# Antennas Used In High Altitude Balloon Telemetry

(last update:  19 Mar 2011)

Common antennas used at ground level do not perform exactly the same way when they are at high altitude. Most antennas rely on a ground plane or are effected by ground planes. It comes as little surprise that the proximity of the antenna to the ground plane has a strong effect on the antenna. The effect often manifests itself in changes to the feed point impedance, the radiation pattern, and often both.

Almost all practical antennas have Gain and Directivity. How these two characteristics interact can make or break an RF link budget. An antenna which works well at ground level (one hundred meters or less), can perform quite poorly at many thousands of meters above ground level.

Why? Because Directivity and Gain can change. The change can cause radiation to be directed away from the receiver. Alternatively the receiver may end up in one of the nulls of the antenna pattern, whereas before it was in one of the peaks.

Note that in this context Directivity refers to a qualitative characteristic and not the quantitative value as in:

\label{equ:Directivity} D = \frac{U}{U_0} = \frac{4 \pi U}{P_{rad}}

Where U0, in equ $$\ref{equ:Directivity}$$, is the average power radiated by an isotropic source. The average is the total power radiation intensity of an isotropic source divided by 4π [Balanis]. The variable U is the power radiated in a particular direction. Note that this definition, although quantitative, does not specify which direction the radiation propagates. It is therefore a scalar quantity, not a vector quantity.

What's an isotropic source?

An isotropic source is a hypothetical antenna, which radiates in all directions. The radiation pattern is a uniform expanding sphere, from the point of origin.

Working from an isotropic source has the additional advantage that the radiation release by it is easily scaled based on gain patterns of other antenna types. In particular this makes it simple to formulate a link budget.

One of the first things to do is to make a guesstimate of how much power will be available for any given antenna on the ground to receive.

To do that some assumptions need to be made.

1) The antenna in the balloon payload is an isotropic source.
2) There are no system losses.
3) The ground station antenna is a dipole.
4) We will neglect antenna polarity.
5) We will neglect antenna non-uniformity gain.

It is certain that the antenna in the payload will not be isotropic in nature. Presuming that it is isotropic allows us to form a baseline of performance, to which other types of antennas used in the payload or on the ground, can be compared. This assumption also makes it easy to run "worst case" scenarios. This will become evident later.

An isotropic antenna will conform to the inverse square law for the propagation of electromagnetic radiation. This makes it easy to find the power density at any given distance from the source. The power per unit area, at a given radius r will be:

\label{equ:IsoPwr} I = \frac{P}{4 \pi r^2}

This can be applied to an effective aperture of a given antenna so that the amount of power delivered to an attached receiver will be:

\label{equ:PwrIso} P_{iso} = I \ A_{eff}

In eq $$\ref{equ:PwrIso}$$ the term Aeff is the the effective aperture of the antenna. An antenna's effective aperture Aeff or simply "aperture", can be related to its gain G,

\label{equ:EffectiveAperture} A_{eff} = G \frac{\lambda^2}{4 \pi}

so if we know the gain of an antenna, and the frequency at which it operates, we can make an estimate of its effective aperture. Note that eq $$\ref{equ:EffectiveAperture}$$ is useful for typical "wire" based antennas, including Uda-Yagi, and various vertical types of antennas. A "wire" based antenna is one where the conductor elements are not surfaces, and the element diameter is << 0.1 λ. It does not necessarily apply to reflector type antennas.

We can now apply some of what we know for a first pass at a link budget. Typical ground based omni-directional antennas have anywhere from a dipole type gain of 2 dB or so, on up to 6.9 dB for a well designed and crafted J-Pole.

Using the center (146 MHz, 2.053 m) of the 2 meter amateur radio band that brackets the the aperture between,

\label{equ:Aeff2mG2.1} A_{eff} = 2.1 \frac{(2.053 m)^2}{4 \pi} = 0.544 m^2

and,

\label{equ:Aeff2mG6.0} A_{eff} = 6.0 \frac{(2.053 m)^2}{4 \pi} = 1.336 m^2

To keep things general we'll choose a value in between the two,

\label{equ:Aeff2mAvg} A_{eff} = 0.75 m^2

What the value of eq $$\ref{equ:Aeff2mAvg}$$ is telling us is that if we build an antenna with gain between 2 dBi and 6 dBi, its effective aperture is about 0.75 square meters. Note that dBi is gain with respect to an isotropic antenna, where as dB is a more general form which may or may not be with respect to a particular power level.

Note that dBi is gain with respect to an isotropic antenna, where as dB is a more general form which may or may not be with respect to a standard level. The term dBm indicates that power levels are with respect to one milliwatt or 10-3 watts.

Armed with an effective aperture, and eq $$\ref{equ:PwrIso}$$, we can make an estimate of the available power at the output of the RECEIVING antenna. In other words we can estimate how much power, in mW, arrives at the ground based receiver, given the distance to the source (the balloon payload).

\label{equ:PwrIsoIntegrated} P_{iso}(pwr, alt, A_{eff}) = I(pwr, alt) \ A_{eff}

If one is directly below a 1 watt transmitter (remember we are using an isotropic radiator) at 31 km (just over 100,000 feet), using a ground station antenna of 0.75 m2 aperture,

\label{equ:PwrIsoIntegratedRes2mAvg} P_{iso}(1 W, 30km, 0.75m^2) = -72.069 \ dBm

Equation $$\ref{equ:PwrIsoIntegratedRes2mAvg}$$ suggests that the available power to our receiver will be 72.069 dB bellow a milli-watt.

Will our receiver be able to do much with this small a signal?

Typical 2m receiver sensitivity is often specified in μV. The value varies but let's use the Kenwood TH-D72A hand held radio's sensitivity for the 2m band 0.22 μV. What does this mean with respect to a milli-watt?

\label{equ:Typ2mSns} P_{sns} = \frac{(0.22 \ \mu V)^2}{50 \ \Omega} = 9.68 \ 10^{-16} \ watt

which in dBm is,

\label{equ:Typ2mSnsdBm} P_{sns} = -120.141 \ dBm

There is some ambiguity in this value. It is often not clear if the manufacturer is claiming an RMS value or a peak value. The value in eq $$\ref{equ:Typ2mSnsdBm}$$ presumes the manufacturer is claiming a peak value. If the manufacturer was claiming 0.22 μVrms, then the sensitivity would be 3 dB better. By presuming a peak voltage for sensitivity, a margin of 3 dB has been incorporated into the calculation, so the sensitivity may well be better by 3 dB or around -123 dBm.

So... eq $$\ref{equ:Typ2mSnsdBm}$$ suggests we have -120.1 dBm of power sensitivity, and eq $$\ref{equ:PwrIsoIntegratedRes2mAvg}$$ suggests we have -72.1 dBm available at the receiver front end. It would seem we should have no trouble receiving the telemetry from the payload, since we have 48.1 dBm of margin.

... or do we?

Don't forget we are NOT using an isotropic antenna in the payload, and we are NOT using one at the ground station. So we still have some figuring to do...

## Accounting For Losses and Gains

Suppose we used J-Pole antennas in the payload, and at the ground station. And suppose we didn't take pains in their design and construction. And suppose we didn't use appropriate feed line.

All of the above are quite possible to varying degrees.

#### Antenna Gain

One of the biggest losses is a characteristic of the J-Pole antenna design. A J-Pole antenna has a deep null along its axis. The null is about -23 dBi when the antenna is simulated in free space. The null rises to -16.77 dBi, 10 degrees off the axis. Beyond 10 degrees the gain continues to recover but stays negative for 72 degrees, either side of the axis. That's a 144 degree swath of radiation pattern that is worse than the isotropic radiator. Below is a simulation of a J-Pole's radiation pattern in free space, on which the numbers are based.

Notice that a 90 degree swath, along the axis, ranges from -3 dBi to -23 dBi. If your ground station is unfortunate enough to be within about 2.7 km of the ground track of the payload, when it is at 31 km of altitude, it will be deep in the null. Your ground station would have to move about 22 km to recover to the -3 dBi power level.

Why simulate in free space?

Because the NEC2 implementation in EZNEC generates some odd behavior when simulated at distances >> λ above a ground plane. A simulation at 100 km yielded gains of almost 8 dBi in a typical hemispheric, azimuthal plot. The results of such a simulation are shown below.

A more typical J-Pole simulation looks like this:

There is a deep null along the axis of the antenna with reasonable gain (5.2 dBi) at low elevation. In the above simulation the antenna is 4 meters above the ground reference plane. If we lower this particular antenna to 2m above the ground plane, which is roughly the height it would be as a back-pack antenna, the radiation pattern looks like this:

This simulation is of a 450 ohm "ladder line" type J-Pole, which has not been fully optimized but the radiation pattern is representative of what an optimized antenna pattern would be. The closer the antenna operates to the ground plane, the lower the gain, and the greater the elevation angle is of the peak lobe. And, of coarse, the ever present deep null along the axis, which is particularly bad at close to -28 dBi.

Mounted at 8m above ground, which would be typical, a good J-Pole should have close to 7 dBi of gain at about 3 degrees elevation. The null will rebound a bit as well and be only about -11 dBi.

#### Adding up the loses and gains

If we add up all the losses in the rest of the system, poor cable choice, bad connections, wrong connector type... etc, we may well lose a substantial fraction of our gain but let us be conservative and estimate the general system losses at 0.5 or -3.01 dB.

We avoid an antenna polarity loss by presuming both antennas are vertical J-Poles. This also forces us into the double null loss mentioned earlier.

We look for a worst case by presuming our ground station is directly below the payload. Adding all those up we have,

\label{equ:AdjAvlPwr1W} P_{avl} = -72.069 + -23 + -27 + -3.01

with a margin of,

\label{equ:PwrMargin1W} margin = P_{avl} - P_{sns} = -1.927 \ dBm

Well that's not so good... we are almost 2 dBm short of our sensitivity limit. And that is with a 2 watt transmitter. If we bump that up to 5 watts then we can expect about 2 dBm above the limit.

Unfortunately 2 dBm isn't much of a margin.

Why not count on 5 watts of transmit power from a hand held transceiver used as a payload transmitter?

#### High Power (5W) May Not Be Possible

The manual for the Kenwood TH-D72A, although confusing on this issue, suggests that the BT-15 alkaline battery pack (9V) will support 5W output for 1.5 hours. The PB-45L (7.4V) rechargeable battery will support 2W for 6 hours.

However, this presumes a transmit cycle of the following:

TX: 6 seconds,
RX: 6 seconds,
Stand-by: 48 seconds

This is not a realistic telemetry profile.

It is more likely that there will be little to no Stand-by time. The receiver must always be active, and ready for commands. Telemetry transmit cycles are commonly on 5 second intervals, and may well be on one second intervals, if commanded to do so. At times the telemetry transmit may be less frequent, up to several minute intervals. However, most of the time 5 second transmit intervals would be the most likely.

This poses a problem for the transceiver. The first and foremost is heat dissipation.

TRANSMITTING AT MAX POWER (5w) AT TYPICAL TELEMETRY INTERVALS WILL OVERHEAT THE RF POWER AMP IN THE TH-D72A.

TRANSMITTER POWER DISSIPATION AT MAX POWER, INSIDE A THERMALLY PROTECTED HOUSING MAY WELL OVERHEAT EVERYTHING INSIDE THE ENCLOSURE.

Remember, at altitude, the air pressure is about 100 mbar, so there isn't much in the way of "air cooling", and the enclosure is designed to keep heat inside the payload chamber. Things could get hot quickly.

Hand-held transceivers are not designed for such high duty cycle operation. In order to prevent damage to the radio, a mid level power setting will have to be used. To achieve this, using the TH-D72A, the PB-45L (7.4V) rechargeable battery should be used in the high power setting, yielding a 2W output.

However, 2 watts, over a 2 hour flight time, is still quite a bit of power. A careful test of internal temperatures should be undertaken, so as to ensure transmitter safety, and general payload safety.

A third possible power setting could be the "L" setting of 500mW. It is likely that this power setting will be safe for the transceiver, and the payload. In any case the internal temperatures of the payload should be checked against this power setting.

Running the numbers once again for a 500mW power setting yields,

\label{equ:AdjAvlPwr500mW} P_{avl} = -75.079 + (-23) + (-27) + (-3.01)

which puts us even farther in the hole with a margin of,

\label{equ:PwrMargin500mW} margin_{\ 500mW} = P_{avl} - P_{sns} = -7.948 \ dBm

So... If a ground station is within about a 2 km radius directly below the payload, they will likely not receive the signal. The station would need to move far enough out from under the payload, so as to claw back 9 dB to 10 dB or so.

Remember that there may be other sources of thermal power dissipation, such as a 5 watt ATV transmitter. If that is combined with a 5 watt telemetry transmitter, then there will be quite a bit of thermal flux being delivered to the payload enclosure, unless some means of thermal conduction is provided to deliver the thermal flux to a radiator external to the payload area.