# VSWR Calculations Summarized

### Key Takeaways

• Reflections in RF systems, quantified by VSWR, impact signal quality by causing destructive interference, leading to amplitude and phase variations in the frequency domain transfer function.

• High-power RF applications face potential hazards from reflections, which can carry substantial power back to the source, potentially damaging the system's source stage.

• Mismatch loss due to reflections, though typically small (often less than 1 dB), affects overall energy efficiency by dissipating power within the system, especially in scenarios of impedance mismatches

Diagram showing reflected vs. transmitted power in an RF system. VSWR calculations quantify how much is reflected vs. how much is transmitted

As an incident signal travels along a transmission line and reaches a load, a portion of its power is inevitably reflected down the line. The efficiency of power transfer is contingent upon the degree of impedance matching between the load and the transmission line. When the impedances are perfectly matched, the entire signal power is effectively transferred to the load. However, in practical scenarios, there is often some level of impedance mismatch, which consequently leads to the occurrence of back reflections. Quantifying the amount of reflected signal vs. transmitted signal is essential in designing and analyzing RF circuits. For this reason, Voltage Standing Wave Ratio (VSWR) serves as a crucial metric for assessing the efficiency of radio frequency (RF) power transmission. Read on as we delve into VSWR calculations.

Various Methods of VSWR Calculations

 VSWR Calculation Related Notes VSWR Calculation using maximum voltage along the transmission line divided by the minimum voltage VSWR Calculation using voltages associated with the forward and reflected waves. VSWR calculation using the reflection coefficient,  Γ. Representing the ratio of the reflected current or voltage vector to the forward current or voltage. When employing these power meters, VSWR calculation uses measurements of forward and reverse power.

## What Is VSWR?

In essence, Voltage Standing Wave Ratio (VSWR) measures how effectively RF power is transmitted through a transmission line to a load. It is quantified as the ratio between the maximum and minimum amplitudes (usually in terms of voltage, sometimes current) of the corresponding field components on a transmission line that supplies an antenna or other RF load.  VSWR  is calculated as a fraction but often is expressed as a ratio, such as 2:1 or 5:1, with a perfect impedance match resulting in a ratio of 1:1 and a complete mismatch, like a short or open circuit, yielding an infinite ratio (∞:1). When expressed as a fraction, its values range from 1 to positive infinity.

To illustrate the practical implications of standing waves, consider microwave ovens, where standing waves are responsible for uneven cooking (partially mitigated by turntables). The wavelength of a 2.45 GHz signal in a microwave oven is about 12 centimeters, resulting in nulls in the radiation and heating that are separated by a distance roughly equal to the wavelength.

### VSWR Specifics

In some cases, VSWR is used as a simplified figure of merit for impedance matching. However, this simplification and its limited definition can sometimes lead to confusion, particularly regarding source-to-load matching. Technically, VSWR is derived from the ratio of the load impedance to the characteristic impedance of the transmission line in which standing waves are present rather than being specific to the source-to-load match. Consequently, many prefer to consider VSWR as a figure of merit and employ the reflection coefficient when dealing with problem-solving.

## VSWR Calculations Summarized

The definition of the Voltage Standing Wave Ratio (VSWR) specifies that it is the maximum voltage along the transmission line divided by the minimum voltage. These voltage variations occur due to the combination of voltage components stemming from both the forward power and the reflected power.

This relationship can also be articulated in terms of the voltages associated with the forward and reflected waves. In essence, within a transmission line, two waves coexist: the forward wave and the reflected wave. The portion of the forward wave that does not become part of the reflected wave is transmitted further down the line.

### VSWR Using the Reflection Coefficient

VSWR is also related to the reflection coefficient, a commonly encountered formula in its calculation. The reflection coefficient, denoted as Γ, represents the ratio of the reflected current or voltage vector to the forward current or voltage.

Where Γ is the reflection coefficient, ZL is the load impedance, and Z0 the source impedance. Γ ranges from -1 (indicating a shorted load) to +1 (indicating an open load), and it reaches 0 when the load's impedance is perfectly matched. Notably, the reflection coefficient is a complex number that provides measurement capabilities for power assessment. This reflection coefficient is determined based on the complex load impedance and the characteristic impedance of the transmission line, both of which may potentially be complex numbers.

### VSWR Using Forward and Reflect Powers

Directional power meters find frequent application in quantifying power in watts or its multiples. When employing these power meters, it proves advantageous to have the capability to translate the measurements of forward and reverse power into a VSWR value. Considering that power is directly proportional to the square of the voltage, it becomes straightforward to formulate a VSWR equation using the readings of forward and reverse power.

### Other Quantifications of Reflected vs. Transmitted Power

• Return Loss (RL) quantifies the power loss redirected back into the system from the load and is typically expressed in decibels (dB). A higher return loss value signifies a greater amount of power lost at the load.

• Mismatch Loss (ML) serves as a measurement that characterizes the power unattainable at the load due to the presence of reflected waves. It quantifies the power dissipated within the system due to impedance mismatches.

• Reflection Coefficient (RC or gamma, as previously mentioned) provides insight into the extent of electromagnetic wave reflection caused by an impedance discontinuity within the transmission medium. This coefficient is the ratio between the amplitude of the reflected wave and the incident wave at the junction. Notably, the magnitude of the reflection coefficient remains unaffected by the length of the transmission line but relies solely on the load impedance and the transmission line impedance.

## Why Having a Good VSWR Is Important: Results of Reflections

Reflections play a significant role in RF systems, leading to various consequences and effects:

• Destructive Interference: Multiple reflections within the system can result in destructive interference, manifesting as amplitude and phase ripple in the system's frequency domain transfer function (S21). This interference leads to a degradation in amplitude flatness and dispersion.

• High-Power Hazards: In high-power applications, such as the interface between a transmitter and an antenna, reflections carry a substantial amount of power that has the potential to damage the source stage of the system.

• Mismatch Loss: Reflections contribute to the loss of energy, often referred to as mismatch loss. Typically, this loss is relatively small, usually less than 1 dB.

• Voltage Variations: Mismatched impedances in a real system result in the reflection of power back toward the source, akin to an echo. These reflections introduce constructive and destructive interference, leading to voltage peaks and valleys that vary with time and distance along the transmission line.

• Ideal vs. Real Systems: In an ideal system, voltage remains constant, resulting in a VSWR of 1.0 (often expressed as a ratio of 1:1). However, when reflections occur, voltage variations arise, causing a higher VSWR, for example, 1.2 (or 1.2:1). Increased VSWR is associated with reduced transmission line efficiency, ultimately affecting the overall efficiency of the transmitter and the system as a whole.

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