# Theoretical and experimental gain of helical 900 MHz antenna

#### PaulEE

Joined Dec 23, 2011
474
Hello all,

I am currently working on finalizing some paperwork with regards to a 900 MHz transmitter for the FCC. They claim that they need this piece of information, specifically for IC documentation. I know a handful of things about RF and antennas, but I do not know enough to feel confident about any numbers that result from experimentation, theoretical equations, and the like. Here is what I have done:

Antenna characteristics:
Length: 18mm
Nturns: 8
Diameter of loop: 4mm
Freq: 900 MHz

Utilizing an equation taken from a paper on helical antennas, I have obtained the following:

g[dBi] = 10.25+1.22*(L / lambda)-0.0726*((L / lambda)^2)

I obtain 10.3 dBi gain reading using approximately the values of antenna characteristics listed above.

Next, a colleague constantly activated a transmitter with NO antenna oriented such that the receiving antenna and transmitter shared the same axis (pointed at one another directly). Then, a spectrum analyzer was used to record the average of peak readings of the transmission. Then, the antenna was replaced, and the readings were taken again.

75 dBuV/m with antenna, 54 dBuV/m without antenna; or 5,623 uV and 501 uV in non-log units. (20 log10(G) used). Dividing 5,623/501 and taking the log10 and multiplying by 10 yields, what Wikipedia claims to be, dBi units. The result obtained was about 10.5 dBi.

My questions:
Is this correct practice, both theoretical and experimental?
Are these measurements consistent with what others have observed for small RF helical antennas operating in normal mode?
The FCC person claims to often hear of readings of 0 dBi, or even -1 to -2 dBi. Should I reconsider what work I've done above, or are those readings a result of someone else not knowing what's going on?

Thank you very much in advance everybody.
Paul

#### Papabravo

Joined Feb 24, 2006
21,325
Something seems more than a bit off. The wavlength of a 900 MHz. signal is approximately 1/3 of a meter or a little over a foot.
Plugging 18 mm = 0.018 M into your equation I get 10.316 which is hardly more than you started with.
What your formula and numbers suggest is that any antenna at all regardless of it's dimensions and orientation will provide 10.25 dBi if L = 0. That's just a bit too much to swallow.
I'm no expert in helical antennas so I could be wrong. How did you come up with 4mm ≈ 0.16" and 18mm ≈ 0.710 as dimensions for the antenna? What is the original length of the wire you used to fabricate the final result?

I estimate:

$$2*\pi*.002*8 \; = \; .1\text M \approx 3.96 \text inches$$

I know a helical antenna will be shorter than the equivalent vertical antenna, but one-third of a wavelength does not seem reasonable.

#### PaulEE

Joined Dec 23, 2011
474
The transmitter and receiver were spaced 3m away from one another. The antenna length is much smaller than the wavelength. The antenna was fabricated by a contract manufacturer. Please see images for dimension derivation...furthermore, you are spot-on with your length estimate; 8 turns, 4mm diameter, pi...8*4*3.14159..= about 100 mm, or nearly 4 inches.

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#### Papabravo

Joined Feb 24, 2006
21,325
Here is what I don't get. Why go to all that trouble for a 10.31-10.25 = 0.06 dB improvement.
Since you start with 10.25 and add a positive term, and then subtract a negative term it seems like there ought to be an optimal length that maximizes the gain. I guess a plot of gain versus length might be revealing. Also revealing might be the inductance of this open core coil at 900 MHz.

Do you have the instrumentation to actually measure the return loss for this particular antenna. That will tell you in a heartbeat if you have something or just a steaming pile.

#### PaulEE

Joined Dec 23, 2011
474
I think there is a little confusion...but I am not sure where.

In a real test, the transmitter was activated and field strength measured at 3 meters. The antenna installed yielded 75 dBuV/m and not installed the setup yielded 54 dBuV/m. Undoing units and calculating dBi from those values, we obtained 10.4 dBi.

Using the textbook equation, we calculate, based on the physical characteristics of the antenna, a gain of 10.3 dBi.

The point was that these values are very close to one another, which tells me (I think??) that both the equation, as well as the real-world implementation, both agree with one another closely.

What I needed to know was if this was an accurate assessment, whether these are typical antenna values for small helical antennas for small wireless transmitters, and whether anybody agrees with the FCC guy as far as readings.

Make sense?

#### Papabravo

Joined Feb 24, 2006
21,325
Now just a minute here. dBi is used to compare an antenna with an isotropic radiator. An isotropic radiator is an antenna that radiates equally in all directions. It says nothing at all about radiation with respect to no antenna at all. I agree with the FCC guy that constructing a useful and efficient antenna is a challenging business. I don't see how your equation dictates the antenna you have. It tells me that ANY antenna you put on the device will produce a similar result. As an isotropic radiator, why not try a stub of wire 3.3 inches long (a quarter wavelength)?

If the isotropic radiator and the helical antenna have the same result then that would account for the 0 dBi number. If the helical antenna is mismatched to the output stage that might account for the -1 dBi or -2 dBi. If instead you get the same results comparing the isotropic stub to the helical antenna then you actually might have something.

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#### Tesla23

Joined May 10, 2009
543
Hello all,

I am currently working on finalizing some paperwork with regards to a 900 MHz transmitter for the FCC. They claim that they need this piece of information, specifically for IC documentation. I know a handful of things about RF and antennas, but I do not know enough to feel confident about any numbers that result from experimentation, theoretical equations, and the like. Here is what I have done:

Antenna characteristics:
Length: 18mm
Nturns: 8
Diameter of loop: 4mm
Freq: 900 MHz

Utilizing an equation taken from a paper on helical antennas, I have obtained the following:

g[dBi] = 10.25+1.22*(L / lambda)-0.0726*((L / lambda)^2)
What you have is a normal mode helical antenna, this behaves like a λ/4 monopole, but is shorter and more narrow band. Think rubber-ducky antenna on small handheld radios (https://en.wikipedia.org/wiki/Rubber_ducky_antenna). A lossless normal mode helix over a perfect ground plane could have 5dBi of gain, but stuck on some appliance, somewhere around 0dBi is more likely.

The formula you have is for an axial mode helical antenna, this is a much larger beast where the circumference and turn spacing are wavelength-like. They can have serious gain.

Antenna gain measurement generally involves comparison with an antenna of known gain in a controlled environment (antenna range), I have no idea what testing 'without antenna' means. You made some measurements where you observed '75 dBuV/m with antenna, 54 dBuV/m without antenna', this means that you had 21dB more gain in the first configuration, no amount of 'dB gymnastics' can change that.

#### PaulEE

Joined Dec 23, 2011
474
(to papabravo)

I'm not agreeing or disagreeing with your assessments - I simply do not know the proper way to do what I am talking about.

I also agree with your assessment regarding dBi and its meaning. I do not have an isotropic radiator around to attach to the circuit (ha ha). My reasoning was that since the entire circuit is about 1/10th the wavelength of the signal we're transmitting, and at 3 meters way, this little circuit looks like a point source. In my mind, it was OK to roughly estimate that this was "isotropic". It is obviously not, but comparing the helical antenna gain equation with the results obtained seemed to support the assumption...or perhaps it was coincidence.

"Undoing" = converting from dBuV to uV, all else equal. Long story short - I measure peak electric field strength with antenna and without in the direction of theoretical maximum gain, calculate the absolute units instead of dBs, and then use dBi = 10 log 10 (Gain = with antenna reading/ without antenna reading) to get dBi reading.

What will most likely occur at the end of all this is that I will instruct the contract manufacturer to send samples to a third-party and have these tests done.

#### PaulEE

Joined Dec 23, 2011
474
(to Tesla23)

Thank you - yes - this antenna was one of the ones I had in mind; but the difference in modes and specific equations for each - I am not familiar with. I read somewhere that when the antenna length is small compared to wavelength, the charge distribution across the entire element is nearly the same, so it was okay to use this equation. Perhaps this is incorrect or I am mistaken; this very well may be. I read a lot very quickly in an attempt to resolve the issue.

I also find it interesting that you support the FCC person in that you claim the gain would go to around 0 dBi once the antenna is attached to the device. This is encouraging.

Regarding the no antenna/antenna test: makes 100% sense. I do not have a known-gain antenna to do this test with, otherwise I would've done this. Perhaps I should purchase one for future quick-checks.

I test report that was done on a previous transmitter (900 MHz, similar construction techniques) cited -5 dBi average recorded gains on proper equipment in a proper lab. This is starting to sound more and more like what I'm working with; and the 10 dBi, though agreeing with funky math, doesn't appear to make sense at all.

Hmm.....

#### Papabravo

Joined Feb 24, 2006
21,325
I think we might be getting closer to the actual situation. If it is not too much trouble I'd like to encourage you to cut a piece of wire to use as a stub radiator. 3.3 incehes should do it. You might or might not gain some insight.

#### PaulEE

Joined Dec 23, 2011
474
I may be able to do this tomorrow; the individual that runs the tests is gone for the day. I'd like to repeat the tests using the same unit and in the same quiet (relatively) area of the building; I am not sure how he had things set up.

What will this tell me?

#### Papabravo

Joined Feb 24, 2006
21,325
I may be able to do this tomorrow; the individual that runs the tests is gone for the day. I'd like to repeat the tests using the same unit and in the same quiet (relatively) area of the building; I am not sure how he had things set up.

What will this tell me?
It will tell you the difference in field strength between a transmitter with no antenna, one with an isotropic radiator, and one with the helical antenna. This should establish if the helical antenna does indeed have 10 dBi gain which was the original question.

#### SLK001

Joined Nov 29, 2011
1,549
Your range technician probably substituted a known dipole antenna as a reference. He definitely did NOT use an isotropic radiator. You probably did not understand what the data was telling you. With the reference antenna values and your antenna values plus knowing the transmitter power, you can calculate the antenna gain. Do NOT try to submit FCC data with isotropic radiator data.

#### Papabravo

Joined Feb 24, 2006
21,325
Your range technician probably substituted a known dipole antenna as a reference. He definitely did NOT use an isotropic radiator. You probably did not understand what the data was telling you. With the reference antenna values and your antenna values plus knowing the transmitter power, you can calculate the antenna gain. Do NOT try to submit FCC data with isotropic radiator data.
That makes a great deal of sense, since transmitting into an open is pretty much guaranteed to be a very poor way to transmit a signal.