# Bandwidth, Q-factor, Radiation Eff calculations

Is it possible to give approximate answers about what an antenna is capable of? There are a lot of formulas out there, but every single one I found is based on actual measurement; input, output, SWR etc.

For example, I want to build a dipole for 450 MHz. What can I expect in bandwidth, Q-factor, impedance matching, SWR?

Is there some kind of standard chart board for different antennas regarding the specs mentioned above? Like standard values you can expect if the construction is not that bad.

Example: A Vivaldi antenna produced by amateurs is often around 50% radiation efficiency with an SWR of 10:1 due to the equipment used in the construction.

• @PhilFrost -- I was wondering originally if the OP in writing SVR was thinking of indicating a standing "voltage" ratio which is correctly given the abbreviation of VSWR. But, now that you corrected the question, I should edit and correct my answer. – K7PEH Oct 27 '15 at 16:12

Actual realistic and therefore useful antennas are not described by simple analytic formulas where you just plug in various parameters to compute a solution. Also, these other features such as bandwidth, impedance matching, SWR is not computed from simple formulas for such antennas.

They can be computed from a numerical modeling program that performs a numerical solution for the antenna. This is what the free program called NEC2 does. You provide an input file describing the geometry of the antenna and one or more other commands to describe excitation and and frequency of operation and then run the program to produce results. NEC2 will produce tables (aka arrays) of numbers.

Application programs such as:

Can all give you graphical output of various kinds of results including antenna impedance, SWR, and antenna Gain at given angles of elevation and azimuth, and other interesting things.

I don't think any of these will compute the Q-Factor for the simple reason that nobody cares to know the Q-Factor.

With EZNEC for example, the SWR plot that is given will tell you for a given operating frequency what the SWR is for nearby frequencies above and below the operating frequency. From this you can easily see the window of operation for the 2:1 (typical cutoff) SWR points below and above thus showing the bandwidth. Note that you can compute the bandwidth for the entire band, say 3.5 to 4.0 MHz for 80-meter band, or whatever for any antenna you model.

You can also model transmission line with some of the programs I have mentioned or you can treat the transmission line separately using some of the other available programs such as TLW made available by ARRL. Just google "ARRL TLW" and you should find a description and how to obtain it. It is freely distributed as part of the annual publication of the ARRL Handbook.

I have used all of the applications cited above but I prefer to use NEC4 (a newer and improved version of NEC2) along with the Mathematica application as the UI front-end. Mathematica Home Edition costs about \$300 or so, the NEC4 license was \$300 when I acquired it several years ago. But, you need to "program" your own graphics displays of the result data produced by NEC2 or NEC4 yourself -- that is what Mathematica does best.

If you want web resources to learn more about antennas than google is your friend. Start with the ARRL if you are a member, if not then buy their Handbook or maybe also their Antenna Handbook. For 2016 there is a brand new version of the Antenna Handbook published.

To get the answers you are looking for though, learn NEC2 and learn how to model simple dipole antennas and interpret the results. The NEC2 User Guide tells you all you need to know. See http://www.nec2.org and download the User Guide. You can also download the Theory and the Program Description to learn more about NEC2.

There are a couple of ways to approximately determine the antenna Q-factor (which is related to the bandwidth) without a full 3D simulation.

• One is to use this MATLAB script, which determines the antenna's theoretical bounds from its polarizability.

• Another approximation of the Q-factor which is from the 40's is to use the Chu limit

$$Q_{\text{Chu}} = \frac{1}{(ka)^3} + \frac{1}{ka}$$

where $k = 2\pi / \lambda$ and $a$ is the radius of the sphere enclosing the antenna.

It is important to note that the first method will give a much better result as it can find the Q-factor for spheroidal shells as well as spherical shells (Chu).

The radiation efficiency of all antenna systems is the quotient of its radiation resistance and the sum of the real (energy-dissipating) resistive losses comprising that system.

Some M-o-M software using NEC (Numerical Electromagnetics Code) reports values identified/expected to be radiation efficiency, but including the effects of propagation loss in those values.

Below is an example of a customized study where the radiation efficiency excludes propagation losses.