4nec2 Model Analysis of Quadcopter "Range Extender" Antennas

Modelling Aftermarket 2.4 and 5.8 GHz Antennas for Miniature UAV Controllers

by Dr. Carol F. Milazzo, KP4MD (posted 22 March 2022)
E-mail: [email protected]

Summary

This paper describes 4nec2 model analysis of the expected performance of 2.4 and 5.8 GHz "Parabolic" reflectors, Yagi-Uda antennas, and combination "ParaYagi" antennas for quadcopter radio control links.


Contents

Introduction

Over the past decade, radio-controlled miniature unmanned aerial vehicles (UAVs) have grown in popularity among recreational hobbyists and for commercial surveillance, aerial photography, and military users.  Early civilian radio-controlled model aircraft used analog modulation on a limited number of control frequencies in the 27, 49, 50, and 72 MHz bands.  With the coming of microprocessor-controlled quadcopter drones, smaller antennas and digital communication protocols on the 900 MHz ISM band and 1.3 GHz video feeds became popular.  Now in the early 21st century, inexpensive spread spectrum control systems in the unlicensed 2.4 GHz and 5.8 MHz frequency bands are increasingly utilized.1

In residential and commercial areas, secure UAV flight control can be compromised by unintentional radio frequency interference (RFI) from devices and other users that share 2.4 GHz and 5.8 GHz, including Bluetooth devices, car alarms, cell phones, computer peripherals, toys, WiFi networks, wireless speakers, microwave ovens, and licensed radar, ISM and amateur radio stations to name a few.  Such RFI can unduly limit the range within which the UAV can safely fly.

UAVs and their controller units typically employ the maximum permitted transmitter power (typically under 1 watt) and a pair of omnidirectional vertical dipole whip antennas for diversity reception.  The UAV must use a non-directional antenna due to its variable orientation; however, a directional antenna on the controller can enhance the control link by increasing the signal strength at the UAV and by reducing the controller's sensitivity to RFI from undesired directions. 

The antenna enhancers that have become popular among UAV pilots are: a passive cylindrical metallic "parabolic" reflector placed behind each dipole; a Yagi-Uda configuration of one reflector dipole and several director dipole elements that slip over the stock dipole antenna; and, a "ParaYagi" combination of the parabolic reflector and the Yagi.  The model dimensions reported here are from Ali Vekta's "ParaYagi P2 Extender" 3D printer files on Thingiverse.com.2  Several UAV pilots have field tested similar antennas using their maximum control range as a measure of the efficiency of each antenna configuration.3,4 

Field test results are subject to variations in the RFI environment and errors and instability in antenna aiming, but are expected to reflect the robustness of the control link when flying within usual distances.  NEC modeling of the theoretical gain and radiation patterns of these antenna configurations can further validate such observations.  These antenna analyses were performed with the 4nec2 modeling software that is free for download at http://www.qsl.net/4nec2.5
Figure 1. The 3D Printed 5.8 GHz
                    "Parayagi" Antenna on a DJI Spark
                    Controller.
Figure 1. The 3D Printed 5.8 GHz "ParaYagi" Antennas on a DJI Spark Controller.

The Stock Dipole Antennas and their 4nec2 Models

The two vertical whips of the DJI Mavic Mini controller (photo below)6 are printed circuit bowtie antennas for 2.4 GHz and 5.8 GHz with a common feed point.  The bowtie consists of two identical dipoles for each band connected in parallel to achieve broader bandwidth than a single dipole.  Similar to WiFi access points, two whips are used to reduce multipath signal fading through diversity reception.  This antenna will exhibit a mostly omnidirectional horizontal donut shaped radiation pattern with nulls directly above and below the antenna (Figures 5 & 6).  The proximity of the two whips to each other will skew the omnidirectional pattern to some degree.

Also below are photos7 of the printed circuit 2.4/5.8 GHz vertical fan dipoles that are glued inside the sides of the DJI Spark quadcopter.  In the DJI Mavic Mini, the dipoles are located inside the vertical portion of the two front arms.  Two antennas are again used to achieve diversity reception.  The position of the antennas with respect to the internal electronics and battery would also cause some skewing of their otherwise omnidirectional radiation pattern.  The controller would observe this as a variation in signal strength as the quadcopter rotates (yaws). Transmitter power and stock antenna parameters for all DJI drones are published in FCC Specifications and Compliance Reports.8

DJI Mavic Mini Controller Dipole
                            Antennas DJI Spark Internal 2.4/5.8 GHz Antenna DJI Spark Internal 2.4/5.8 GHz Antenna
Figure 2. The vertical whips of the DJI Mavic Mini controller.6 Figures 3 & 4. The printed circuit 2.4/5.8 GHz vertical fan dipoles in the DJI Spark quadcopter.7

The dimensions are assigned to defined variables to facilitate the future use of 4nec2's optimization function on the models. 
The dipole model lengths are selected to resonate mid-band at 2.437 GHz and 5.785 GHz. 
The dipoles are modeled with 3mm diameter to match the Yagi elements.  "Leg lengths" are one-half of the full length of each element.
All element segmentation is selected to approximate the 4mm segment length of the "parabolic" reflector model.

Table 1.  NEC Dipole Model Variable Definitions
Variable definitions
Symbol 2.4 GHz
5.8 GHz
Dipole leg length (m)
dr 0.0277
0.01166
Dipole number of segments
s 13
7
Radius of dipole (m)
rad
0.0015
0.0015
Table 2.  Dipole Model Parameters
Dipole Characteristics
2.4 GHz
5.8 GHz
Maximum gain dBi
2.14
2.14
3 dB Horizontal Beamwidth
omni omni
3 dB Vertical Beamwidth
40 40

Dipole Horizontal
                  Radiation Pattern
Figure 5. Dipole Horizontal Pattern

Figure 2. Dipole
                  Vertical Radiation Pattern
Figure 6. Dipole Vertical Radiation Pattern


The "Parabolic" Reflector Models

The 4nec2 Geometry Builder program is used to construct the wire frame simulation model of the 90 reflector.
The reflector is truly cylindrical, not parabolic.
The reflector frame is 45mm high, but the height of the metal reflector is 40mm with an 80mm aperture width. 
The center of the reflector is spaced 25mm behind the dipole.

3D Reflector
                            Model 4nec2
                            Reflector Model
Figure 7.  The 3D "Parabolic" Reflector Model Figure 8.  The 4nec2 "Parabolic" Reflector Model

In the 4nec2 model horizontal and vertical plane radiation patterns and tables:

  1. The blue traces represent the stock antenna, and the red trace represent the comparison antenna.
  2. The effects of ground reflections are ignored.
  3. dBi is decibel gain over a theoretical isotropic radiator.
  4. The desired heading is 90 in the horizontal plane and 0 in the vertical plane (to the right) in all cases.
  5. The 3 dB beamwidths are the angles from the maximum at which gain is 3 dB down.
4nec2 Cylinder Reflector Variables
Figure 9. Cylinder Reflector Variables

Table 3.  "Parabolic" Model Parameters
"Parabolic" Model Parameters
2.4 GHz
5.8 GHz
Maximum gain dBi
5.04
7.66
Maximum lobe direction
270 (rear)
90
3 dB Horizontal Beamwidth
100 20
3 dB Vertical Beamwidth
33 42


2.4 GHz "Parabolic" reflector horizontal and vertical radiation patterns compared to the stock dipole antenna.

At 2.4 GHz the "parabolic" reflector model shows equal gain to the dipole in the forward 90 heading and 5.04 dBi gain towards the rear direction (270).
This paradoxical behavior at 2.4 GHz would occur because the reflector is vertically shorter than the half-wave dipole. Likewise, this reflector's horizontal aperture width is under one wavelength, too little for forward gain.9
In agreement with this analysis, "DJI Alex" documented no significant difference with the stock antennas or the "parabolic" reflectors in his 2.4 GHz field test video at https://youtu.be/3ALXqGrJxJ4?t=458.3

The 2.4 GHz horizontal
                            radiation pattern of the 'parabolic'
                            reflector compared to the stock dipole
                            antenna. The 2.4 GHz vertical
                            radiation pattern of the 'parabolic'
                            reflector compared to the stock dipole
                            antenna.
Figure 10.  The horizontal radiation pattern of the 2.4 GHz 'parabolic' reflector Figure 11.  The vertical radiation pattern of the 2.4 GHz 'parabolic' reflector

5.8 GHz "Parabolic" reflector horizontal and vertical radiation patterns compared to a dipole antenna.

At 5.8 GHz the 4nec2 model of the "parabolic" reflector shows 5.4 dB gain over the dipole in the desired direction.
The reflector's horizontal pattern displays most forward gain is confined +/- 15 from the 90 desired heading.  Its vertical pattern shows significant signal power is dispersed 30 above and below the desired direction.

The 5.8 GHz horizontal
                            radiation pattern of the 'parabolic'
                            reflector compared to the stock dipole
                            antenna. The 5.8 GHz vertical
                            radiation pattern of the 'parabolic'
                            reflector compared to the stock dipole
                            antenna.
Figure 12.  The horizontal radiation pattern of the 5.8 GHz 'Parabolic' reflector Figure 13.  The vertical radiation pattern of the 5.8 GHz 'Parabolic' reflector

The Yagi Antenna Models

Here are the 3D model diagrams of the 2.4 GHz and 5.8 GHz Yagi antennas. 

2.4 GHz
                          Yagi 3D Model 5.8 GHz
                          Yagi 3D Model
Figure 14.  2.4 GHz Yagi 3D Model
Figure 15.  5.8 GHz Yagi 3D Model



Table 4.  Yagi Model Variable Definitions
Variable definitions
Symbol 2.4 GHz
5.8 GHz
Dipole leg length (m)
Position (m)
dr

0.0277
0
0.01166
0
Dipole and reflector
# of segments
s 13
7
Directors # of segments
s
13
5
Radius of elements (m)
rad
0.0015
0.0015
Reflector leg length (m)
Position (m)
r
xr
0.03
-0.022
0.01225
-0.01
Director 1 leg length (m)
Position (m)
d1
xd1
0.024
+0.0115
0.00725
+0.01
Director 2 leg length (m)
Position (m)
d2
xd2
0.0245
+0.0307
0.00725
+0.02
Director 3 leg length (m)
Position (m)
d3
xd3
0.024
+0.0557
0.00725
+0.03
Director 4 leg length (m)
Position (m)
d4
xd4

0.00725
+0.04
Director 5 leg length (m)
Position (m)
d5
xd5

0.00725
+0.05


Table 5.  Yagi Model Parameters
Yagi Antenna Model Characteristics
2.4 GHz
5.8 GHz
Maximum gain dBi
9.97
10
Maximum lobe direction
90
90
3 dB Horizontal Beamwidth
35 34
3 dB Vertical Beamwidth
27 27

2.4 GHz Yagi horizontal and vertical radiation patterns compared to the stock dipole antenna.

The 2.4 GHz Yagi antenna exhibits 7.8 dB greater gain than the stock dipole antenna in the desired heading.  The Yagi antenna offers approximately +/-30 focusing of the beam in both the horizontal and vertical planes.
"DJI Alex" documented greater than 2260m range with the Yagi compared to 1600m range with the stock dipole antenna in his field test video at https://youtu.be/3ALXqGrJxJ4?t=560.3

2.4 GHz
                          Yagi Antenna horizontal radiation pattern 2.4 GHz Yagi Antenna vertical radiation
                          pattern
Figure 15.  The horizontal radiation pattern of the 2.4 GHz Yagi antenna
Figure 16.  The vertical radiation pattern of the 2.4 GHz Yagi antenna

5.8 GHz Yagi horizontal and vertical radiation patterns compared to the stock dipole antenna.

At 5.8 GHz, the Yagi antenna exhibits 2.4 dB additional gain and better directivity compared to the "Parabolic" reflector.  The Yagi antenna offers approximately +/-30 focusing of the beam in both the horizontal and vertical planes.
Nick Daly demonstrated similar results in his 5.8 GHz comparison of the Yagi and parabolic reflector in his YouTube video https://www.youtube.com/watch?v=3JlziZsGBdM4

5.8 GHz
                          Yagi Antenna horizontal radiation pattern 5.8 GHz Yagi Antenna vertical radiation
                          pattern
Figure 17.  The horizontal radiation pattern of the 5.8 GHz Yagi antenna Figure 18.  The horizontal radiation pattern of the 5.8 GHz Yagi antenna


The "ParaYagi" Antenna Models

The "ParaYagi" models combine all the elements and dimensions of the respective "parabolic" reflector and the Yagi antenna models. 

The
                          Parayagi 3D model The
                          Parayagi 4nec2 model
Figure 19.  2.4 GHz and 5.8 GHz "ParaYagi" 3D Models Figure 20.  5.8 GHz "ParaYagi" 4nec2 Model
Table 6.  "ParaYagi" Model Parameters
"ParaYagi" Model Characteristics
2.4 GHz
5.8 GHz
Maximum gain dBi
9.79
10.4
Maximum lobe direction
90
90
3 dB Horizontal Beamwidth
37 30
3 dB Vertical Beamwidth
26 30

2.4 GHz "ParaYagi" Antenna horizontal and vertical radiation patterns compared to the stock dipole antenna.

At 2.4 GHz, adding the "parabolic" reflector slightly enlarges the rear lobe of the Yagi antenna pattern.  The reflector adds no significant effect to 2.4 GHz Yagi antenna's forward gain and directivity.

2.4 GHz
                          "Parayagi" Antenna horizontal
                          radiation pattern
2.4 GHz
                          "Parayagi" Antenna vertical
                          radiation pattern
Figure 21.  2.4 GHz "ParaYagi" Antenna horizontal radiation pattern
Figurre 22.  2.4 GHz "ParaYagi" Antenna vertical radiation pattern

5.8 GHz "ParaYagi" Antenna horizontal and vertical radiation patterns compared to the stock dipole antenna.

At 5.8 GHz the "ParaYagi" combination antenna suppresses the rear lobes of the Yagi antenna.  The addition of the reflector offers 0.4 dB increase in forward gain over the Yagi antenna alone.

5.8 GHz
                          "Parayagi" Antenna horizontal
                          radiation pattern
5.8 GHz
                          "Parayagi" Antenna vertical
                          radiation pattern
Figure 23.  5.8 GHz "ParaYagi" Antenna horizontal radiation pattern
Figure 24.  5.8 GHz "ParaYagi" Antenna vertical radiation pattern

Discussion

The observed field test signal strengths agree with the model prediction of greatest signal strength with the Yagi antennas and least signal strength with the stock dipole antennas.

Miniformer published their laboratory gain measurements of various 5.8 GHz antenna extenders.10  Despite some errors introduced by their environmental variables, it is interesting to compare the Miniformer results against the 4nec2 model gain calculations for those antennas.  Table 8 lists the Miniformer power measurements in microwatts, their dBu unit equivalents, and these values normalized to the 2.14 dB gain of the stock dipole antenna.

Table 7.  Summary of 4nec2 Model Parameters
4nec2 Models
Dipole Parabolic
Yagi
ParaYagi
Parameters
2.4 GHz
5.8 GHz
2.4 GHz 5.8 GHz 2.4 GHz 5.8 GHz 2.4 GHz
5.8 GHz
Maximum gain dBi
2.14
2.14
5.04
7.66
9.97
10
9.79
10.4
Maximum lobe direction omni
omni
270 (rear) 90 90 90 90 90
3 dB Horizontal Beamwidth
omni
omni
100 20 35 34 37 30
3 dB Vertical Beamwidth
40 40
33 42 27 27
26 30
Table 8.  Comparison of 4nec2 Model Parameters and Miniformer Observations
5.8 GHz Antennas
Dipole Parabolic
Yagi
ParaYagi
Miniformer power W
0.9
2.7
3.0
3.6
Miniformer power dBu
-0.46
4.31
4.77
5.56
Miniformer power normalized
2.14
5.99
6.45
7.24
4nec2 theoretical gain dBi
2.14
5.04
9.97
9.79
Variance dB
0
0.95
-3.52
-2.25


MAVIC MINI
                            antenna test comparison - Parayagi,
                            Parabolic & Yagi Range Extenders &
                            Yagi
MAVIC MINI antenna test comparison - Parayagi, Parabolic & Yagi Range Extenders MAVIC MINI antenna test comparison - Parayagi, Parabolic & Yagi Range Extenders



5.8 GHz Quadcopter Extender Antenna Comparison Tested 2.4 GHz Yagi > Reflector > Stock Antennas

These data agree in that both the Yagi and ParaYagi antennas exhibit greater gain than the Parabolic antenna with no greater than 3.5 dB variance between expected and observed values.


Conclusions

  1. The "Parabolic" reflector offers a moderate contribution to the forward gain and directivity of the stock antenna at 5.8 GHz.  The reflector contributes no significant effect to the stock antenna at 2.4 GHz.
  2. The Yagi antenna provides improved signal gain and directivity over a "Parabolic" reflector at both 2.4 GHz and 5.8 GHz.
  3. The "Parabolic" reflector exerts little additional effect when combined with the 2.4 GHz Yagi antenna.  At 5.8 GHz, adding the "Parabolic" reflector suppresses the rear lobes of the Yagi antenna pattern.

I now rarely observe signal dropouts and video feed lag in my field tests with the 5.8 GHz Yagi or ParaYagi antennas.  While flying at a distance, I have observed loss of signal when I divert the antennas more than 30 vertically or horizontally from the direction of the quadcopter.  The stable and correct aim of these directional antennas is increasingly important for flight control over greater distances.

References

  1. Radio Control, Wikipedia
  2. PARAYAGI P2 Extender, Ali Vekta, Thingiverse, 7 July 2021
  3. DIY Range Extenders VS Parabolic - MAVIC MINI, DJI Alex, 15 May 2020
  4. Parabolic Mirrors vs Yagi Antennas | Mavic Mini Video Comparison, Nick Daly, 21 June 2020
  5. 4nec2 antenna modeling software, Voors, A.
  6. DJI Mavic Mini Controller Antenna, DJI Mavic Mini Forum, 15 May 2020
  7. DJI Spark Internal Antenna, DJI Spark Forum, 29 Jan 2018
  8. DJI FCC Specifications and Compliance Reports, https://www.fccid.io/SS3
  9. Antenna Aperture, Wikipedia
  10. Mavic Mini Antenna Test Comparison - Parayagi, Parabolic & Yagi Range Extenders, Miniformer, 2 July 2020

Appendix

4nec2 Model Files
4nec2 Models 2.4 GHz 5.8 GHz
Dipole
2GHzDipole.nec
5GHzDipole.nec
Parabolic
2GHzPara.nec
5GHzPara.nec
Yagi
2GHzYagi.nec 5GHzYagi.nec
ParaYagi
2GHzParaYagi.nec 5GHzParaYagi.nec

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