RF Coaxial Cables

Signal Integrity and Propagation
To explain how to maintain signal integrity, it is necessary to review how the signal is configured in a cable and how it propagates. Ignoring digital signals for this discussion we will identify the issues that deal with the integrity of a sine wave. Consider a coaxial cable consisting of an inner conductor surrounded by a dielectric material and then an outer conductor. The outer conductor may be a braid, a foil, or a solid metal.

An electromagnetic wave traveling in a coaxial cable produces an electric and a magnetic field between the inner conductor and the outer conductor (Figure 1). The electric (E field) is radial and varies in time. An alternating current flows along the inner conductor and the outer conductor. An oscillating magnetic field (H field) circles the inner conductor.

Figure 1
Electric field (E) and magnetic field (H) belong to the principal mode in a coaxial line.

The alternating current on a conductor is not spread throughout the conductor but is strongest at the surface and decays exponentially at points further into the conductor. This is called the skin effect. At a frequency of 1MHz, three skin depths is 0.0078" (95% of the current is within three skin depths of the surface) and at 10GHz three skin depths is 0.00078". As a result, the current is on the outer surface of the inner conductor and the inner surface of the outer conductor over the entire range of interest for most RF systems. The dimensions and material beyond several skin depths have no effect on the wave; gold plated plastic will propagate as well as gold plated copper at sufficiently high frequencies.

Attenuation
A wave loses energy (attenuates) in several ways:

Characteristic Impedance
A parameter which defines the behavior of a cable, connector, or any propagating system is Characteristic Impedance, Zo. The characteristic impedance of a lossless cable is related to the inductance per unit length, L, and the capacitance per unit length, C, as follows:

The equivalent circuit of a transmission line is shown in Figure 4. R represents the conductor resistance for a unit length.

Figure 4

For a coaxial cable the characteristic impedance is given by:

where "D" is the inner diameter of the outer conductor and "d" is the outer diameter of the inner conductor, respectively. Similar equations apply for other geometries such as two parallel wires.

As can be observed from this equation, the impedance is a function of the diameters. Generally the conductor diameter can be very accurately controlled, but the dielectric diameter can vary based on the accuracy of the process. If the impedance changes are a consistent spacing of one 1/4 wavelength, this can cause signifigant signal loss.

Reflections
When the characteristic impedance changes in a transmission line system, part of an incident wave is reflected. The reflection coefficient can be calculated as:

Where Vi and Zo are the incident voltage and impedance of the first media. VR and ZR represent the reflected voltage and impedance of the media that caused the reflection. The decibel loss due to reflection is given by:

VSWR
The traditional way to determine the reflection coefficient is to measure the standing wave caused by the superposition of the incident wave and the reflected wave. Traditionally the voltage is measured at a series of points using a slotted line. The ratio of the maximum divided by the minimum is the Voltage Standing Wave Ratio (VSWR). The VSWR is infinite for total reflections because the minimum voltage is zero. If no reflection occurs the VSWR is 1.0. VSWR and reflection coefficient are related as follows:

Present instrumentation measures the return loss.

Multiple Reflections
If there is a series of impedance changes, each one will cause a reflection. The total reflection is the vector addition of each of the individual coefficients accounting for the distance between discontinuities. Even though the calculations are difficult, a total VSWR can still be measured.