In: Resources 03 Mar 2017 Tags: , , , , , ,

The Antenna Factor

By Ron Hranac, Senior Technology Editor

In the world of electromagnetic compatibility (EMC) and electromagnetic interference (EMI) testing, a parameter known as “antenna factor” commonly is used. Antenna factor is not widely known in the cable industry, although it is built in to the calculations used for signal leakage measurements as the “0.021” and “f” (frequency) in the microvolts per meter-to-dBmV conversion formula. ( For more on the mathematics of field-strength measurements, see my June 2008 column at www.cable360.net/ct/operations/bestpractices/30008.html).

Wikipedia defines antenna factor as “the ratio of the incident electromagnetic field strength to the voltage V (units: V or µV) on the line connection of an antenna. For an electric field antenna, field strength is in units of V/m or µV/m, and the resulting antenna factor AF is in units of 1/m: AF = E/V.

“The antenna factor for a given antenna is related closely to the load impedance Z0 connected to the antenna’s terminals.”

In other words, antenna factor is the ratio of the field strength of an electromagnetic field incident upon an antenna to the voltage produced by that field across a load of impedance Z0 connected to an antenna’s terminals. (Subsequent references to “antenna terminals” in this article assume those terminals are connected to a suitable load of the desired impedance Z 0).

The field strength can be calculated by multiplying the voltage at the antenna’s terminals by the antenna factor. Many prefer to work in the world of logarithms and decibels, and antenna factor commonly is expressed in decibel format rather than the previously discussed linear format. When antenna factor is stated in decibels, field strength in decibel-microvolts per meter (dBµV/m) is calculated by adding the signal level at the antenna terminals in decibel-microvolts (dBµV) to the antenna factor in decibel/meter (dB/m).

“Whoa!” you say. “We measure signal level in dBmV, not dBµV; and field strength in microvolts per meter (µV/m) rather than dBµV/m.” That’s true in North America, but much of the rest of the world uses dBµV and dBµV/m. Fortunately, it’s not that difficult to convert between dBµV and dBmV, or between dBµV/m and µV/m.

To convert a value in dBµV to dBmV, simply subtract 60 from the dBµV value. Going the other direction, adding 60 to a value in dBmV gives dBµV. For example, +117 dBµV is +57 dBmV, and 0 dBmV is +60 dBµV. Our familiar 20 µV/m signal leakage field strength limit is converted to dBuV/m using the formula:

20log10(value in µV/m)

20log10(20 µV/m)

20 * [log10(20)]

20 * [1.301]

26.02 dBµV/m

Converting from dBµV/m to µV/m is done with the formula µV/m = 10 (value in dBµV/m divided by 20).

Consider a signal-leakage measurement made at 121.2625 MHz (CEA Channel 14’s visual carrier) using a resonant half-wave dipole. We can calculate the antenna factor for that dipole knowing the field strength and the signal level at the antenna terminals.

For instance, assume that the field strength produced by a leak is the previously mentioned 20 µV/m. ( Note: When making a field strength measurement for the purpose of determining antenna factor, ensure that the measurement is in the far field as opposed to the near field; the antenna has been aligned to the same polarity as the electromagnetic field being measured; and that the antenna has been oriented to produce the maximum level at its terminals.) The signal level in dBmV at the antenna’s terminals is found with the formula:

dBmV = 20log10[(E/0.021f)/1000]

where E is the field strength in µV/m and f is the frequency in megahertz.

dBmV=20log10[(20/0.021 * 121.2625)/1000]

= 20log10[(20/2.5465)/1000]

= 20log10[7.8539/1000]

= 20log10[0.0079]

= 20 * [log10(0.0079)]

= 20 * [-2.1049]

= -42.1 dBmV

Now, add 60 to -42.1 dBmV to get the level in dBµV: +17.9 dBµV. We already know that 20 µV/m equals 26.02 dBµV/m, so the antenna factor of our dipole is 26.02 dBµV/m – 17.9 dBµV = 8.12 dB/m. This antenna-factor value applies to this particular antenna at this frequency.

If we make a field-strength measurement at another frequency, the antenna factor will be different than what was just calculated for 121.2625 MHz. For example, if a leak produces a 20 µV/m field strength at 782 MHz, and we measure that field strength with a resonant half-wave dipole for the higher frequency, the level at the antenna’s terminals will be -58.29 dBmV, or +1.71 dBµV. Knowing that 20 µV/m equals 26.02 dBµV/m, the antenna factor is 26.02 dBµV/m – 1.71 dBµV = 24.31 dB/m.

A couple of interesting things become apparent. First, the leakage field strength is 20 µV/m for both frequencies, yet the levels at the two antennas’ terminals are quite different: -42.1 dBmV at 121.2625 MHz versus -58.29 dBmV at 782 MHz. The difference is 16.19 dB, which happens to be equal to the difference between the two antenna factors: 24.31 dB/m – 8.12 dB/m = 16.19 dB.

You’ve probably seen tables or charts that show resonant half-wave dipole antenna levels in dBmV versus frequency for a given signal-leakage field strength. For instance, 20 µV/m field strength produces dipole levels of -42.1 dBmV on Channel 14 (121.2625 MHz), -42.5 dBmV on Channel 15 (127.2625 MHz), -42.9 dBmV on Channel 16 (133.2625 MHz), -43.3 dBmV on Channel 17 (139.25 MHz) and so forth. The reason for the variation in the level at the antenna terminals versus frequency is because of the difference in antenna factor at different frequencies.

So far, I’ve been talking about measurements made using Z0 = 75 ohms impedance equipment (a dipole in free space has an impedance of approximately 73 ohms). EMC and EMI measurements usually are done using Z0 = 50 ohms impedance equipment, making antenna factor slightly different. Half-wave dipole antenna factor in 50 ohms impedance is calculated easily with the formula:

AF50? = 20log10(f) – 10log10(G) – 29.7707

where

AF50? is the antenna factor for a half-wave dipole connected to a load of Z0 = 50 ohms, f is frequency in megahertz and G is the dipole’s numeric gain (1.64). 10log10(1.64) gives a dipole’s gain in decibels, or 2.15 dBi. For the earlier examples of 121.2625 MHz and 782 MHz, a Z0 = 50 ohms impedance scenario’s half-wave dipole antenna factors are 9.76 dB/m and 25.95 dB/m, respectively.

I’ve not seen a similar antenna factor formula for Z0 = 75 ohms impedance, but it’s easy to sort out. I came up with the following, using Z0 = 73 ohms, a dipole’s approximate free-space impedance:

AF73? = 20log10(f) – 10log10(G) – 31.4142

where

AF73? is the approximate antenna factor for a half-wave dipole, f is frequency in megahertz, and G is the dipole’s numerical gain (1.64). This formula agrees closely with the earlier calculation, where an antenna factor of 8.12 dB/m was sorted out for 121.2625 MHz. Here it works out to 8.11 dB/m. If Z0 = 75 ohms is used, the formula changes very slightly to:

AF75? = 20log10(f) – 10log10(G) – 31.5315

As you can see, antenna factor for a given antenna is related closely to the load impedance Z0 connected to the antenna’s terminals. In a real-world field-strength measurement, a dipole antenna will be connected to an instrument like a spectrum analyzer via a length of coaxial cable. There might be a bandpass filter or preamplifier in-line, too. One must account for the insertion loss of the coax and such devices as filters (or gain, in the case of a preamplifier) to come up with what the signal level would be at the antenna’s terminals with the load directly connected to the antenna.

But back to the load impedance Z0: A spectrum analyzer might have an input return loss of around 20 dB with input attenuation switched in (it will be lower with the input attenuator set to 0 dB). That 20 dB return loss equates to a voltage standing wave ratio (VSWR) of 1.22:1, which means the actual load impedance Z0 “seen” by the antenna’s terminals could be anywhere in the 61.36 ohms-91.67 ohms range (I’m leaving reactance out of the impedance discussion as well as the contribution of the coax to keep things simple). Using these two extremes of possible load Z0, the calculated antenna factors for a half-wave dipole at 121.2625 MHz work out to 8.8663 dB/m (Z0 = 61.36 ohms) and 7.1229 dB/m (Z0 = 91.67 ohms).

If an unknown field strength at 121.2625 MHz produces a level at a dipole’s terminals of 17.9 dBµV (-42.1 dBmV), we get a range of possible field strengths of 17.9 dBµV + 7.1229 dB/m = 25.02 dBµV/m to 17.9 dBµV + 8.8663 dB/m = 26.77 dBµV/m. In our more familiar microvolts per meter, these values are 17.8 µV/m and 21.8 µV/m, respectively.

In practice, commercial antennas used for EMC/EMI purposes include antenna factor-versus-frequency data provided by the manufacturer.

 

About the author:

Ron Hranac is technical leader, broadband network engineering at Cisco Systems and senior technology editor for Communications Technology. Contact him at rhranac@aol.com.

Article published with the permission of the author.

 

In: Products, Resources 16 Jun 2014 Tags: , , , ,

To create the Standard-RM propagation model that is faithful to Fresnel’s theory (for frequencies > 30 MHz), it took more than 20 years of research and development and more than 50 iterations of implementation in our software, which has been verified with hundreds of thousands of measurements.

Standard-RM includes the Fresnel complex integral, diffraction (2D and 3D), Ducting, Troposcattering, Climate, Reflections, Refraction, Scattering…

 

Since 1988, we there have been many different methods for calculating diffraction that we have implemented in our software (Epstein Peterson, Bullington and Deygout). All these methods have one thing in common: they do not take into account the effects of multiple paths that sum together at a given point at a given frequency.  This aspect can be accounted for in various ways as in the following models:

  • Propagation curves CCIR/ITU (370, 1546) with the notion of effective height
  • Okumura-Hata with the notion of effective height
  • Wojnar or Deygout (94) with FPL (fourth-power law)
  • Durkin (with the slope factor corrections altering the fundamental model)
  • Two-ray plane earth models
  • Longley Rice (ITM)
  • Delta-Bullington
  • Etc.

 

Recommendation ITU-R P.526-13 offers a method of calculating diffraction “sub-path”, inspired by our different models. In this model, the Fresnel integral treated approximately so it is incomplete, however, it demonstrates that when calculating propagation deterministically, that the Fresnel model is important.

 

2014 ATDI integrates its model RM-Standard in its software ICS and HTZ.

The version released yet incorporates so far FPL + Deygout diffraction, and we only use this to determine the minimum attenuation. Once we have finished checking the new model with measurements, it will become redundant.

 

This model is entirely dependent on the input data: model quality and accuracy of emission and reception parameters. We noticed that unlike most models which are more “permissive”, an approximate antenna pattern greatly reduces the correlation. In addition, its sensitivity to the accuracy of terrain data requires new cartographic data, including the need to calculate attenuation due to vegetation with an absorption model.

 

In conclusion, this model does not give “better” results than another, if it is used with data of moderate quality. It is faithful to the physics of waves. Used with qualified data, we have observed a standard deviation of error <2.5 dB instead of 3.2 / 3.4 dB with previous implementations.

 

Advantages:

  • End of approximations!
  • A pure model faithful to the geometry of the terrain
  • Allow the true validation of the parameters of a plan

 

Disadvantages:

  • Very long computation time
  • Requires an accurate and reliable terrain model
  • Requires the actual station parameters

 

Applications:

  • Propagation prediction above 30 MHz
  • A reference model for comparison

 

Base model:

Fresnel Integrals
Diffraction (GTD, 2D, 3D)
Subpath switching (for compatibility with all the diffraction methods)

Support:

Troposcattering
Ducting (multi-layers)
Mixed path
Gaz attenuation
Rain attenuation
Slant path
Scattering
Absorption
Reflection (2D, 3D)
Gradient
Fog
Snow
Clutters and buildings (flat attenuations, dB/km attenuations, mixed diffraction/absorption…)

Outdoor, Outdoor/Indoor, Indoor, 2D 1/2 and 3D terrain models
Coverage calculation, Point to Point and Point to Multi-Points, Path budget
Clutter tuning

Avalaible in ICS telecom, ICS designer, ICS LT and HTZ

 

 

The Standard-RM model will soon be released (both formulas and method). Check for further announcements on our website

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In: Products, Services 23 May 2014 Tags: , , , , , ,

Making buildings reach the sky is easy. Making radio waves reach around them is the tricky part. Whether the obstacle is an industrial complex or a proposed new building, the problem is the same: anything made of steel, concrete and brick impedes the propagation of radio waves. Anything big enough made of steel, concrete and brick stops them completely. The task of the radio engineer is to ensure that radio spectrum users who have – or are projected to have – a substantial structure between them and a transmitter actually receive the signals they need.

To see how this is achieved check out the latest white paper, Click here

 

Complex