The characteristic impedance is a very important electrical parameter when designing and selecting coaxial RF cables. This article introduces several commonly used characteristic impedance measurement methods in production from the perspective of engineering applications.

Coaxial RF cables are widely used as transmission lines in communication systems. The characteristic impedance is the first electrical parameter to consider when designing and selecting coaxial RF cables. The maximum power transmission and minimum signal reflection depend on the characteristic impedance of the cable and its matching with other components in the system. In practical applications, the working state of the transmission line can be conveniently analyzed based on the characteristic impedance of the cable, so it is crucial to accurately measure its value.

I. Definition of Characteristic Impedance

When electromagnetic waves propagate in a cable, there are usually forward-propagating incident waves and backward-propagating reflected waves, and the incident waves and reflected waves superimpose to form standing waves. The ratio of the total voltage to the total current at any point on the transmission line is defined as the input impedance of that point looking towards the load end. In general, the input impedance of the transmission line is related not only to the length of the line but also to the frequency. However, when the transmission line is infinitely long, there are only forward-propagating waves (traveling waves) on the transmission line. At this time, the input impedance at any point on the transmission line is independent of the length of the line and is equal to a constant value Zc, which is called the characteristic impedance of the transmission line.

In addition, when the end of the transmission line is connected to a constant pure resistive load, the input impedance at any point on the transmission line is also equal everywhere and independent of the length of the line. This constant resistance value is the characteristic impedance of the transmission line. The characteristic impedance Zc of the coaxial RF cable depends only on the diameter of the inner and outer conductors of the transmission line and the equivalent dielectric constant of the filling medium between them, and is independent of the length of the line.

II. Measurement Methods of Characteristic Impedance

The characteristic impedance of coaxial RF cables can be measured by frequency domain or time domain methods. The frequency domain method generally uses a vector network analyzer to test the performance of the cable. Because the vector network analyzer uses bandpass filters and digital filters, it has very low background noise, so it can accurately measure the characteristic impedance of the cable. According to the different transmission directions of the test signal, the frequency domain method can be divided into transmission measurement and reflection measurement. Among the currently commonly used measurement methods for the characteristic impedance of coaxial RF cables, the transmission phase method, the transmission phase difference method, and the open or short circuit resonance method belong to the transmission measurement in the frequency domain method, while the newer single connector measurement method belongs to the reflection measurement in the frequency domain method.

Transmission Phase Method The measurement principle of the transmission phase method is based on the relationship between the characteristic impedance Zc of the transmission line and the phase, frequency, and total capacitance of the cable:

Z=2πfC×10

(1) where ϕ is the absolute transmission phase of the cable sample being tested; f is the test frequency, in MHz; C is the total capacitance of the cable, in pF. As long as the total capacitance of the cable sample and its absolute phase at a certain frequency point are measured, the characteristic impedance of the cable can be calculated according to the above formula.

Transmission Phase Difference Method The measurement principle of the transmission phase difference method is based on the relationship between the characteristic impedance Zc of the transmission line and the phase transmission speed VP:

Z=C1

(2) where C is the capacitance per unit length of the cable. The phase change of the wave propagating in the transmission line is 2π, and the relationship between the phase transmission speed VP and the frequency difference Δf corresponding to the phase change of 2π is VP=Δf1, then

Z=ΔfC10

(3) As long as the frequency difference and the total capacitance of the cable are measured, the characteristic impedance of the cable can be calculated according to the above formula.

Open Circuit or Short Circuit Resonance Method When one end of the cable is open or short-circuited, the change in frequency will cause periodic changes in the input impedance of the cable, which is manifested as periodic changes in the detector reading. The difference between two adjacent parallel resonances or series resonances (i.e., two adjacent maximum or minimum values) is half a wavelength, i.e., a phase difference of π. As long as the frequency difference Δf′ (in MHz) between two adjacent maximum (or minimum) values on the cable sample is measured, and the total capacitance C of the sample cable (in pF) is measured according to the standard GB 4098.2-1983, the characteristic impedance of the cable can be calculated according to the following formula:

Z=Δf′C2π

(4)Single Connector Method When the terminal of the cable is connected to the load, the relationship between the input impedance Zin of the cable, the characteristic impedance Zc of the cable being tested, and the reflection coefficient T is:

Zin=Zc(1+T)/(1−T)

(5) When a vector network analyzer is used for reflection testing, the voltage standing wave ratio of the RF coaxial cable assembly can be measured through the S11 or S22 parameters. The reflection coefficient T reflects the degree of mismatch between the input impedance of the cable under test and the nominal impedance Z0 of the system. It has the following relationship with the input impedance Zin of the cable and the nominal impedance Z0 (50Ω or 75Ω) of the test system:

Z0=Zin(1+T)/(1−T)

(6) From the above formula, as long as we measure the reflection coefficient T, we can calculate the input impedance Zin of the cable. Since the reflection coefficient T is a vector, and the currently measured data is a scalar voltage standing wave ratio, and the reflection coefficient T can only obtain the input impedance, not the characteristic impedance, it must be measured by measuring the voltage standing wave ratio of a single RF connector to obtain the characteristic impedance of the cable. The measured voltage standing wave ratio of the cable assembly is the superposition of the standing wave ratios of two connectors and a section of cable, which includes the unevenness of the cable, impedance deviation, and discontinuity and impedance deviation of the connector.

The voltage standing wave ratio of the RF connector is mainly caused by the uneven impedance inside the connector and the deviation from the characteristic impedance of the cable. Since the characteristic impedance of the RF connector is easy to control (such as (50±0.5) Ψ), the uneven impedance inside it, including the standing wave ratio caused by the discontinuous capacitance generated by the size mutation, is very small, and at low frequencies (such as 200MHz) Below the section, the standing wave ratio of the connector is generally only around 1.005, much smaller than the voltage standing wave ratio of the cable assembly, so the voltage standing wave ratio of the connector can be ignored, but the reflection caused by the uneven impedance inside the measured cable cannot be ignored. During the test, this part of the impact should be eliminated, so that the main reflection source in a single connector comes from the deviation of the cable impedance from the standard impedance, and finally the characteristic impedance of the measured cable can be obtained directly by measuring the voltage standing wave ratio of a single connector.

In the RF band, the characteristic impedance of the RF cable is independent of frequency, so it is only necessary to measure it at any frequency within the 30～200MHz frequency range specified by the national standard GB 4098.3 "Measurement Method of Characteristic Impedance of RF Cables" using the transmission phase method. Since the error of the transmission phase difference method is relatively large, it is best to use it with caution. The single connector method is simple to operate, the measured data is accurate, and it is directly linked with the voltage standing wave ratio, has strong practicality, is a convenient and practical good method for measuring the characteristic impedance of RF cables, and is recommended for preferential use.

[Source: Fiber Optic and Cable and Its Application Technology]