Impedance mismatches cause reflections, an unwanted effect in high-frequency test systems. For AC signals, any change in dielectric constant between materials can result in a change in characteristic impedances and an impedance mismatch. For example, when a sine wave travels from a 40.9-W transmission line and a 50-W load, some of its energy will be reflected back into the transmission line. Understanding how and why signals reflect can lead to improved test setups and measurements, especially at higher frequencies.

Although power loss due to reflections is a phenomenon applicable to all AC systems, measurement errors due to such power loss become noteworthy only when the length of the transmission line in the system is greater than 1/100th the wavelength of the signal traversing through it. Because RF signals have short wavelengths, they are more susceptible to power loss due to reflections than lower-frequency signals.

The relationship between cable length and signal wavelength can be shown with an example comparing the propagation characteristics of a 1 MHz sine wave with a 1 GHz sine wave through a 1 m long coaxial cable. The wavelength of both signals can be calculated using Eq. 1.

where:
λ = the wavelength of the signal,
f = its frequency, and
VF = the velocity factor of the cable. Assuming the cable type in both systems has a velocity factor of 0.66, the following values result:

For a signal (signal 1) with frequency of 1 MHz,

For a signal (signal 2) with frequency of 1 GHz,

The length of cable is relatively small compared to the wavelength of signal 1 (Fig. 1). Any variations in potential at different points along the cable are negligible as a result. Because signal 1 does not traverse the cable in the form of a wave, it does not suffer power loss due to reflections. But the wavelength of signal 2 is one-fifth the length of the cable so that five cycles of signal 2 propagation through the cable at any instant. This shorter wavelength signal assumes the form of a wave when propagating through the cable, and will be reflected at junctions with different characteristic impedances.

The characteristic impedance of an RF component is not a DC resistance. Rather, it can be defined for a given point on a transmission line as the ratio of a single pair of current and voltage waves at that point in the absence of all reflections. In practicality, the frequency and per-unit resistance, conductance, capacitance, and inductance of a line determine this voltage and current ratio. Thus, they also define characteristic impedance (Z_o). The characteristic impedance of one unit length of a transmission line (Fig. 2) can be calculated using Eq. 2:

where:
L = the inductance per unit length,
R = the resistance per unit length,
G = the conductance per unit length,
C = the capacitance per unit length,
Ω = 2pf, and
j = (–1)^0.5

A typical RF transmission system consists of a source that generates a signal, a transmission line to transport the signal, and a load to analyze or broadcast the signal. In the example system (Fig .3), P_in represents the power of the signal generated by the source, P_out is the signal power at the output of the transmission line, and Preflected is the power loss due to signal reflections arising from impedance mismatches in hardware. Because of manufacturing tolerances and material defects, real-world hardware will always suffer some mismatches and the value of Preflected will never be zero. Therefore, in real-world systems, the value of P_out will always be less than P_in.

Power loss due to reflections can be measured in several ways. One is by calculating return loss, which is a logarithmic ratio of the power of the signal reflected back at the source to the power emitted by the source:

Return loss values range from infinity for a perfectly matched system (all components have identical characteristic impedance values) to zero for open and short circuits. Voltage standing-wave ratio (VSWR) is another measure of impedance matching and reflected power in RF systems. As its name implies, VSWR is the ratio of the largest to the smallest amplitude values of the standing wave created by the combination of the incident and reflected waveforms. VSWR values range from one for a perfectly matched system to infinity for an open or short circuit.

To better understand VSWR, the system of Fig. 4 will be used as an example. The power originating from the source is assumed to be constant. Any decrease in signal power reflected back to the source results in a corresponding decrease in signal power reaching the load. Reflections due to component impedance mismatches occur when the wave traveling through the 75-W coaxial cable encounters a 50-W termination. In order to calculate VSWR for this example, the reflection coefficient (Γ) must first be found:

The value of the reflection coefficient shows that 20 percent of the incident wave will be reflected back to the discontinuity between the transmission line and the load. This value can then be used to calculate VSWR of the system:

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