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=====ETA313-07: Theory Lesson 3: Antennas, Transmission lines, Propagation =====

[[user:kurser:ham_vt2025|Back to course information]]

**Recommended reading: KonCEPT page 191-229 (chapter 7 + 8) **

Start with transmission line (TL), the most difficult component.

characterized by: Characteristic impedance, Z_0, a geometry and material parameter. Length and the speed of light in the transmission line. Two metal conductors that guide the fields. 

Used for high frequency signals. Lambda = 300/f [MHz], Lambda similar to length in size. 

Waves propagate along transmission lines. Reflections along a TL are similar to light in a glass/water. Explain transmission/reflection coefficients. 

Reflections cause standing waves and non-optimal power transfer/losses 

VSWR = Voltage Standing Wave Ratio = Z1/Z2 OR Z2/Z1 so a x:1 relation is formed. 

We want to "match" the antenna, transmission line and radio to minimize losses. 

Balanced/unbalanced (differential/single-ended) TL are important and difficult. Explain this in detail.  

balanced TL folded out -> dipole antenna! Nice SWR achieved. L = lambda/2 = 300/(2*f) ~=(0,96*lambda/2)

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**Antennas**
\\ de SA6KRZ

Updated 2026-03-02

In this segment, possible exam questions have been marked //**POSSIBLE EXAM QUESTIONS**//.

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==What is an antenna?==

An antenna is a device that converts EM waves between a bound medium and a free medium, for instance between a cable and free space.

Alternative: //Antenna = two port that converts energy from propagating in a transmission line to propagation in free-space.//

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==Antenna types==

There are many different types of antennas, since different antenna designs are optimised for solving different problems. There is no antenna that is perfect for every single operational situation. However, the opposite is true; there are indeed antennas that are quite bad at everything.

A selection of different antenna types, roughly in order of most common -> least common
  * Dipole
  * Monopole
  * Loop antennas
  * Yagi (Yagi-Uda)
  * (Parabolic dish reflectors)
  * PCB/PIFA
  * Patch
  * Quad
  * Waveguide slot
  * Ground plane antenna (GP-antenna)
  * Horn antenna
  * Spiral/Helical
  * Vivaldi
  * J-pole
  * Bowtie

Antennas may often be combined together for different effects. Such a group of antennas acting together as one, is known as an //antenna array// (SE: gruppantenn). Some antenna array designs are more common than others, for example:
  * Log-periodic dipole array (LDPA) antenna

... however, in practice there is nothing prohibiting an antenna array from being built using any antenna type.

Very often, specific antennas are are combination of other antenna types. For example, the very common Yagi-Uda antenna, is usually built using a combination of three (or more) dipole antennas, and one magnetic loop antenna.

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==Antenna parameters and characteristics==

All antennas can be characterised using //at least// the following parameters:
  * Input impedance, Z_in
  * Standing wave ratio, SWR
  * Operational frequency band
  * Resonance frequency, f_0
  * Directivity, D, dBi, dBd
  * Antenna gain
  * Far-field distance = d_f > 2*D^2/λ, given d_f >> D, d_f >> λ
  * Radiation efficiency, η
  * Radiation pattern, E & H patterns
  * Polarisation and x-pol suppression

Many of these parameters can be analysed using a vector network analyser or an antenna analyser.

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==Introductory important terminology==

The actual metal sticks that point at different directions on an antenna, are commonly known as //elements// (SE: antennelement, spröt).
These elements are often mounted to a frame of sorts, like a large metal bar that supports all elements. This bar is known as the //boom// (SE: bom).

Often, antennas are shielded from the evil world of rain, snow, pidgeons etc. by placing them inside a plastic cover shell. This cover shell is known as a //radome// (SE: radom).

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==Direction==

The most ideal antenna is a single charge floating in free space, radiating as a sphere equally strongly in all directions. Such a single charge is known academically as an //isotropic radiator//. Practically, antennas are real objects and thus not single charges, meaning that the "radiation sphere" (made-up word) is very much not a sphere. Most antennas only //illuminate// (actual term) a smaller part of that hypothetic sphere, meaning that most of the EM field is sent/recieved from/to the antenna at that specific direction in space. The illuminated area is known as the //beam area// (SE: ??).

How small that illuminated segment of the sphere is as opposed to size the entire sphere, is known as the //antenna directivity//. The directivity is often given in dB with respect to that ideal //isotropic radiator//. The unit is thus **dBi**. A very large part of an antenna's design specification, is its directivity. Different types of antennas have very different directivities.

A higher directivity means that more of the emitted/recieved field is sent through a smaller portion of that sphere around the antenna. The antenna is in a way "pointing more" towards one direction. A high directivity thus means that the antenna is very good as emitting/receiving to that specific direction. And as a drawback, the antenna becomes worse at emitting/receiving in every other direction.

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==dBd==

Practically, it is not uncommon to describe the directivity of some antenna with respect to something more real. Such as, a dipole antenna's directivity. How much more "directive" (made-up word) is our antenna, in comparison to a dipole antenna?

A dipole antenna is -2.15 dB less "directive" than an isotropic radiator. Thus, the unit **dBd** = dBi - 2.15.
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//dBd = directivity in dB with respect to an ideal dipole antenna.//

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== Lobes (SE: Strålkäglor) ==

Important: almost always, antennas do not emit/receive in a single direction. Most antennas emit/receive in one "very good" direction, and a small set of "less good but OK" directions. How well an antenna is emitting to a particular direction, is known as a //lobe// (SE: strålkägla).

The direction with the highest directivity of the antenna, is known as the //main lobe//. Thus, the smaller lobes are known as //sidelobes//. The main lobe defines which way the antenna is pointing, both by convention and often in practice.

Simple antennas, like a monopole antenna, only have a single lobe. Very complex antennas, may have lobes that are shaped practically in any way imaginable. Example: an antenna in a satellite orbiting above a nation, might have an antenna with a lobe pattern (SE: strålningsdiagram) that is shaped according to the borders of that nation. The antenna is thus good at transmitting/receiving to/from that nation, and worse at transmitting/receiving to/from locations outside of that nation's borders. In practice, it is very hard to design an antenna with such a complicated lobe pattern. Companies approach this problem for instance using evolutional AI algorithms that brute-force designs until the lobe pattern is achieved. Another very common approach, is to make a very large array of antennas, and control the phase of the signal reaching each antenna, in order to achieve a more complicated lobe pattern.

A different example is the antenna running along the edge of your smartphone, disguised as a metal border rim. Having such a weird shape allows for a very high bandwidth, but the antenna must be paired with an always-on autotuner inside the phone for matching.


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==Shaping the lobes + Terminology 2==
The EM wave that we wish to transmit/recieve to the outside world, will travel along a cable into the antenna. Where that cable meets the antenna, is almost always at an antenna element. In a way, you could say that this antenna element is what is in fact transmitting inside of the antenna. This element is known as the //driven// element (SE: drivelement). An antenna may have several driven elements.

The resulting lobe pattern from the driven element, is then by-design usually deformed using other elements that are in fact not connected to the cable that fed the antenna. All elements on the antenna that are not driving the EM wave, are known as parasitic elements (SE: parasitelement).

These parasitic elements have different purposes. They could be used to direct the lobe pattern into some wanted direction; such elements are known as //directors// (SE: direktorer). Or, those elements could be to block off the lobe pattern from emitting/receiving into some direction; such elements are known as //reflectors// (SE: reflektorer).

Example: the Yagi-Uda antenna, has one driven element on its boom. To get the signal pointing forwards, three dipole directors are mounted at the front of the antenna. And to get the lobe pattern pointing less backwards, a reflector is mounted at its back.

In practice, reflectors are usually checkerboard-shaped meshes of wires.


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==A stricter definition of directivity==
The directivity of an antenna, is the maximum transmitted power in the main lobe, divided by the average power transmitted across the entire sphere. From this ratio, we may derive that the directivity D = (4*pi) / (beam area).

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==How wide is a lobe?==
Stand in front of a transmitting antenna with a power detector. Assume that the strongest power in the main lobe is denoted P. As you move to the side, you see the power going down. The point at which the power has dropped 3 dB, is known as the //-3 dB point// (SE: halvvärdesbredd). By convention, the lobe is said to end at this point. Even though there is some power being transmitted beyond that point, as you move to the side further. Another (less common) datasheet specification, is also the -10 dB point.
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Now, let's assume that you've found the -3 dB points to the left and to the right of the main lobe. If you draw a triangle between these two points and the antenna, you'll create some angle α at apex point of the triangle (at the antenna). This angle is known as the //beamwidth// of the lobe (SE: öppningsvinkel).\\

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==Gain and antenna efficiency==
In a datasheet, you will typically find an entry for //gain// (SE: antennvinst). Different sources will have different opinions on what is the gain of the antenna. Here, we choose to define the antenna gain as the //power gain// of the antenna. The power gain G is related to the directivity of the antenna as\\
G = η * D

... where η is the so-called efficiency factor of the antenna. In practice, there will be unexpected ohmic losses in the antenna, leading to an η that is smaller than 1.

It is thus useful to discuss a real antenna in terms of its gain, rather than in terms of its theoretical directivity.

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==Emitted power: p.e.p. and e.i.r.p==
The HAM radio band plan sets radiation emission limits in terms of power, either as **p.e.p.** or **e.i.r.p.** (peak emitted power, equivalent isotropic radiated power).

  * The p.e.p. limit defines how much peak power may be fed into your antenna.
  * The e.i.r.p. limit takes antenna gain into account as well, meaning that no lobe may peak above a certain power.

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//**POSSIBLE EXAM QUESTION**//
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In the 5.3515-5.3665 MHz band, a HAM radio operator may at most transmit with 15 W e.i.r.p. Are you allowed to transmit at 5.36 MHz with 10 W using a +3 dB gain directional antenna?
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Answer: No, this is not allowed. An antenna with +3 dB gain, would make a 10 W radiated emission seem as if we're transmitting with 20 W, which is above the e.i.r.p. limit.

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//**POSSIBLE EXAM QUESTION**//
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In the 1850-1900 kHz band, a HAM radio operator may at most transmit with 10 W p.e.p. Are you allowed to transmit at 1875 kHz with 10 W using a +20 dB gain directional antenna?
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Answer: Yes, this is allowed, since p.e.p. sets the limit of how much power is fed into the antenna, and does not account for directivity.

==Wavelength==
Size-wise, antenna //elements// are usually 0.25 · λ or 0.5 · λ in length/size. An antenna with several elements of different lengths, can usually operate fairly well across a span of frequencies.



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//**POSSIBLE EXAM QUESTION**// → Show on board, hard to visualise.
\\
You have a 40 m dipole antenna. What frequency would create a standing wave pattern on the antenna, that has 5 nodes?

  * 3.5 MHz
  * 7 MHz
  * 14 MHz
  * 28 MHz
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\\ Answer: (300 / 40) gives us a frequency of 7.5 MHz; this is the frequency of the current on the antenna that create one full-wave standing wave on the antenna, with one node at each of the two ends of the dipole. If we look at the half-wavelength frequency → 15 MHz, which has three nodes; one at each end of the dipole and one in the very centre. If we look at the quarter-wavelength frequency → 30 MHz, we get yet another two nodes of the standing wave pattern on the antenna. Thus, 28 MHz seems to be the most reasonable answer.


==Realistic design factors (SE: förkortningsfaktor)==
Antenna component dimensions have to be scaled down when making real antennas. There are various factors that all make up a 0-1 scaling factor, that effectively makes it so that your antenna is shorter than what it would have been if you only accounted for the wavelength of some frequency. Often, you may see that some factor is given as 0.95, 0.96 or 0.98 etc. For instance, aluminium tubing typically has a factor of 0.96.

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//**POSSIBLE EXAM QUESTION**//
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You are building a full-wavelength delta-loop antenna for 7.1 MHz. The wire has a scaling factor of 0.95. How much wire will you use in total?

  * 20.07 m
  * 40.14 m
  * 21.13 m
  * 42.25 m
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Answer: ( 300 / (1.0 · 7.1) ) · 0.95 = 40.14 m
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//**POSSIBLE EXAM QUESTION**//
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Roughly how long is the vertical element of a quarter-wavelength vertical antenna for 145 MHz?

  * 50 cm
  * 70 cm
  * 2 m
  * 4 m
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Answer: (300 / 145) · 0.25 ≈ 50 cm


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==Polarisation==

All antennas emit/receive EM waves. Meaning, that the antenna emits electric and magnetic fields. By convention, the orientation of the //electric// field is said to define the //polarisation// of the antenna. Example: let's say that the antenna is //vertically// polarised, then that would mean that the E-field is sent from the antenna like a sine wave moving up (and down) along the Z-axis, i.e. vertically with respect to the ground. Vice versa, //horizontal// polarisation means that the E-field is propagating like a sine wave that is laying down flat with respect to the ground.

Very often, it's fully possible to simply look an an antenna, and figure out its polarisation. "Where are the antenna elements pointing?"

Why polarisation is important: typically, the best transmission efficiency between two antennas, is achieved when their polarisations are matching.

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==Complicated: circular polarisation==

Let's imagine an antenna with two transmitting elements. Thus, there are two electric (E) fields to consider. Let's say that one is vertically polarised, and the other one horisontally polarised. Let's describe the first E field like a cosine with some phase, and the second E field like a sine with some phase.\\
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If we stand directly in front of where the antenna is pointing, we can see both the cosine and sine waves like composants in a complex vector. As time progresses, and the E cosine goes up/down while the other E sine goes left/right, that complex vector will thus be spinning around in a circle as time progresses. This type of polarisation is known as a circular polarisation; the emitted/received EM field is in a way "spinning around" in a circle, due to there being two transmitting E fields.

Circular polarisation is common in public FM radio broadcast (SE: rundradio). The advantage is that the receiver can be rotated at almost any direction with respect to the ground, and still be somewhat optimal to the transmitter. Another example is in satellite-to-Earth transmissions.

Common misconception: even though many circularly-polarised antennas are shaped like round objects, it is not necessary to have a round antenna to create circular polarisation. The circular polarisation itself stems from the E field composants spinning a complex vector around in a circle, with respect to the direction of the propagating EM wave. This effect is achievable using two antenna elements rotated 90 degrees like an "X", and then phase-shifting the fed signal to one of the antenna elements with 90 degrees. Assuming both elements were transmitting with equal magnitude.


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== Antenna impedance matching ==
Different antenna types have different ideal input impedances. And, the the input impedance is typically frequency dependent. For instance, a given antenna may look like a 50 Ω impedance at 5 MHz, but may look more like an open circuit at 10 MHz.

Example: the ideal dipole antenna has a 73 Ω input impedance. Feeding this antenna with a coaxial cable of 50 Ω characteristic impedance, leads to a 50 Ω -> 73 Ω impedance interconnect. This impedance difference will result in signal reflections, which are unwanted for several reasons.

Overcoming impedance differences in antennas may for instance be done using matching networks.

Matching an antenna gets harder as the operational band of the antenna grows larger.


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==Far-field==
All commonly used formulas related to antennas, assume simplifications that happen once we are standing at a large distance away from the antenna.
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The far-field distance = d_f > 2*D^2/lambda, given d_f >> D, d_f >> lambda.

Meaning, that for very high frequencies, our simplifications and thus our formulas, are valid already fairly close to the antenna. The opposite of the far-field is known as the near-field, where most of our formulas stop being valid, and in practice the behaviour of the antenna has to be numerically simulated. 



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== Propagation ==

**HF/short wave**

  1) Ground wave (20-40 km typical)
  2) Space wave (global range)
    * Reflections from the ionosphere's D, E, F regions. Sunlight ionize the ionosphere.
    * Reflections affect polarization chaotically.
    * D = 60-90 km height. 
      * "Dämpningsskiktet" attenuates signals
      * Only daytime
      * Attenuate <10MHz
    * E = 90-110 km
    * F = F1 + F2 = 150-350 km - reflection. 
      * Reflect <30-50MHz depending on sun activity
      * Created during daytime, slow to unionize

**3.5-7 MHz**
  * Attenuated by D
  * skyward wave/antenna can reflect back to local contacts (E/F)
  
**14-30 MHz**
  * Not really affected by D
  * skyward wave/antenna cannot reflect back to local contacts (E/F)
  * Sporadic-E might enable local connections

DX -> 10 degree max antenna gain is best

**VHF/UHF/...**
  * Penetrates the atmosphere, EME possible
  * Basically only local line-of-sight connections possible
  * Troposphere propagation possible. Heat and humidity gradients guide waves. Ex. hearing Danish FM radio in Göteborg. 
  * northern lights reflections >25 MHz. Distorts signals, phone sounds creepy.
  * Moon/meteor/satellite/airplane scatter
    * Reflect signals from big things

**Microwaves**
  * Moon/meteor/satellite/airplane scatter
    * Reflect signals from big things
    * Also rain scatter

Fading example with cellphone if possible 


Radio Antenna Fundamentals Part 1 1947

https://www.youtube.com/watch?v=JHSPRcRgmOw&ab_channel=GerryTrenwith 

Vocabulary

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