Estimating transmission line mismatch under thermal exposure conditions

1. Introduction

The growing present-day requirements to weaponry and combat equipment items make it imperative for the manufacturers to advance the entire cycle of development, production and testing of products. The expanding geography of military materiel usage determines the importance of reconceptualising the approaches to climatic testing of electronic equipment of military-purpose complexes and systems. At this stage, of no small importance is the metrological support, including estimation of the measurement uncertainty of electronic equipment parameters under climatic testing conditions, which makes it possible to avoid false acceptance or false rejection of products [1]. The study discussed in this paper aims at determination of regularities in the effects of temperature non-uniformity of the medium, arising due to zoning of test conduct location, on the measuring line mismatch degree.

In the measurement of frequency-dependent parameters of tested equipment, the test bench transmitting lines have their share in the error and uncertainty of the measurement results. When considering and analysing transmission systems operating through cable, it is normally a uniform line model that is taken as a guiding system. In real conditions, the connecting line may have non-uniformities, which affects the wanted signal being transmitted. Such non-uniformities, reflecting part of the wanted signal, can be described by reflection coefficients (Г). Their influence on the measurement results is proportional to the quantity of measuring circuit elements and depends also on a number of external influencing factors [2].

This paper offers a methodology for estimating mismatch of transmitting lines in the estimation measurements that are the first stage of contemporary measurement process. During estimation measurements, certain characteristics of the device under test, as well as of the measuring circuit, are coarsely determined for further optimisation of the measurement. This allows to save time and avoid errors and incorrect results [3].

2. Mismatch estimation

To estimate transmitting line mismatch, measurements were made according to the circuit given in Fig. 1.

The measurements were taken in two stages. At the first stage, normal climatic conditions (NCC) were established in the chamber. The microwave cable being tested, loaded to a matched load and connected to a vector network analyser, was passed through a climatic chamber. The points of cable passage through the chamber wall were gateways provided with elastic thermal plugs. Under such layout, the temperature impact affects the cable only, with no influence on the load parameters. The vector analyser was calibrated; the data of the standing wave ratio (SWR) and network total impedance values were recorded. Since at that moment the system is matched to the maximum, the load reflection coefficient was taken equal to Г₀. The readings of vector network analyser are shown in Fig. 2.

At the second stage, temperature in the climatic chamber was lowered down to a required value, and the cable was held so for a period of time as necessary for constant temperature setting along its entire length. Within the scope of investigations performed, the duration of transient processes was determined experimentally on the basis of statistical stability and repeatability of the measurement results.

In Fig. 3, differences can be observed between the characteristics of a transmitting line with temperature transition and a line under NCC. The SWR marker, set on a fixed frequency, shifted from antinode to node, which means a change in the wave phase. The SWR value grew from U₁ = 1.0262 to U₂ = 1.1152. The impedance, as represented by a Wolpert – Smith circular diagram, changed as well. The real part decreased from Ω₁ = 51.289 Ω tо Ω₂ = 50.595 Ω, while the imaginary part transitioned from the circular diagram capacitance half at –j230.39 mΩ to the inductance half at j5.4551 Ω. This is explained by the fact the characteristics of the cable part that had been in the chamber changed.

The aggregate of all the changes can be expressed through an additional reflection coefficient Г_t , which is an equivalent of all reflective non-uniformities occurring at the measuring line segments that are inside the chamber. From the above values we can calculate Г₀, as well as Г_общ = f{Г₀, Г_t } [4]:

(1)

(2)

It is known that for unitary reflection coefficient, transmission ratio К_п = 1 – Г. According to formula 8 from [5], system attenuation coefficient а_зс = ∏ⁿ_i=1(1/(1 – Г_i )), wherefrom it follows that а_зс = ∏ⁿ_i=1(1/(К_п)). Since the attenuation coefficient is a magnitude inverse to the transmission coefficient, we have it that the transmission coefficient of a non-uniformity system К_пс= ∏ⁿ_i=1(1 – Г_i ) [5]. Proceeding from this, if there are several successive reflection coefficients in the transmission line, with only their resultant value (Г_общ) known, then it is proposed to consider the latter as:

(3)

Using formula (3), we can represent Г_общ = 1 – (1 – Г₀) (1 – Г_t ) and calculate Г_t= 0.042.

Reflection coefficient Г_t depends on the length of the transmitting line part which is subjected to the temperature non-uniformity impact. Given in Table 1 are the results of impedance measurement of a cable with waveguide load, which demonstrate deterioration in the transmission parameters as the length of cable residing in the chamber is increased.

The results presented have been obtained on cable assemblies Huber + Suchner, of models Sucotest 18RF and Sucotest 18 Armored, and vector analyser Rohde&Schwarz ZVA24. It is worth mentioning that multiple measurements have also shown an increase in the mismatch effect in case of armoured cable assemblies intended for heavy-duty operating conditions and provided with additional protective layers for better strength and interference immunity. It occurs because the diameter of dielectric layers of those cables exceeds the diameter of standard cable assemblies more than twice. For this reason, changing of their linear dimensions under the action of temperature occurs more intensively, and hence, the impedance change is more substantial. The difference between parameter values of the line before its exposure to temperature and after recovery of normal temperature is no greater than 5 %. Validity of the presented inferences is confirmed by repeatability of the results obtained in the series of experiments.

3. Practical effect

The value of the coefficient of reflection occurring in a coaxial cable in a situation of significant thermal transition, as calculated in this paper, lies within the same order of magnitude as the reflection coefficients of the input and output connectors of the measuring instruments. Hence, parameter Г_t must also be accounted for in the measurements made in climatic chambers with pass-through transmission lines.

The practical effect can be considered when estimating measurement uncertainty of the reflection coefficient for a given test object (TO).

According to diagram given in Fig. 4, the reflection coefficient measurement uncertainty δG under NCC is equal to [2, 6]:

(4)

The first term under the root sign in formula (4) accounts for matching during calibration, while the other two – for matching during measurement. Since under the action of temperature upon those transmission line segments that are inside the chamber (highlighted in blue in Fig. 4) the transmission parameters become different from the calibration values, these changes can be expressed through additional reflection coefficients Г_Ω1 and Г_Ω2. For calculation of an updated uncertainty by formula (4), Г_A1 is substituted for Г_a1 = 1 – (1 – Г_A1) (1 – Г_Ω1) and Г_A2 – for Г_a2 = 1 – (1 – Г_A2) (1 – Г_Ω2) by formula (3). With Г_A1 =  Г_A2 = 0.11, δG = 0.24. At the same time, in the event of Г_Ω1 = Г_Ω2 = 0.042, δG = 0.29. A measurement uncertainty increase by 20 % is observed.

To understand the importance of uncertainty change, let us consider the following example. If the TO is expected to have a gain factor of at least 3 dB, while the measurement accuracy is ±0.24 dB, then it is only an article with transmission coefficient of 3.24 dB or higher that can be accepted based on the test results. On the other hand, if the accuracy is ±0.29 dB, then the threshold of transmission coefficient for acceptance purposes will rise to 3.29 dB, which, with all else being equal, will increase the number of rejected articles. The issue of setting an acceptance interval, tolerance limits, and a guard band is considered in more detail in [1].

The general rules and ways of decreasing mismatch during measurements are specified in [7]. However, in case of transmission lines passing through temperature non-uniformities, the following options should be considered as well:

a) calibration with cooled cables. This option is quite difficult to implement in practice, as it will imply placing calibration loads into climatic chamber (where their impedance will change under the action of temperature) and handling frozen cables, which become brittle and susceptible to damage at low temperatures;
b) use of gateways. Arrangement of separate gateways or heat-traced routes for the transmission lines in order to reduce cable length subjected to the low temperature effects;
c) drawing on the results of experimental measurements, one should account for the fact that reinforced cable assemblies, including armoured and interference-immune ones, are more susceptible to the mismatch effect under a significant thermal transition. Therefore, their application shall be justified, and in the absence of major interference or mechanical impacts on the transmission lines they shall be replaced by standard HF cables.

It should also be noted that the various methods of network mismatch correction introduced in [3] (e.g., measurements in the time domain) have a number of limitations and are only implemented in certain meter models, which do not support many measurement types (such as measurement of noise factor by the Y-method, measurement of spectral density of phase and amplitude noise).

Before conducting TO measurements, it is proposed to run an estimation of the applied cables according to configuration given in Fig. 1. In that case the length of cable part inside the climatic chamber shall correspond to that of the cable part which will be located inside the chamber when measuring TO parameters. In this way it can be possible to estimate in advance the mismatch degree of selected transmission line at a given test temperature value and then use these data in calculation of the measurement uncertainty.