Measuring antenna gain with a VNA

I've found many post on this topic but none of them cleared all my doubts.

I want to measure the gain of one antenna using a VNA and a standard horn antenna (with gain data-sheet).

The idea is to use Friis formula in this way:

1) Pr = P0 Gt Gr λ^2 / (4πR)^2

where Pr is the power received, P0 is the power accepted by the TX antenna, Gt is the gain of the TX antenna (a standard gain horn) and Gr the gain of the RX antenna (the unknown gain antenna). In dB terms, Friis formula can be written as:

2) GTX + GRX = 20log(λ / (4πR)) - 10log(P0/Pr)

where GTX and GRX are the gains expressed in dB of the TX and RX antennas respectively.
The unknown variables are GRX (GTX is given in the standard gain horn data-sheet), P0 and Pr. Can I use the VNA to calculate P0 and Pr as

3) P0 = 1 - abs(S11)^2
4) Pr = abs(S21)^2

and therefore measure GRX using equation (2)?
If not, could you please explain me why and suggest a different setup/method with the available equipment?

cheers

you can do it much simpler..use a horn antenne also as receiver (for which you know the gain)
, next measure S21. replace the horn with your antenna to be measured. remeasure S21.

I guess you know the simple math after that...

cheers!

Thx Darkcrusher for your reply but I don't understand what you mean, I only have 2 antennas: the standard gain horn and the unknown gain antenna.

The standard gain horn is used as TX antenna and is always plugged at VNA's port 1 whilst the unknown gain antenna is used as RX and always plugged at VNA's port 2.

Cheers

Measure a dipole to get a gain reference. The dipole can be just two wires tuned for actual frequency.

Thats a possibility too. Express your gain as dBd instead of dbi

Hello,

I would use P0 as input power for the standard gain horn. If your S11 is that high that you really have to correct for this, I should not trust the standard gain horn.

|S11| = 0.33 results in 0.5 dB loss (equivalent to VSWR = 2).

When you do your calibration with the same cables as you use during the measurements, Pr/P0 = |S21|^2.

Though theoretically use of friis formula is simple, practically things can go wrong. A reflection from a nearby object that arrives at the DUT 10 dB below the incident radiation, results in -3.3..+2.4 dB error.

To check influence of reflections, increasing measurement distance should follow the -6 dB/(distance doubling) rule.

When the distance between the two antennas is less then the sum of the far field distances for both antennas, the rule will not apply and you get useless measuring results.

If you move the complete setup over distance and the results change, you have a reflection problem.

As suggested by Darkcrusher, E Kafeman, I would also use the substitution method. It eliminates the gain from the standard gain horn. A dipole can be made from two wires AND a balun / common mode suppression means. When the DUT has |S21| 3 dB more then the dipole, your gain is 3 dBd = 5.14 dBi.

If both methods give different results, then you know there is something wrong.

WimRFP said:

To check influence of reflections, increasing measurement distance should follow the -6 dB/(distance doubling) rule.

Click to expand...

Indeed very usefull

E Kafeman said:

Measure a dipole to get a gain reference. The dipole can be just two wires tuned for actual frequency.

Click to expand...

He does have a standard horn antenna with gain data-sheet. I would use that as the known reference for the substitution method.

Possible but complicated to use the horn antenna data sheet antenna gain for anything useful as he needs a measured reference point in fare field for a whole system, not for an single antenna.
Two antennas are needed to make one calibrated reference point for the measurement setup including system levels antenna gain, environment and cable losses.
One of the antennas must remain in same place during both calibration and actual measurement. It is advantageous to keep the horn antenna at this place during both operations due to its antenna characteristic for horn antennas in general such as wavefront shape, directivity and ease of polarization control. It is less practical to also use same antenna at the reference point even if it is possible.
Reflection free fare field or anechoic chamber is assumed as measurement range.

E Kafeman said:

Possible but complicated to use the horn antenna data sheet antenna gain for anything useful

Click to expand...

Why?

I am not an antenna guy, but here is what I would do:

I would use a third antenna on one side (may be unknown) and the reference antenna / device under test on the other side.
This gives one S21 value for the reference antenna and a second S21 value for the device under test. Knowing the gain for the reference antenna, it should be straightforward to calculate the DUT gain from the difference in S21.

What do you think?

Grendhell: What is your actual frequency band of interest? What is the expected gain for the DUT and do you need to measure the complete radiation pattern (with deep nulls) also?

In an typical antenna measurement setup in an anechoic chamber do we have an antenna that is placed such that its radiation gives a quite zone (planar waves) in the measurement point, typical at top of a turntable. This antenna can not be replaced during calibration and measurement phase against another type of antenna as it will add uncertainty even if both antenna characteristic is known. The gain of this antenna is of less importance as we anyway must measure whole system, such as cable attenuation, VNA nonlinearity, losses in connectors, PA gain.. It is an advantage if this antenna have small side lobes and a well defined wave front as it reduces phase or reflection errors at measurement point so it is a rather common selection to use a horn antenna for this. Pretty much as Grenhell describes it with the horn antenna fixed connected at one port of VNA. At the turntable do we want a uncritical antenna as reference, wide directional, as even smaller antenna alignment error else can cause calibration error. A simple dipole is uncritical in its placement and direction on turntable, easy to find its polarization, wide band and with well known gain if you have some experience how to make them so that is is to prefer above using a directive antenna on the turntable. One single S21 measurement is then enough get a offset value which can be assumed to be 2.14 dBi. In this calibration procedure is not the gain or losses of the individual parts of interest, not even for the horn antenna.

To reduce influence of reflections, you want close distance between horn and DUT, but for getting meaningful results, you need a certain minimum distance.

Sometimes people forget that when you do your calibration with a dipole at the position of the DUT, everything may be fine, but when you replace it with a high gain DUT, it will go wrong completely. The high gain DUT needs a larger volume with near plane wave behavior. This mostly requires you to increase the measuring distance when using a horn (or many other antennas).

Using the sum of the horn's and DUT's far field distance is a good starting point. If you know what you are doing, you can reduce this distance (depending on current distribution in the DUT and required accuracy).

If you look at the equation,

GTX + GRX = 20log(λ / (4πR)) - 10log(P0/Pr)

and realize -10log(P0/Pr) = S21 then you should be done. You may never know P0 and Pr absolutely but their ratio is the only quantity necessary to determine the gain of the unknown antenna. Of course trying to get a far field measurement without local reflections and adjusting for cables that others have mentioned is important.

GRX = 20log(λ / (4πR)) + S21 - GTX

thx all for the helpful and interesting replies.

I decided to use the gain comparison method so I'm looking for a 3rd antenna to use as TX and then I'll compare the DUT S21 with the standard gain horn's. This should lead to more precise results rather than the way I was planning to do.

Thx also for spotting a mistake in my equations, I should use

-10log(P0/Pr) = S21

rather than

-10log(P0/Pr) = -10log( (1 - abs(S11)^2) / abs(S21)^2)

Cheers

grendhell said:

thx all for the helpful and interesting replies.

I decided to use the gain comparison method so I'm looking for a 3rd antenna to use as TX and then I'll compare the DUT S21 with the standard gain horn's. This should lead to more precise results rather than the way I was planning to do.

Thx also for spotting a mistake in my equations, I should use

-10log(P0/Pr) = S21

rather than

-10log(P0/Pr) = -10log( (1 - abs(S11)^2) / abs(S21)^2)

Cheers

Click to expand...

|S21|^2 = (Pr/P0), S21 is a voltage relation

S21 = Vreceive_into_50Ohms / Vtrans_incident
the incident voltage you get when the transmitting port is terminated with 50 Ohms.

So if your reference has |S21| = 0.05 and the DUT has |S21| = 0.1, the gain of the DUT is 6 dB above the gain of your reference.

WimRFP,

You are technically correct that the S21 is a voltage relationship, but most VNA I have used display S21 as a power ratio.

read this paper
IEEE Xplore - Accurate measurement of antenna gain and polarization at reduced distances by an extrapolation technique
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