Phone Antenna S11: What Return Loss Means for Radiated Power

What S11 measures

S11 is the reflection coefficient seen looking into the antenna port. It is the ratio of the wave coming back from the antenna to the wave sent into it. On a plot it is usually shown in dB, as a negative number such as −10 dB.

Return loss is the same quantity with the sign flipped. S11 of −10 dB is a return loss of 10 dB. A larger return loss means less power comes back. Some plots label the axis "S11", others "return loss", and mixing the two up is a common source of confusion.

S11 answers one question: how much of the power sent toward the antenna is not accepted at the port? It does not say where the accepted power goes. That distinction matters for the rest of this article.

From return loss to reflected power

The magnitude of the reflection coefficient follows from return loss in dB:

Power goes as the square of amplitude, so the fraction of power reflected is:

The accepted fraction is what remains:

For 10 dB return loss, |Γ| = 10^−0.5 = 0.316. The reflected power is 10 percent and 90 percent is accepted. For 6 dB, 10^−0.6 = 0.251, so about 25 percent is reflected.

The other rows below follow from the same formulas.

Return loss	|Γ|	Reflected	Accepted	VSWR
3 dB	0.708	50.1%	49.9%	5.85
6 dB	0.501	25.1%	74.9%	3.01
10 dB	0.316	10%	90%	1.92
20 dB	0.100	1%	99%	1.22

Going from 10 dB to 20 dB gains only 9 percentage points of accepted power. Going from 3 dB to 10 dB gains about 40. The first few dB of improvement matter far more than the last few.

The echo plot below shows the same trend. A bigger return loss means a quieter echo.

VSWR and the same numbers

VSWR carries the same information as |Γ|:

With |Γ| = 0.316 this gives (1 + 0.316) / (1 − 0.316) = 1.92. So a 10 dB return loss and a VSWR of 1.92 are the same mismatch, written two ways.

Handset antennas are often judged against a return-loss line on the plot, while VSWR is more common in antenna datasheets. The chart below converts between them. Use it to translate a spec written in one form into the other. For the derivation and mismatch loss in dB, see the VSWR explainer.

Worked example: 10 dB return loss

Take 100 units of incident power at the antenna port, with a return loss of 10 dB at the frequency of interest.

1. |Γ| = 10^(−10/20) = 0.316.
2. Reflected power = |Γ|² × 100 = 10 units.
3. Accepted power = 100 − 10 = 90 units.
4. VSWR = (1 + 0.316) / (1 − 0.316) = 1.92.

The mismatch costs the link budget 10·log10(0.9) ≈ −0.46 dB at this port. That is small. At 6 dB return loss the accepted fraction is 0.749, which is about −1.25 dB.

The drawing shows where the 100 units go. It shows 10 reflected, 90 accepted, and the accepted power splitting into a radiated part and a part lost as heat.

The split on the right of the drawing is marked "not shown by S11". The port cannot tell the two paths apart. Both look like power that was accepted.

Why a good S11 is not good radiation

Total efficiency is the product of two things: the fraction accepted, and the fraction of accepted power that is actually radiated.

S11 only fixes the first factor. The second factor, radiation efficiency, depends on losses inside the antenna structure and in nearby materials. In a phone those include the hand, the case and other lossy parts close to the antenna.

As an illustration only, suppose half of the accepted power were lost as heat. With the 90 percent accepted at 10 dB return loss, only 45 percent of the incident power would be radiated. The S11 plot would look identical to that of a more efficient antenna.

The reverse also happens. A lossy structure can improve S11, because loss absorbs power that would otherwise be reflected. A deep, wide S11 notch is therefore not proof of a good radiator.

Reading a plot in practice

Use these checks when you look at an S11 plot:

• Read the dB value at the band edges, not only at the dip. The dip is the best case.
• Convert the number. 10 dB is 10 percent reflected, 6 dB is about 25 percent.
• Ask whether the plot was taken in free space or with a hand and case. Nearby materials change both the match and the loss.
• Treat S11 as the first filter. It can show a bad match, but it cannot confirm a good radiator.

For how return loss differs from the loss through a part, see Return Loss vs Insertion Loss.

In plain words · for students and beginners

Antenna return loss in plain words

Think of a window

Picture sunlight hitting a window. Some light bounces back, and the rest goes through. Return loss is a measure of how much bounces back. A big return loss number means very little bounces back.

The comparison breaks down in one place. Light that goes through the window is still light on the other side. Power that goes into an antenna can end up as heat instead of radio waves, and the return loss number cannot see that.

The same example in simple steps

Say 100 units of power head toward the antenna, and the return loss is 10 dB.

1. A 10 dB return loss means the echo is 10 percent of the power.
2. So 10 units bounce back.
3. The other 90 units go into the antenna.
4. Of those 90, some become radio waves and some become heat in the antenna, the case or your hand.

The return loss only tells you about steps 1 to 3. Step 4 needs a different measurement.

For comparison, 6 dB means about 25 percent comes back. So 6 dB is a worse match than 10 dB.

Mistakes beginners make

• Thinking a deep dip means a great antenna. The dip only says the port accepts power. It does not say the power is radiated.
• Mixing up S11 and return loss. S11 of −10 dB and a return loss of 10 dB are the same thing. Only the sign differs.
• Chasing a very high return loss. Going from 10 dB to 20 dB adds only 9 percent more accepted power. That effort is often better spent checking losses.
• Forgetting the hand. A phone held in a hand behaves differently from one on a bench.

Remember

• Reflected power fraction is 10 to the power of minus return loss over 10. At 10 dB that is 10 percent, and 90 percent is accepted.
• A 10 dB return loss matches a VSWR of 1.92. About 6 dB reflects about 25 percent.
• A good S11 does not mean good radiation, because accepted power can still become heat.

Related pages on RF View

• VSWR Explained: Reflection Coefficient and Mismatch Loss
• Return Loss vs Insertion Loss: What Each Number Tells You