Measuring VSWR to quantify impedance mismatch in transmission lines

Definition and background

　　In RF transmission systems, the standing wave ratio (SWR) is used to measure the efficiency of the RF signal from the power source through the transmission line to the load. For example, a power amplifier is connected to an antenna through a transmission line.

　　SWR reflects the ratio of the incident wave to the reflected wave. The higher the SWR, the lower the transmission line efficiency and the greater the reflected energy, which may cause damage to the transmitter and reduce the transmission efficiency. Since SWR is usually expressed as a voltage ratio, it is also called voltage standing wave ratio (VSWR).

　　VSWR and System Efficiency

　　An ideal system is to transfer 100% of the energy from the power source to the load, which requires the signal source impedance, the characteristic impedance of the transmission line and other connectors to be accurately matched with the load impedance. Since there is no interference in the ideal transmission process, the signal AC voltage remains the same at both ends of the transmission line.

　　In real systems, impedance mismatch will cause part of the power to be reflected back to the signal source (like an echo). Reflections cause additive and destructive interference, resulting in voltage peaks and troughs on the transmission line at different times and distances. VSWR is used to measure the changes in these voltages. It is the ratio of the highest voltage to the lowest voltage at any location on the transmission line.

　　Since the voltage remains constant in an ideal system, its VSWR is 1.0, usually expressed as 1:1. When reflection occurs, the voltage changes and the VSWR increases, for example, making the VSWR reach 1.2 or 1.2:1.

　　Reflected Energy

　　When an incident wave reaches a boundary, such as a load through a lossless transmission line (Figure 1), part of the energy is transmitted to the load, while part of the energy is reflected back. The reflection coefficient represents the ratio of the incident wave to the reflected wave:

　　Γ = V-/V+ (Equation 1)

　　Where V- is the reflected wave and V+ is the incident wave. The relationship between VSWR and voltage reflection coefficient (Γ) is:

　　VSWR = （1 + |Γ|）/（1 – |Γ|）（式2）

　　Figure 1. Transmission line circuit illustrating the impedance mismatch between the transmission line and the load.
The reflection at the boundary is Γ, with the incident wave being V+ and the reflected wave being V-.

　　VSWR can be measured directly using an SWR meter. RF test instruments such as vector network analyzers (VNA) can be used to measure the reflection coefficients of the input port (S11) and the output port (S22). S11 and S22 are equivalent to the reflection coefficients Γ of the input and output ports. VNAs mathematical models can also be used to directly calculate and characterize VSWR.

　　The return loss of the input and output ports can be calculated using the reflection coefficient S11 or S22:

　　RLIN = 20log10|S11| dB (Equation 3)

　　RLOUT = 20log10|S22| dB (Equation 4)

　　The reflection coefficient can be calculated from the characteristic impedance of the transmission line and the load impedance using the following formula:

　　Γ = (ZL - ZO)/(ZL + ZO)(式5)

　　Where ZL is the load impedance and ZO is the characteristic impedance of the transmission line (Figure 1).

　　VSWR can also be expressed in terms of ZL and ZO. Substituting equation 5 into equation 2, we get:

　　VSWR = ［1 + |(ZL - ZO)/(ZL + ZO)|］/［1 - |(ZL - ZO)/(ZL + ZO)|］ = ＼(ZL + ZO + |ZL - ZO|)/ (ZL + ZO - |ZL - ZO|)

　　如果ZL > ZO, |ZL - ZO| = ZL − ZO

　　but:

　　VSWR = (ZL + ZO + ZL - ZO)/(ZL + ZO - ZL + ZO) = ZL/ZO.(式6)

　　如果ZL < ZO, |ZL - ZO| = ZO - ZL

　　but:

　　VSWR = (ZL + ZO + ZO - ZL)/(ZL + ZO - ZO + ZL) = ZO/ZL.(式7)

　　We note that the VSWR mentioned above is a ratio relative to 1, for example, the VSWR is 1.5:1. There are two special cases of VSWR, ∞:1 and 1:1. When the load is open, the VSWR is ∞:1, and when the load is completely matched with the characteristic impedance of the transmission line, the VSWR is 1:1.

　　The definition of VSWR comes from the standing wave generated by the transmission line itself:

　　VSWR = |VMAX|/|VMIN|（8／）

　　Among them, VMAX is the maximum value of the standing wave voltage on the transmission line, and VMIN is the minimum value of the standing wave voltage on the transmission line. The maximum value is generated by the superposition of the incident wave and the reflected wave in the same direction. Therefore:

　　VMAX = V+ + V- (Equation 9)

　　The minimum is generated by the reverse superposition of the incident and reflected waves:

　　VMIN = V+ - V-（式10）

　　Substituting equation 9 and equation 10 into equation 8, we can get:

　　VSWR = |VMAX|/|VMIN| = （V+ + V-）/（V+ - V-）（式11）

　　Substituting equation 1 into equation 11, we get:

　　VSWR = V+（1 + |Γ|）/（V+（1 - |Γ|） = （1 + |Γ|）/（1 – |Γ|)(式12）

　　Formula 12 is equal to Formula 2 in this paper.

　　VSWR detection system

　　The MAX2016 is a dual-channel logarithmic detector/controller that is used with a circulator and attenuator to monitor the VSWR/return loss of an antenna. The MAX2016 outputs the difference between the two power detectors.

　　The MAX2016, together with the MAX5402 digital potentiometer and the MAX1116/MAX1117 ADC, forms a complete VSWR monitoring system (Figure 2). The digital potentiometer is used as a voltage divider for the MAX2016 output reference voltage. The internal voltage reference provides a typical current of 2mA, which is used to set the threshold voltage (CSETL) of the internal comparator. When the output voltage is above or below the threshold voltage (COUTL), an alarm output is generated. The operating voltage of the MAX1116 ADC is 2.7V to 3.6V, and the operating voltage of the MAX1117 ADC is 4.5V to 5.5V. The ADC can also use the MAX2216 to provide a voltage reference. The ADC and the microcontroller jointly monitor the VSWR of the antenna.

　　Figure 2. The companion ADC is used to build a real-time VSWR monitoring system,
and an external digital potentiometer is used to configure the comparator output (COUTL) alarm threshold.

　　Summarize

　　This tutorial explains that SWR or VSWR is a way to measure the imperfections and efficiency of a transmission line. VSWR is related to the reflection coefficient. A higher ratio indicates a greater mismatch, while 1:1 is a perfect match. Match or mismatch is determined by the maximum and minimum amplitude of the standing wave. SWR is the ratio of transmitted energy to reflected energy. The MAX2016 is used as an example to illustrate how to create a system to monitor the VSWR of an antenna.