Techniques for advanced cable testing

August 17th, 2016, Published in Articles: EngineerIT


To successfully test or troubleshoot anomalies on transmission lines, an understanding of transmission line theory and the limitations associated with coaxial and waveguide transmission lines is required.

When the purpose of a transmission line is to interconnect devices and distribute signals, the physical geometries of the conductors and dielectric properties of the supporting material will be uniform across the length of the line. When a change occurs in these characteristics, such as point of contact between two different lines or damage along the line, these discontinuities may result in signal reflection and higher line attenuation.

Fig. 1: Frequency response and TDR response of a short coaxial cable terminated in a short.

Fig. 1: Frequency response and TDR response of a short coaxial cable terminated in a short.

Characterising and troubleshooting transmission lines and systems require measuring the performance in both the frequency domain and time domain.

Frequency domain measurements are typically used to verify the RF performance over the specified frequency range of interest. Time domain and distance domain measurements are typically used to physically locate discontinuities along the line. Figs. 1a and 1b show typical frequency domain and time domain measurements. Fig. 1a shows the measured amplitude and phase response for the reflected (S11) signal over a range of 12 GHz. In this case, the device under test (DUT) is a short length of coaxial cable terminated with a short.

Fig. 1b shows the measured input impedance of the same cable/short as a function of time. The time domain data is shown in a time domain reflectometry (TDR) format which makes it easy to identify the 50 Ω cable and the location of the short. This application note will provide techniques to enable this.

Measurements made on a transmission line already installed into a system can be uniquely challenging as both ends of the line may be physically separated, making it impossible to directly connect both ends of the line to the test equipment. Fortunately, there are measurement techniques available for characterising long transmission lines when both ends are physically separated in the system.

Fig. 2: Cross sectional geometry for coaxial cable and two-wire transmission lines.

Fig. 2: Cross sectional geometry for coaxial cable and two-wire transmission lines.

A transmission line can have a variety of physical configurations which support propagation of energy. Fig. 2 shows two popular types, namely the coaxial cable and two-wire line. Both of these transmission lines were investigated in the early days of telephone, television and telegraph as suitable for signal transmission over large distances. The characteristic impedance, Zo, of the lines is related to the cross sectional dimensions of the two conductors and dielectric constant of the insulating material. For example, Fig. 2a shows the geometry of a coaxial line with centre conductor diameter defined as d and outer conductor diameter, measured from the inner surface of the outer conductor, as D. Typically an insulator, having dielectric constant εr, is used to hold the inner conductor symmetrically within the outer conductor. The characteristic impedance is related to the ratio of the diameters of outer to inner conductors. The characteristic impedance of the line is inversely related to the square root of the dielectric constant. Typical impedance values for coaxial cable are 50 Ω and 75 Ω. Fig. 2b shows the cross-sectional geometry of a two-wire transmission line with wire diameter defined as d and wire spacing D. In this figure, the wires are surrounded by air but typically the wires are coated in an insulator to maintain the correct spacing between the wires for a specific characteristic impedance. The two-wire configuration has been used in 300 Ω twin-lead, 100 Ω twin axial, and 100 Ω twisted pair. Table 1 shows the equation for calculating the characteristic impedance of the coaxial cable and two-wire.

Selection of the characteristic impedance is often related to propagation characteristics of the transmission line. For example, Fig. 3 shows the curves for the attenuation, power handling and voltage breakdown on a coaxial cable as a function of ratio D/d. The values shown in the figure have all been normalised to their respective minimum or maximum values for comparison purposes.

Fig. 3: Propagation characteristics of coaxial cable as a function of D/d.

Fig. 3: Propagation characteristics of coaxial cable as a function of D/d.

From Fig. 3, coaxial cables have a minimum attenuation when the D/d ratio is 3,6. Using the equation in Table 1, this leads to an impedance of 76,9 Ωs. As the attenuation curve is fairly broad in the range around this value, the broadcast cable industry settled on 75 Ωs for the transmission of signals over very long distances. For the relative attenuation curve shown here, it is assumed that the operating frequency is fixed. In this case, the attenuation changes as a function of conductor geometry and associated impedance. When considering that the operating frequency could change, the dielectric losses in coaxial line are linearly proportional to frequency and the conductor losses are proportional to the square root of the frequency so that at the higher frequencies, the dielectric loss of the medium is more important.

When examining the power handling capability of coaxial cable, the peak power capability occurs when the D/d ratio is 1,65 resulting in an impedance of 30 Ωs. The D/d ratio with the highest voltage breakdown occurs at 2,7 or equivalently 59,6 Ωs. As the voltage breakdown curve is also relatively flat in the area of 59,6 Ωs, a compromise was reached between power and voltage breakdown to settle on 50 Ωs as the impedance for most other systems. In this case, the voltage breakdown is 98% of the peak and the power handling is 86% of the peak. Other research includes examining the performance of braided, polyethylene filled coaxial cable and has shown that cables for general-purpose use are optimised at 50 Ωs and for those applications where low attenuation is of prime importance, 75 Ωs is ideal.

Other key parameters when selecting transmission lines are shielding requirements for cable-to-cable crosstalk and immunity to external interference. Coaxial lines abandon electrical balance and depend entirely on metallic shielding resulting in a higher cost when compared to balanced two-wire lines. Two-wire transmission lines often operate in a balanced feed where the two wires are of the same gauge and material. The crosstalk between two adjacent coaxial cables falls off very rapidly as the frequency is increased. This effect is different for unshielded two-wire systems that rely on balance to limit the coupling. For both types of lines, more shielding is often required to limit external interference than is required to limit cross talk. This is one reason that some two-wire systems introduce a shielded conductor surrounding the two-wires, often called twinaxial, which has controlled impedance with improved propagation velocity over a larger range of frequencies. Twinaxial is often designed for 100 Ω characteristic impedance.

Table 1: Equation for characteristic impedance.

Table 1: Equation for characteristic impedance.

Twisted-pair is another two-wire transmission line that is extremely popular in data networking applications including the  CAT-5 and CAT-6 cable series. These cables combine four pairs of wires bundled within a common outer sheath. Fig. 4b shows the cross section of a twisted pair cable. This configuration allows four independent signals to travel in parallel along the same cable to improve the total data capacity of the cable. Inexpensive twisted-pair cables are typically unshielded. Higher operating frequency can be achieved when a common shield is placed around the four pairs of wire. Twisted-pair lines are designed for 100 Ω impedance.

Microstrip and stripline are transmission lines that are primarily used in printed circuit board and integrated circuit applications. They are ideal for connecting transmission lines with surface mount components including integrated circuits in small packages. The geometry of the conductors and dielectric properties of the supporting material determine the impedance and propagation characteristics for the line. While the coaxial and other two-wire cables are appropriate for use over long distances, microstrip and stripline are used within small devices including radio and radar components and systems.

The last transmission line type to mention is waveguide. This is the one transmission line structure that does not require two separate conductors. This hollow tube can be constructed using a rectangular cross section, or using circular or elliptical cross sections. Electromagnetic field theory is required to understand how the signal travels along this rigid transmission line but key features for using waveguide are the relatively low insertion loss and high power capability.

Transmission line phase and velocity factor

In the context of transmission line propagation, what is the signal frequency, and associated wavelength, that makes a cable or other two-wire system a transmission line? Considering the nature of a signal propagating along a transmission line, the answer is relatively simple: when its physical length is comparable to the wavelength for the signal of interest. At one extreme, when a cable or two-wire line is operating with a signal at DC or very low frequency, the voltage and current values are the same at all points along the line and therefore would not be considered a transmission line. As the operating frequency is increased, the voltage and current values become functions of position as the cable length becomes proportional to the wavelength.

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