We have discussed the importance of impedance matching in RF systems. This section of the tutorial will elaborate on what happens when characteristic impedances of components in such systems are not matched. In the system depicted in Figure 5, an RF source is connected to a load via a transmission line that has a characteristic impedance of ZO. Some of the power traveling into the line makes it out the other side (Pout), some is dissipated in the resistance and conductance of the cable itself, and some is reflected back to the source (Preflected).
Figure 5. Illustrating Power Flow for a Simple Circuit
One measure of the amount of reflected power is return loss, which is a logarithmic ratio of the power of the signal reflected back to the source to the power output by the source. Values for return loss range from infinity, for a perfectly matched system, to zero for open or short circuits. Some signal sources are sensitive to power being reflected back to them and require an overall system performance with lower return loss designed to minimize impedance discontinuities and signal reflection. Return loss can be calculated using the following formula:
To understand reflection loss better, let us assume that the output power of the source is constant. In such a case, an increase in power of the signal reflected back to the source would cause a corresponding decrease in power of the signal that arrives at the load. Again, because variations in characteristic impedances of components within the system are what cause such signal reflections, it can be deduced that systems with poor impedance matching will experience more return loss than well matched systems.
VSWR (voltage standing-wave ratio) is another measure of impedance matching and reflected power in an RF system. As its name implies, VSWR is calculated by taking the ratio of the largest to the smallest amplitude values of the standing wave created by the combination of the incident and reflected waveforms. Values of VSWR range from one for a perfect impedance match to infinity for an open or short circuit.
A simple example using a single impedance discontinuity will be used to illustrate VSWR. In the circuit shown in figure 6, an incident wave traveling in a 75 Ω coaxial cable will encounter a 50 Ω termination. When this occurs a portion of that signal will be reflected back causing a standing wave. The location of the impedance discontinuity will be at distance x=0.
Figure 6. Single Impedance Discontinuity
The reflection coefficient (denoted as G) can be calculated using the following formula:
At one particular instant in time, the waveforms will look like those shown in Figure 6 below. The source is set to output a 1 Vpp sine wave. This particular scenario shows the largest possible magnitude of the standing wave because both the incident and reflected waves are in phase (the standing wave has an amplitude that is the vector sum of the incident and reflected wave). In Figure 7, it can be seen that the amplitude of the standing wave (in light blue) is 1.2 Vpp, which is the sum of amplitudes of the original signal (1 Vpp) and the reflected wave (0.2 Vpp)
Figure 7. Voltage Waveforms at Time Instant 1
The smallest possible standing wave must then occur when the incident and reflected waves are 180 deg out of phase. Figure 8 shows the behavior of all four waveforms at this time instant. You will notice that the amplitude of the standing wave is 0.8 V (amplitude of the original signal minus the amplitude of the standing wave)
Figure 8. Voltage Waveforms at Time Instant 2
If the standing waves for both time instants are put on the same graph, the magnitude difference is easy to see.
Figure 9. Standing Waveforms from Both Time Instants
To calculate VSWR for this interface, simply take the ratio of the largest standing wave to the smallest standing wave. In this case:
Because VSWR and return loss are two ways to measure the same property, you can use the following equations to convert between the two:
To understand these theoretical concepts better, let’s consider a practical example system in which a source and load with 50 Ω termination impedances will be connected to each other via a 1 m 75 Ω coaxial cable. The two impedance discontinuities in this system will both cause power to be reflected back to the source.
Figure 10. Circuit with Two Impedance Mismatches
If the transmission line is initially assumed to be lossless, the graph in Figure 11 shows that there is as much as 0.7 dB of insertion loss due exclusively to the reflections caused by the two impedance discontinuities. Recall that when power gets reflected back to the source it can never make it to the load, therefore this reflected power must also cause an increase in insertion loss, which is based on how much power makes it to the load. The distance between peaks and valleys in the graph is directly related to the length of cable used.
Figure 11. Insertion Loss due only to Power Reflection
For a cable model including conductive and resistive losses in the cable, Figure 12 shows the insertion loss performance of the system. The slope of the line is mainly due to conductive and dielectric losses in the cable, and the ripple is due to variation of return loss over frequency (as much as 0.7 dB in this example).
Figure 12. Total Insertion Loss for the Circuit in Figure 9