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.
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 (Zo). The characteristic impedance of one unit length of a transmission line (Fig. 2) can be calculated using Eq. 2:
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), Pin represents the power of the signal generated by the source, Pout 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 Pout will always be less than Pin.
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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The VSWR can be calculated with these equations for simpler circuits with few discontinuities. But for more complex circuits, finding the VSWR requires the analysis of incident, reflected, and resultant waves on a vector network analyzer (VNA) to determine the ratio of maximum standing-wave amplitude to minimum standing-wave amplitude. Figure 5 provides illustrations of waveforms observed on an analyzer for the incident, reflected, transmitted, and standing waves propagating through the RF system of Fig. 4 at two different instances in time. At the first instant, the output from the source, which is a 1 Vpp sine wave, is in phase with the reflected signal. Therefore, at this time, the amplitude of the standing wave (1.2 Vpp) is the vector sum of the voltages of the incident (1 Vpp) and reflected waves (0.2 Vpp) This is also the largest possible magnitude of the standing wave. At the second time instant, the incident and reflected waves are 180 deg. out of phase from each other. Therefore, the magnitude of the standing wave (0.8 Vpp) at this time is the smallest possible value and is the difference between (or vector sum of) the voltages of the incident (1 Vpp) and reflected waves (0.2 Vpp).
If the maximum and minimum values of the standing wave are known, the VSWR for the system of Fig. 4 can be calculated:
The VSWR can also be used to calculate the return loss:
Total transmission-line insertion loss is usually the sum of the losses caused by power dissipated in the line, also known as conductive or resistive loss, and the losses due to reflection, which are caused by impedance mismatches in the system. In the RF system shown in Fig. 6, a 50-W source and load are connected via a 1-m, 75-W coaxial cable. The total power reflected in this case is the result of two impedance discontinuities, the first between the source and transmission line and the second between the transmission line and load.
Even assuming that the transmission line of Fig. 6 is lossless, the graph on the left-hand side of Fig. 7 shows as much as 0.7 dB of insertion loss solely due to impedance discontinuities in the system. The distance between peaks and valleys in the graph depends primarily on the length of cable used. The graph on the right-hand side of Fig. 7 assumes that the transmission line has some conductive and resistive loss. The slope of the line in this graph is representative of the conductive and dielectric losses in the cable, while the ripple is due to the variation of return loss over frequency (as much as 0.7 dB in this example).
Reflections occur not only in mismatched RF systems but also in mismatched RF system components. For this reason, impedance matching is a concern not only for the end-user but also for the manufacturer of RF instruments and devices such as generators, analyzers, and switches. A PXI RF switch, for example, consists of several different components including printed-circuit-board (PCB) traces, internal cables, and the RF relay. Impedance mismatches between any of these components can severely affect the VSWR and return-loss specifications of the switch. Because RF switch module design and components differ so much from one vendor to another, each product's VSWR and insertion loss specifications should be checked to ensure that the magnitude of potential signal reflections caused by the switch, as well as examine insertion loss to determine if the RF switch module fits the needs of a particular test system.
A high-performance RF switch uses components and design that minimize impedance mismatches and keep insertion loss and reflections to a minimum to reduce measurement errors at higher frequencies. The quality of the actual relay used in the RF switch for example can have a colossal impact on its performance metrics. PCB mounted relays and coaxial switches are the two most common relay types used for constructing RF switch modules.
PCB mounted relays are available in several configurations including Form C single-pole double-throw (SPDT) relays. Multiple SPDT relays can be mounted on a PCB to build larger topologies such as multiplexers (SP4T and higher throw counts) or switch matrices. The model PXI-2547 50-W, 2.7-GHz, 8 1 multiplexer from National Instruments (www.ni.com), for example, is constructed using seven Form C PCB-mount SPDT relays.
Several vendors produce PCB mount relays for building multiplexers, and some models have acceptable performance up to several gigahertz. Because, in PCB mount designs, the relay leads are soldered to PCB, the switch module manufacturer must find a way to interface I/O connectors to the relays in an impedance-controlled manner. This requires using appropriate length PCB traces with suitable geometries, and high-quality connectors, and cables. A 75-W switch module using 50-W PCB traces is an example of a poorly designed module. Such a product will cause significant power loss on high-frequency signals due to impedance mismatches between the PCB trace and other components used to construct the switch. For these reasons, switch manufacturer design expertise plays a major role in determining the performance of modules that use PCB mounted devices. Although the internal impedance of the relays cannot be changed, the usage of appropriate design techniques can minimize the effect of reflections caused by impedance discontinuities. In the case of the NI PXI-2547 (Fig. 8), careful design considerations have helped keep insertion loss specifications well under 3 dB (typically less than 1.6 dB at the bandwidth of 2.7 GHz).
Modules that use coaxial switches or "cans" have several performance advantages over PCB mounted components. Because their entire RF transmission path can be contained within the housing with coaxial connectors providing the interface to test signals, coaxial switches can achieve low insertion loss. However, they do so at a higher cost than PCB-mount relays, while also taking up more space in the system. The National Instruments PXI-2596 26.5-GHz dual 6 1 multiplexer is an example of a coaxial-switch-based module, with less than 0.6 dB insertion loss at 26.5 GHz.
As mentioned earlier, switch module design is more important in PCB mount switch modules because, unlike coaxial switches, interfacing to the relay in such modules is done through separate cables and PCB traces. Connectors can often be a source of signal reflection, so they must be chosen carefully. In the case of most PCB mount designs, the highest frequency at which a module needs to operate determines the connector type used. The SMA connector, which offers performance in a small footprint, is a common choice for most 50-W applications. Their 50-W characteristic impedance makes them unsuitable for use in 75-W switch modules, however.
The PCB trace must also be considered when designing a PCB-mount switch module. PCB trace impedance, which must be matched with the relay and connectors, depends on the geometry of the copper and dielectric material used. The most common transmission-line types for switch module PCB construction are microstrip, stripline, and coplanar waveguide (CPW). Each has its strengths and weaknesses. For example, stripline offers superior isolation to that of the microstrip. However, because stripline traces need a ground plane above and below the signal trace, they require via-holes (which are difficult to impedance match) for good electrical connections. CPW can maintain characteristic impedance even with changes in trace width, although the width of the gap to ground must be changed accordingly.
It is important to consider all of these factors when designing an RF switch system. High-quality RF products are integral to all high-performance RF test systems. Yet they cannot compensate for poor system design. Even the best, most expensive 50-W RF switch can cause significant reflections if used to route signals in a 75-W test environment. For this reason, a high-performance RF measurement system should always incorporate impedance-matched components.