so perfectly.
It is extremely important to understand the problems associated with analysis, calibration, measurement and synthesis of structures and devices located within a bounded volume of spacetime when the very tools and methods we use do not allow any longitudinal fields at their connection locations. These boundaries are considered as planar in order to contain the DUT but within a high impedance context our existing methods do not properly reflect experience.
So We Continue While Remaining Aware of Our Limitations…
For these experiments, calibration is established by a 1-path 2-port VNA calibration over a frequency range deemed suitable to the particular fixture type, available standards and experiment being performed. Some experiments use only lumped transformers for fixturing. With these lumped element fixtures the useful frequency range tends to be smaller than for experiments using tapered transmission line transformer fixturing due to the conflicting requirements of low frequency response and simultaneous avoidance of resonance within the transformers at the high end of the range. Toroidal and binocular shapes and core types have limited useful range over which permeability, self resonance and loss are simultaneously adequate. These limitations are most extreme where high transformation ratio is attempted, where even achieving one octave of useful bandwidth can be a challenge. Tapered transmission line transformers while also having low frequency limits can sometimes be fabricated with considerably more than a decade of bandwidth. Appendixes 1 and 2 describe some of these.
2-History
3-Experiment 80 foot length of 2-conductors of AWG #28 magnet wire separated by 9” drinking straw spacers
4-Experiment 80 foot length of 2-conduct of AWG #28, one conductor cut and terminated in wet sod
5-Experiment 64 foot length of 1m-spaced AWG#28, fixtured using 200 ohm input Klopfenstein tapered transformer
6-Experiment 64 foot length of 1m-spaced AWG#28 wire, fixtured using 200 ohm input tapered transformers. Bend measurement with Styrofoam.
7-Experiment 64 foot length of 1m-spaced AWG#28, one of the conductors extended in length by 1 meter
8-Experiment 64 foot length of single conductor AWG#28 wire, 3" square shorts at line center
9-Experiment 64 foot length of single conductor AWG#28 wire, fixtured using the original QEX SWTL launchers
10-Experiment 64‘ length of hybrid transmission lin, single wire split, without and with inserted 1m extension
11-Experiment 80’ length of 1.5” spaced balanced line made with conductors obtained from CAT5 cable
12-Sample Experiment SOLT or TRL calibrated measurement techniques s and tools for use by other experimenters
14-Experiment SWTL with 2-way split-to-2nd wire sloping down to a termination.
15-Experiment SWTL Reference -Styrofoam measurement
16-Experiment SWTL-Bends bends of several different radii
17-Experiment Field Probe calibration
18-Experiment Field Probe Radiation Measurement
19-Experiment Obstructions (pending)
20-Appendix-1 Lumped transformer fixture details.
21 Appendix-2 Tapered transmission line transformer fixtures details.
22-Appendix-3 Line Fabrication
23-Appendix-4 Data Acquisition and Analysis Tools
Commentary Additional detail about the Experiments
Deep Magic Thoughts & Fundamental Questions that arise from the evidence.
Introduction to the Propagating Wave on a Single Conductor, G. Elmore, 2009
Another Look at Transmission Lines, G. Elmore, RadCom Plus, Vol. 4, No. 1, RSGB 2020 p. 24
Electromagnetic theory, Stratton J, 2007 reprint by IEEE press Series on Electromagnetic Wave Theory, John Wiley & Sons Inc. ISBN13 9780470131534,1941, p533
Understanding VNA Calibration Basics, Rrohde & Schwarz,