An isotropic radiator is a theoretical point source of electromagnetic waves which radiates the same intensity of radiation in all directions. It has no preferred direction of radiation. It radiates uniformly in all directions over a sphere centred on the source.
Isotropic radiators are used as reference radiators with which other sources are compared.
Source: Wikipedia - Isotropic Radiator
One Word Key "theoretical" -KM6PNZ
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Isotropic antennas are ideal (theoretical) antennas that have equal power in all directions. They are used as references for antenna gain.
The word "isotropic" means "uniform in all orientations/directions".
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When the feed point impedance matches the impedance of the feedline and transmitter, the Standing Wave Ratio (SWR) will be 1:1, the minimum SWR.
If we know, for example, that the feedline and antenna impedance is 50 Ohms, we would need the antenna's feed point impedance to also be 50 Ohms.
Coaxial cable feedlines are often designed to exhibit an impedance of 50 Ohms. Transmitters are also often designed to have an output impedance of 50 Ohms.
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Feed point impedance is the sum of radiation resistance, ohmic loss (pure resistance), and reactance caused by non-resonance.
Antenna height Radiation resistance is proportional to height; it decreases as antenna is closer to the ground.
conductor length/diameter ratio Radiation resistance is inversely proportional to thickness; thicker conductor gives less radiation resistance.
location of nearby conductive objects buildings, other antenna.
summarized from AARL's extra class manual.
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Feed point impedance is the sum of radiation resistance, ohmic loss which is pure resistance and reactance caused by non-resonance which is not included in the possible answers.
One Word Key "ohmic"- KM6PNZ
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The beamwidth of an antenna is the width of the radiation of the main lobe from the antenna. As gain increases, it can be expressed as making the main lobe thinner and longer or decreasing its beam's width. see: http://en.wikipedia.org/wiki/Beamwidth
-deanwj
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Antenna gain is usually defined as the ratio of the power produced by the antenna from a far-field source on the antenna's beam axis to the power produced by a hypothetical lossless isotropic reference antenna, which is equally sensitive to signals from all directions. Usually this ratio is expressed in decibels, and these units are referred to as "decibels-isotropic" (dBi). An alternative definition compares the antenna to the power received by a lossless half-wave dipole reference antenna, in which case the units are written as dBd. Since a lossless dipole antenna has a gain of 2.15 dBi, the relation between these units is: gain in dBd = gain in dBi − 2.15 dB.
https://en.wikipedia.org/wiki/Antenna_gain
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Bandwidth is a measurement of frequencies, as in the width of a range of frequencies.
An antenna's bandwidth is the range of frequencies it works best on.
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Antenna efficiency is a term that relates what portion of the power delivered to the antenna actually gets radiated.
The total resistance is the resistance that is seen at the terminals of the antenna and is composed of two parts:
Loss resistance turns the power into heat instead of radiating it into the air, while radiation resistance is the part that turns the energy into useful radio waves.
Example An antenna has an input resistance of \(500\) Ohms and a radiation resistance of \(25\) Ohms.
Antenna efficiency would be: \begin{align} \text{antenna efficiency} &= \frac{\text{radiation resistance}}{\text{total resistance}} \times 100\%\\ &=\frac{25 \:\Omega}{500 \:\Omega} \times 100\%\\ &=5\% \end{align}
So \(5\%\) of the power delivered to the antenna gets radiated, the other \(95\%\) is wasted as heat.
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One of the ways you can improve an antenna's efficiency is to reduce losses from resistance. Anything that dissipates the energy of your RF increases total resistance and soil resistance can be significant.
When you install a system of radial wires at the base of a ground-mounted vertical antenna current flows into the radials instead of into the soil, thus reducing losses.
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A 1/2-wave dipole antenna has approximately \(2.15 \text{ dB}\) of gain over an isotropic antenna. So \[6 \text{ dB} - 2.15 \text{ dB} = 3.85 \text{ dB}\]
(The directive gain of a half-wave dipole is 1.64. It has a 2.15 gain over an isotropic antenna or \(10\log_{10}(1.64)\approx2.15\text{ dBi}\))
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Given: It's well-known that a half-wave dipole has \(2.15 \text{ dB}\) gain over an ideal isotropic radiator.
Let \(H =\) the gain of an ideal isotropic radiator
Let \(W =\) the gain of a half-wave dipole
Therefore \(W = H + 2.15 \text{ dB}\), or solving for \(H\), \(H = W - 2.15 \text{ dB}\)
Now, let \(X =\) the gain of the antenna in question
If that antenna in question exhibits \(12\text{ dB}\) over an isotropic antenna, then
\(X = H + 12 \text{ dB}\)
Substituting, we get
\(X = W - 2.15\text{ dB} + 12\text{ dB}\) \(= W + 9.85 \text{ dB}\)
Therefore, the antenna in question (\(X\)) exhibits a gain of \(9.85\text{ dB}\) over that (\(W\)) of a half-wave dipole.
Remember that a half-wavength dipole has 2.15 dB gain over an ideal isotropic radiator. Then take the difference between 12 dB and 2.15 dB to arrive at the answer of 9.85 dB.
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The electrical resistance of an antenna is composed of its ohmic resistance plus its radiation resistance. The energy lost due to radiation resistance is the energy that is converted to electromagnetic radiation.
It isn't the combined losses of antenna elements and feed line because radiation resistance is not related to feed line losses.
It isn't the specific impedance of the antenna because the radiation resistance is only a portion of the antenna's impedance.
It isn't the resistance in the atmosphere that an antenna must overcome because the radiation resistance is not a property of the atmosphere. It is determined by the geometry of the antenna.
The correct answer is therefore the value of a resistance that would dissipate the same amount of power as that radiated from an antenna
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The power gain G in dB is given by the following equation: \[\text{Gain } G= 10\log\left({P_2 \over P_1}\right)\] where:
We may algebraically solve for \(P_2\):
\[P_2 = P_1\left(10^{G/10}\right)\] We now have a simple formula for other similar problems.
The input power is \(P_1 =150 \text{ W}\). The net gain is \(G=7-4.2 = 2.8 \text{ dB}\). Applying the formula: \begin{align} P_2 &= 150\cdot10^{2.8/10}\\ &= 150\cdot10^{0.28}=285.82\\ &\approx286\text{ W} \end{align}
Here's yet another way...
When I was studying for this exam, I came across a much easier way to calculate ERP. This method converts the transmitter power to dB Watts so that you can easily add and subtract gains and losses. This technique requires a calculator that has a log function, which is allowed at the exam.
Using this question as an example: \[10\log(150)=21.8\]
Now you have apples and apples so you can add and subtract gains and losses: \[21.8 -2 -2.2 +7 = 24.56091259\]
Next you will need to divide by 10: \[24.56091259/10 = 2.456091259\]
TIP: You may want to store this temporarily in memory before proceeding.
Finally, apply the inverse log to return the gain (or loss) in Watts): \begin{align} InvLog(2.456091259)&=10^{2.456091259}\\ &\approx285.8\approx286\text{ W} \end{align}
Or use the "cheat": The net gain is \(7 - 4.2 = 2.8 \text{ dB}\). We know that \(3 \text{ dB}\) gain is double, so \(2.8\) is just under that. Double would be \(300\) watts so \(286\) is the only answer that is close.
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Sum the losses in the various stages:
\(4 \text{ dB} + 3.2 \text{ dB}+ 0.8\text{ dB}\) adds up to \(8\text{ dB}\) of loss in the total feed system. However, the antenna system gives us \(10\text{ dB}\) of gain (relative to a dipole). Fortunately, the question asks for the effective radiated power (ERP) relative to a dipole so no change to the antenna gain figure is needed.
\(10\text{ dBd}\) antenna gain minus \(8\text{ dB}\) feed system loss gives us an overall gain of \(2\text{ dB}\).
\(\text{Gain }G = 10\log\left(\frac{P_2}{P_1}\right)\), and we need to solve for \(P_2\), the ERP:
\[2\text{ dB} = 10\log\left(\frac{P_2}{200}\right)\]
Divide both sides by \(10\) giving:
\[0.2\text{ dB} = \log\left(\frac{P_2}{200}\right)\]
Take the inverse log of both sides:
\[10^{0.2} = \frac{P_2}{200}\]
evaluate:
\[1.585 = \frac{P_2}{200}\]
Multiply both sides by \(200\):
\[(1.585)(200) = P_2\]
Solve:
\[P_2 = 316.98\]
Alternatively, we may algebraically solve for \(P_2\): \begin{align} P_2 &= P_1 \left(10^{G/10}\right)\\ &= 200\times10^{2/10} = 200\times10^{0.2}\\ &=316.98\\ &\approx317 \text{ W} \end{align}
We now have a simple formula for other similar problems.
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In this example, the net gain after subtracting the total losses is equal to: \[7\text{ dB} – (2 \text{ dB} + 2.8 \text{ dB} + 1.2 \text{ dB}) = 1 \text{ dB} \] That’s equivalent to a ratio of \(1.26:1\), so the effective radiated power (ERP) is $200 \text{ W} \times 1.26 = 252 \text{ W} $.
Or
\[P_2 = 200 \times 10^{0.1} = 251.8 \text{ W} \]
Where does 0.1 come from? \begin{align} \mathrm{ERP} &= \mathrm{TPO} \times \log^{-1} \left(\frac{\text{system gain}}{10}\right) \\ &= \mathrm{TPO} \times \log^{-1} \left(\frac{1}{10}\right) \\ &= \mathrm{TPO} \times \log^{-1} (0.1) \\ &= 200 \times 10^{0.1} \end{align} Inverse log = \(b^y\) where \(\mathrm{base} = 10\) and \(y = 0.1\)
transmitter power output (TPO)
Where does the ratio \(1.26:1\) come from?
Actually it can be reverse calculated after you find the ERP BY THE 2ND METHOD
For additional information: https://www.kb6nu.com/extra-class-question-of-the-day-effective-radiated-power/
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Effective radiated power (ERP) is used to describe the highest concentration of RF energy that is radiated in a particular direction. As such, it includes all of the gains and losses of the antenna system, including focusing the radiated power. Yagi antennas, and other designs, have "gain" over a reference dipole, and must be considered when calculating effective radiated power. If the antenna has gain in a particular direction, that gain has to be calculated as part of the ERP. If an antenna design results in 3dBd gain (3dB greater than a dipole), then the ERP is twice what it would be with a dipole.
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