# 4NEC2 – summary statistics discussion

I am a frequent user of 4NEC2 despite its many defects. It is a great work of software, in need of improvement that I suspect will never happen. Its author explained some time ago that it was developed in VB6 and with Windows upgrades, he no longer has a working VB6 development platform.

So, despite its defects, it is a very useful tool.

I will sometimes substitute _ for – in some 4NEC2 quantity labels for clarity in mathematical expressions.

Let us draw on the IEEE standard dictionary of electrical and electronic terms (IEEE 2013) for widely accepted meanings for some key terms.

### Radiation Sphere (for a given antenna)

A large sphere the center of which lies within the volume of the antenna and the surface of which lies in the far field of the antenna, over which quantities characterizing the radiation from the antenna are determined.

The definition of Radiation Sphere is important in that it defines where radiation is to be observed, it is to be observed in the far field.

The ratio of power radiated by an antenna to the square of the RMS antenna current referred to a specific point.

Note that Radiation Sphere requires that radiated power must be measured / determined / summed in the far field.

The ratio of the total power radiated by an antenna to the net power accepted by the antenna from the connected transmitter.

Note that Radiation Sphere requires that radiated power must be measured / determined / summed in the far field.

Radiation fields decay inversely proportional to distance, other fields immediately around an antenna decay more quickly and are insignificant for the purpose of radio communications at great distances. Hence, Radiation is the usual objective of radio communications antennas.

### Directivity

The ratio of radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions.

## 4NEC2 main form 4NEC2's main form has several related calculated results that bear comment / explanation. These values are all calculated from the NEC output report file which can be viewed by clicking the tenth button on the toolbar.

This article discusses interpretation of the form for the simple case of a single source.

## Input power

Input power is the value specified in 4NEC2's settings. This does not set the amplitude of sources, but is used to scale the report values to displayed results so that input power is the specified value.

Note that NEC uses peak values to specify amplitudes, and 4NEC2 effectively transforms these values to RMS for display.

Radiat-power would appear to be Input Power less Structure Loss less Network Loss.

Structure Loss is the reported loss from the NEC report due to the structure, eg conductor loss, loads etc. The value is calculated for the simplest runs.

Network Loss is the reported loss from the NEC report due to the network elements, eg due to NT elements. The value is calculated for the simplest runs.

The displayed value is scaled as discussed under Input Power.

The quantity Radia-power does NOT mean the total radiated power, and it is inconsistent with the use of radiation elsewhere in 4NEC2.

## Efficiency

Efficiency appears to be calculated as $$Efficiency=(1-\frac{StructureLoss+NetworkLoss}{InputPower}) \cdot 100%$$.

The value is calculated for the simplest runs, and does not capture all system losses so it deserves a qualified name.

Radiat-eff appears to be calculated as the sum of power in the far field divided by the InputPower

$$Radiat_eff= (1-\frac{StructureLoss+NetworkLoss+GroundLoss}{InputPower}) \cdot 100%$$. The value is calculated only for for runs that calculate the “Far Field pattern”. Since it depends on summing the far field, it requires a model run of sufficient resolution to give good accuracy.

## RDF (dB)

RDF is for Relative Directivity Factor is not an industry standard term, but there is a Wikipedia page. which states

it is the antenna gain in the forward direction divided by the gain in all other directions.

This is equivalent to the industry standard term Directivity expanded earlier… hams do tend to invent terms for things rather than use industry standard terms and meanings.

W8JI also liberally uses the term Receiving Directivity Factor (directivity). Disciples of ON4UN seem to like the term.

So, RDF appears to be calculated as the maximum power in the far field divided by the total power in the far field and is equivalent to industry term Directivity.

## Inferred quantities

Radiation resistance is used with a variety of meanings, especially among hams. Let's use the definition given earlier and the specific point is the feed point.

Let's denote the real part of feed point impedance Impedance as Rf.

Rr can be calculated from the summary form statistics as $$R_r=Radiat_eff \cdot R_f$$

### Equivalent structure+network loss resistance

Rsn can be calculated from the summary form statistics as $$R_{sn}=(1-Efficiency) \cdot R_f$$

### Equivalent ground loss resistance

Rg can be calculated from the summary form statistics as $$R_g=R_f-R_{sn}-R_r$$

### Worked example

From the form above:

$$R_f=Real(Impedance)=Real(47-\jmath 0.37)=47 \Omega$$ $$R_{sn}=(1-Efficiency) \cdot R_f=(1-\frac{89.06}{100}) \cdot 47=5.14 \Omega$$ $$R_r=Radiat_eff \cdot R_f=\frac{38.91}{100} \cdot 47=18.29 \Omega$$ $$R_g=R_f-R_{sn}-R_r=47-18.29-5.14=23.57 \Omega$$

## What about the surface wave (ground wave)?

In the strict sense that radiation is detached energy that is dispersed in space without loss and the power density falls as the square of distance, the surface wave is not quite that. It's attenuation is faster than radiation in a vacuum and it will often be attenuated sufficiently to be insignificant are great distances. To that extent, the attenuation of the surface wave (ie absorption by the natural ground) can be accounted for as part of ground loss.

In a ground wave application, one might want to perform analysis at some lesser distance and  include the power in the ground wave at that distance, but perhaps it should not all be lumped together under the title radiation.

A particular installation might be licenced for a given cymomotive force at some specific distance, and one could calculate an efficiency figure for the system being the power required with lossless antenna and ground to achieve that objective as a percentage of that actually required with real system losses… but it is not Radiation Efficiency as defined in (ITU 2013).