# Reflected Power and VSWR

Posted by Fred C (W6BSD) on Apr 25 2021

Our main goal as Amateur Radio Operators is to make sure that as much of the power coming out of the radio as possible is radiated by the antenna. The maximum power transfer occurs when the power source, the radio in our case, and the load or the antenna are a match. When the source and the load are a match, all the power is absorbed by the load. On the other hand, if there is a mismatch between the source and the load, some of the power is reflected back. Reflected power is always undesirable.

The maximum power transfer is achieved when the impedance of the source and the load match. In the ham world, we talk about an impedance of $$|50|\Omega$$. In reality, the impedance is a complex number consisting of both the real resistive part $$R$$ and the imaginary reactive part $$jZ$$ such as $$R+jZ\Omega$$. The resistive part does not change with frequency, but the reactive part will change.

The professional world uses Return Loss in dB to quantify the reverse power levels. We prefer to use the Voltage Standing Waver Ratio (VSWR) or commonly called SWR, in the amateur world.

• Return Loss is nothing more than the difference in dB between the forward and reflected power: $$F_P(\mathrm{dB}) - R_P(\mathrm{dB}) = R_L(\mathrm{dB})$$. For example, if we have a forward power of $$20dB$$ and a reflected power of $$3.5dB$$, we have a return loss of $$16.5dB$$. The return loss is always a positive number and higher is better.

• The Voltage Standing Wave Ratio is the ratio between the highest and the lowest voltage in the standing wave. The following graph shows a simulation of a transmission. The green wave represents the forward power, the red wave represents the reflected power, and the blue wave represents the standing wave. The forward and reflected power remains constant. The blue wave combines voltage of the forward and reflected power, and rise and fall over time. In this following example, the Standing Wave Ratio is 3:1.

$$VSWR = \frac{Vmax}{Vmin}\\ ...\\ \frac{1.5}{0.5} = 3$$

See a standing wave animation where 100% of the power is reflected.

The VSWR can easily be converted into Return Loss ( $$R_L$$ ) using the following formula:

$$R_L = 20 \log_{10}{\left(\frac{VSWR+1}{VSWR-1}\right)}$$

The following equation is especially useful when using a directional power meter. It allows you to calculate the VSWR from the forward and reverse power.

$$VSWR = \frac{1+\sqrt{\frac{P_{ref}}{P_{fwd}}}}{1-\sqrt{\frac{P_{ref}}{P_{fwd}}}}$$

## Reflected power

The following graph and table show the percentage of reflected power versus VSWR

VSWR % Reflected
1:1 0
1.5:1 4
2:1 11
2.5:1 18
3:1 25
4:1 36
5:1 44
6:1 51

The percentage of reflected power climbs fast. With a 1:1 VSWR, 100% of the energy gets absorbed by the antenna. At 2:1 VSWR, 11% of the power is reflected, and with 3:1, 1/4 of the power is reflected. When we reach 6:1, half of the energy is reflected back to the transmitter.

## Dealing with reflected power

There are two particular cases: short and open. In these two cases, 100% of the power is reflected back to the source.

Having too much reflected power can cause malfunction or failure of the source (the transmitter). Our modern transmitters have a built-in foldback circuit that reduces the transmitted power to a reasonable level. For example, suppose our transmitter is safe with 25 Watt of reflected power. With a low mismatch of 2:1 VSWR and 100 Watt of forward power, only 4 Watts are reflected. With a 4:1 VSWR, we have 36 Watt of reflected power, exceeding the 25 Watt safe limit. The transmitter automatically cuts down the forward power to 90 Watts. The reflected energy is now down to a safe level at 22 Watt.

Most of today's ham radio transmitters can safely handle a 3:1 VSWR before the foldback circuit is triggered.

## Maximizing the power transfer

To ensure maximum power transfer, a circuitry that corrects the mismatch is placed between the source and the load. It is best to put the matching network1 as close as possible to the source of the mismatch. The matching networks use only reactive components such as inductances and capacitances. By carefully selecting the capacitance and inductance values, we can change the overall load complex impedance and match the purely resistive source impedance.

## In summary

• The maximum power is absorbed by the load when all the impedances match.
• When there is an impedance mismatch, some of the power is reflected.
• The voltage and currents from the forward and reflected wave sum up and form a standing wave.
• The VSWR can be easily calculated and measured.
• Capacitance and inductances can be used to build a matching network to eliminate reflected power.
• The matching network needs placed where the mismatch is located.

1. A matching network is a circuit that corrects the impedance mismatch.