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Ham radio: Antenna Theory

[last updated: 2024-03-01] ...
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(link to:) MIT presentation on antennas

(link to:) antenna-theory.com
(link to:) electronics-notes.com

This page is a collection of notes from several sources, much of it from the MIT presentation linked above
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  • The Basics: Antennas are designed to convert RF energy generated by your transmitter into electromagnetic waves that will propagate as far as possible away from your antenna.

  • Radio waves (electromagnetic fields) are composed of an electric field and a magnetic field.
    • Both the electric and magnetic fields are vector quantities, meaning that any measurement/calculation of the strength of either field will have two components: a magnitude/amplitude and a direction.
        The direction of the magnetic field is perpendicular to that of the electric field.
    • Radio waves propagate spherically (ie. in all directions) from each point on a physical antenna.
      However the net propagation from the sum total of all points on a given antenna will have a shape/distribution that is characteristic of the shape and configuration of the antenna elements.
    • Radio waves propagate with a 1/r factor, meaning that the strength of a signal, as measured at some distance from an antenna, will have a strength proportional to 1/r, where r is the distance from the antenna to the point being measured.
    • Radio waves propagate at the speed of light through a vacuum, and at lesser speeds in air or wires (search for "velocity factor")
      • Wavelength (meters/cycle) = Speed-of-Light (meters/sec) / Frequency (Hz=cycles/sec)
        ...

        Speed-of-Light = 300,000,000 meters/sec, denoted "c"
        W (m) = 300 / f (MHz)
        W (ft) = 984 / f (MHz)

    • antenna propagation maps are showing the Electric field

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  • In practice:
      In ham radio, there are 3 things we care about:
    • Efficiency:
      For a given amount of power sent into an antenna system, how much of it actually goes out as radio waves
    • Reflected power:
      For a given amount of power sent into an antenna, how much of it comes back down the line back into our transmitters.
      This is important because too much reflected power can damage the transmitter.
    • Directivity:
      Most antennas are not omnidirectional, that is, they radiate more power in some directions than in others.

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  • Metrics to evaluate antennas and their radiation properties:

    • Directivity:
      D = (maximum power density [which is a function of angle]) / (average power density [Prad/sphere-area])
      This formula is from the MIT presentation, but I confess I don't understand it's nomenclature
      The minimum Directivity is 1, which would be an antenna that radiated equally in all directions.

    • Polarization:
      In a receiving antenna composed of a wire (ie. a conductor), the incident/transmitted radio signal can only induce a current in that conductor (ie. be heard by the receiving antenna) if the physical orientation of the receiving antenna conductor is aligned (pointing in the same direction as) the electric field vector of the transmitted signal.
        from: https://blog.pasternack.com/antennas/antenna-polarization-matter/
        RF antenna are either linearly or circularly polarized. Linear polarized antenna are generally either vertically polarized or horizontally polarized, while circularly polarized antenna are either left-hand or right-hand circularly polarized. There is a third common type of polarization, which is a complex combination of both linear and circular polarization, known as elliptical polarization.

    • Impedance: (see also: Impedance Basics)
      Every component of a system will have an input and an output impedance. This applies to your transmitter, the transmission line connecting the transmitter to the antenna, and the antenna itself. In order to maximize the transfer of power from one component to the next, the output impedance of the first must match the input impedance of the next in the signal path.
      • Transmission Lines are the cables that connect your transmitter to your antenna.
        The voltage at a point on a transmission line divided by the current at that point = the "characteristic impedance" of the transmission line.
      • If the impedance of a transmission line is different than the impedance of the antenna, some portion of the signal will be reflected back to the transmitter.

        reflection coefficient

      • The amount that's reflected is quantified with "gamma" the reflection coefficient, which is the ratio of reflected to transmitted voltage (or current): "gamma" = V- / V+
      • Smith Charts map impedance onto reflection coefficient.
    • SWR:
      (see: https://www.antenna-theory.com/definitions/vswr.php)
      • "Standing Wave Ratio", also called VSWR ("Voltage ...")
        SWR is always a dimensionless (no units, ie. it's a ratio) positive number, equal to or greater than 1.0
      • VSWR is calculated from "reflection coefficient" (denoted by Greek capital Tau), which is also called "Return Loss" or "S11".
        VSWR = (1 + [abs value of] Tau) / (1 - [abs value of] Tau)
      • Reflection Coeff is greater than 0 and less than 1.

    • Efficiency:
      • Somewhere in here she talks about "electrically small antennas", but I'll have to re-watch the video to pull out an understanding of the details...
      • Efficiency is the ratio of: power actually radiated from the antenna, to the power delivered to the antenna.

    • Bandwidth:
      • Like a lot of electrical concepts in antenna theory, bandwidth is easier to understand with a picture, which I don't have at the moment. However if you imagine a graph of SWR for an antenna, it will mostly be a horizontal line, but will have a dip at the antenna's resonant frequency. Bandwidth is basically a measure of how sharp and narrow the dip is.
      • Q is "Quality factor", and is the inverse of bandwidth. The Chu limit states that "small antenna" bandwidth is (at best) proportional to the cube of "electrical size"
      • [formula]Chu ... 1 / (ka)^3
        where a is the physical size, and k is the "wave number"
        wave number is in units of reciprocal meters: 1/m
        k = (2*pi) / wavelength (meters)
        • for ka < 1 (a little less than 1/2 a wavelength), the antenna is by definition an "electrically small" antenna.
      • Antennas with 'fat' (high diam) wires tend to have higher bandwidth (reasons unknown)

      • Another way of defining/calculating it:
        Plot return loss in dB vs. freq. The bandwidth is defined as the freq delta between the points on either side of resonance peak that are at 10dB return loss. (??)

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  • Antennas are either loops or dipoles. If they're terminated with an open circuit, then they're dipoles, and if they're terminated with a short circuit, then they're loop antennas.
    • For dipoles, open-circuit-terminated antennas:
      Impedance at the open end will be infinity by definition
      At the open end, current will be zero, and voltage will be high
    • For loops, short-circuit-terminated antennas:
      Impedance at the shorted end will be zero by definition
      At the shorted end, current will be high, and voltage will be zero

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  • Misc Notes:

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