VSWR(SWR) Calculation

About VSWR(SWR)
When setting up an antenna and transmitter system, it is important to avoid impedance mismatching anywhere in the system. Any mismatch means some proportion of the output wave is reflected back toward the transmitter and the system becomes inefficient. Mismatches can occur at interfaces between various equipment e.g. transmitter, cable and antenna. Antennas have impedance, which is typically 50 ohms (when antenna is of the correct dimensions). When reflection occurs, standing waves are produced in the cable.

What are Standing Waves
A load is connected to the end of the transmission line and the signal flows along it and enters the load. If the load impedance does not match with the transmission line impedance, then part of the travelling wave is reflected back towards the source.

When reflection occurs, these travel back down the transmission line and combine with the incident waves to produce standing waves. It is important to note that the resultant wave appears stationary like and does not propagate like a normal wave and does not transfer energy toward the load. The wave has areas of maximum and minimum amplitude called anti-nodes and nodes respectively.

When connecting the antenna, if a VSWR of 1.5 is produced, then power efficiency is 96%. When a VSWR of 3.0 is produced, then the power efficiency is 75%. In actual use, it is not recommended to exceed a VSWR of 3.
vswr

Formula for VSWR and reflection coefficient
Eq.1 - Reflection coefficient  Γ is defined as:

ZL = The value in ohms of the load (typically an antenna)
Zo = The Characteristic impedance of the transmission line in ohms

Calculated values are between -1 ≦ Γ ≦ 1.

#When value is “-1”.
Means 100% reflection occurs and no power is transferred to the load. The reflected wave is 180 degrees out of phase (inverted) with the incident wave.

#When value is “1”.
Means 100% reflection occurs and no power is transferred to the load. The reflected wave is in phase with the incident wave.

#When value is “0”.
Means no reflection occurs and all power is transferred to the load. (IDEAL)

Eq.2 - The VSWR or voltage standing wave ratio:


Given that ρ will vary from 0 to 1, the calculated values for VSWR will be from 1 through to infinity.

The ideal case is when ρ is 0, giving a VSWR of 1 or a 1:1 ratio.

With open circuit
This is an open circuit condition with no antenna connected. It means that ZL is infinite and the terms Zo will disappear in Eq.1, leaving  Γ=1 (100% reflection) and  ρ=1.
No power is transferred and VSWR will be infinite.

With short circuit
Imagine the end of the cable has a short circuit. It means ZL is 0 and the Eq.1 will calculate  Γ=-1 and  ρ=1.
No power is transferred and VSWR is infinite.

With correctly matched antenna.
When a correctly matched antenna is connected, then all energy is transferred to the antenna and is converted to radiation. ZL is 50 ohms and Eq.1 will calculate  Γ to be zero. Thus VSWR will be exactly 1.

With incorrectly matched antenna.
When an incorrectly matched antenna is connected, the impedance will no longer be 50 ohms and an impedance mismatch occurs and part of the energy is reflected back. The amount of energy reflected depends on the level of the mismatch and so VSWR will be a value above 1.

When using cable of incorrect characteristic impedance.
The cable / transmission line used to connect the antenna to the transmitter will need to be the correct characteristic impedance Zo. Typically, coaxial cables are 50ohms (75ohms for televisions and satellite) and their values will be printed on the cables themselves. The amount of energy reflected depends on the level of the mismatch and so VSWR will be a value above 1.




Instructions on how to use
- Please enter the values into the light and dark yellow boxes, then push ENTER key.

1. Confirm your cable characteristic impedance and enter into the box.

2. Confirm the load impedance, reflection coefficient, VSWR etc. and press ENTER to calculate.

3. If complete reflection occurs, then POWER REFLECT [%] shows 100% and Output Power graph shows 0%.
Look carefully at where it says D=0. Both waves become “in phase” (both circles moving together) or “Out of phase” (both circles moving in opposite direction) depending on the value of the reflection coefficient.

4. The output power can be calculated by subtracting Mismatch Loss (in dB) from Input Power (dBm) to give output power (dBm)

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