Glossary

47 terms, 13 concepts, and 29 formulas, each linked to the lessons that teach it. Search matches names, abbreviations, aliases, and definitions.

• A circuit is a closed loop, and current is the same all the way round it

  conceptintro

  Current only flows in a complete loop. In any single loop the same current passes through every element, and the voltages dropped across those elements sum to the voltage applied.

  Why it matters. This is the mental model that makes troubleshooting possible. A dead radio is almost always a broken loop — a blown fuse, a corroded ground, a connector that looks seated and is not. Finding it means asking where the loop opens, not which component "failed".

  Common mistakes (1)

  • ✗ Current is used up as it goes round the circuit, so less comes back than went out.
    ✓ Charge is conserved. The current leaving the supply equals the current returning to it. What is consumed is energy, and that shows up as the voltage dropped across each element.

  Taught in: charge current voltage, ohms law

• A decibel is always a comparison

  conceptcore

  Decibels express how much bigger one quantity is than another. Without a stated reference, a bare dB figure describes a change, not a level.

  Why it matters. It lets you add gains and losses along a signal path instead of multiplying them: 100 W in, minus 3 dB of feed line, plus 6 dB of antenna gain, is simply +3 dB overall. Suffixed units (dBm, dBW, dBd, dBi) attach the missing reference.

  Common mistakes (2)

  • ✗ An antenna with 6 dB gain amplifies the signal.
    ✓ It is passive and adds no energy. It concentrates radiation in some directions by taking it away from others, and the gain figure compares it with a reference antenna — an isotropic radiator for dBi, a dipole for dBd.
  • ✗ Doubling power doubles your signal strength at the far end.
    ✓ Doubling power is 3 dB, and one S-unit is conventionally 6 dB. Going from 50 W to 100 W is half an S-unit — usually not the difference between a contact and no contact.

  Taught in: decibels

• A squelch tone is a filter on your receiver, not a lock on the channel

  conceptintro

  CTCSS and DCS decide when your own receiver's squelch opens. They do not encrypt, do not prevent others from hearing you, and do not prevent you from transmitting on top of someone else.

  Why it matters. Radios sold as having "privacy codes" teach a false model, and operators who believe it double or transmit over other users constantly — because their radio was silent, so they assumed the channel was clear. The practical rule is to turn tone squelch *off* to listen before transmitting.

  Common mistakes (2)

  • ✗ Setting a privacy code means nobody else can hear my conversation.
    ✓ Anyone monitoring the channel with squelch open, or with the same tone, hears everything. The transmission is plain FM voice.
  • ✗ If my radio is quiet, the channel is free.
    ✓ Your radio is quiet because the tone did not match. Open the squelch or switch tone decoding off and listen before you transmit.

  Taught in: repeaters and tones

• Antenna Gain

  termunit: dBcore

  How much more strongly an antenna radiates in its favoured direction than a reference antenna — dBi against an isotropic radiator, dBd against a half-wave dipole.

  More

  dBi and dBd differ by 2.15 dB (dBi = dBd + 2.15), and manufacturers naturally prefer the larger number. A passive antenna adds no power; gain in one direction is always paid for from another.

  Taught in: antennas

• Bands are named by wavelength, radios are tuned by frequency

  conceptintro

  An amateur band's name is the approximate wavelength of the signals in it. Dividing 300 by the frequency in megahertz gives that wavelength in metres.

  Why it matters. Band plans, antenna lengths, and casual conversation all use wavelength, while the radio's display uses frequency. Converting in your head — 146 MHz is 2 metres, 14 MHz is 20 metres, 440 MHz is 70 centimetres — makes both the exam and on-air conversation much faster.

  Common mistakes (1)

  • ✗ The band name gives the exact wavelength of every signal in the band.
    ✓ It is a round-number label for the band's neighbourhood. The 2 metre band runs 144-148 MHz, where true wavelength ranges from about 2.08 m to 2.03 m.

  Taught in: what a radio wave is, frequency and wavelength

• Bonding

  termcore

  Connecting all ground rods, equipment grounds, and the electrical service ground together with heavy conductor, so no potential difference can develop between them.

  More

  Multiple separate grounds are worse than one: a surge raises one rod's potential relative to another, and the difference appears across whatever equipment bridges them. Bonding removes the difference.

  Taught in: electrical safety

• Capacitance

  Ctermunit: Fintro

  The ability to store energy in an electric field between conductors, measured in farads. A capacitor opposes a change in voltage.

  Do not confuse with: inductance

  Taught in: capacitance and inductance

• Capacitive reactance

  formulacore

  XC = 1 / (2 * pi * f * C)

  Taught in: reactance and impedance

• Certification attaches to the radio, not to your licence

  conceptcore

  A Part 95 service authorises specific *transmitter types*, certified by the FCC for that service. Holding a licence does not make an uncertified radio legal to transmit with on those channels.

  Why it matters. It is the single most common unintentional violation in the personal radio services. An inexpensive programmable handheld will happily tune GMRS frequencies; that it *can* is not a statement that it *may*. Section 95.1761 goes further and forbids certifying a GMRS transmitter that is also capable of operating in a service which requires no certification — which is precisely what an amateur-capable handheld is.

  Common mistakes (2)

  • ✗ I have a GMRS licence, so I can use any radio on GMRS channels.
    ✓ The licence authorises you; certification authorises the equipment. Both are required. A radio certified only for the Amateur Radio Service is not certified for GMRS, and cannot be.
  • ✗ The amateur service also requires type-accepted radios.
    ✓ It largely does not — home-built and modified equipment is a normal part of amateur radio. That asymmetry is exactly why one handheld cannot lawfully serve both.

  Taught in: frs gmrs murs

• Characteristic Impedance

  Z0termunit: ohmcore

  The impedance a transmission line presents to a wave travelling along it, set by the line's geometry and dielectric — not by its length.

  More

  Common values are 50 ohms for station coax, 75 ohms for video and broadcast feeds, and 300-600 ohms for open-wire line. A line terminated in its own characteristic impedance shows no standing wave at any length.

  Taught in: feed lines

• Compliance is the licensee's job, and it is re-evaluated on change

  conceptintro

  The station licensee is responsible for ensuring nobody is exposed above the FCC limits, and must re-evaluate the station whenever anything that affects exposure changes — power, antenna, mode, or location.

  Why it matters. An evaluation is not a one-time certificate. Moving an antenna, adding an amplifier, or switching to a high-duty-cycle digital mode all invalidate the previous result.

  Common mistakes (1)

  • ✗ Once my station passes an RF exposure evaluation, I am done.
    ✓ The evaluation must be repeated whenever a change could affect exposure. It describes a configuration, not a station.

  Taught in: rf exposure

• Conductance

  Gtermunit: Score

  The reciprocal of resistance, measured in siemens. Handy for parallel circuits, where conductances simply add.

  Taught in: series and parallel

• Continuous Tone-Coded Squelch System

  CTCSStermintro

  A sub-audible tone transmitted alongside speech that keeps a receiver's squelch closed unless the matching tone is present.

  More

  Consumer radios label these "privacy codes", which is the single most damaging piece of marketing in the personal radio services. A tone determines what *your* radio lets you hear. It does not encrypt anything, it does not stop anyone from hearing you, and it does not stop you from transmitting over someone already using the channel.

  Do not confuse with: dcs

  Taught in: repeaters and tones

• Control Operator

  termcore

  The licensed amateur designated by the station licensee as responsible for the emissions from a station. Every transmission has one, and the privileges of their licence class set what the station may do.

  More

  The station licensee and the control operator are separate roles that are usually the same person. When they differ, both are responsible for proper operation, and the control operator's class governs the privileges — which is how a Technician may transmit on an Extra's station under that Extra's supervision, and why the Extra must be present at the control point.

  Taught in: automatic control and international

• Current

  Itermunit: Aintro

  The rate at which charge flows past a point in a circuit, measured in amperes. One ampere is one coulomb per second.

  More

  Current is measured *through* something, which is why an ammeter goes in series and a voltmeter goes in parallel. Getting that backwards is how people destroy multimeters: an ammeter across a supply is a short circuit.

  Do not confuse with: voltage

  Taught in: charge current voltage

• DC power law

  formulaintro

  P = E * IE = P / II = P / E

  Taught in: power and heat

• Decibel

  dBtermunit: dBcore

  A logarithmic unit expressing the ratio between two powers, voltages, or currents. It is always a ratio — never an absolute quantity — unless a reference is attached, as in dBm or dBW.

  More

  Three anchors cover most exam questions: 3 dB is a factor of two in power, 10 dB is a factor of ten, and 0 dB is no change. Everything else is those combined. Note the two coefficients: 10*log10 for power ratios, 20*log10 for voltage or current ratios.

  Taught in: decibels

• Decibels from a power ratio

  formulacore

  dB = 10 * log10(P2 / P1)

  Derivation · machine-proved

  1. $$\mathrm{dB} = 10\log_{10}\!\left(\frac{P_2}{P_1}\right)$$

     the definition: a decibel is a tenth of a bel, and a bel is a decade of power

  2. $$P = \dfrac{V^2}{R}$$

     power in terms of voltage across a fixed resistance

  3. $$10\log_{10}\!\left(\frac{V_2^2/R}{V_1^2/R}\right) = 10\log_{10}\!\left(\frac{V_2}{V_1}\right)^{2}$$

     the $R$ cancels, provided both are measured into the same impedance

  4. $$= 20\log_{10}\!\left(\frac{V_2}{V_1}\right)$$

     $\log(x^2) = 2\log x$ — the 20 is the square, not a different convention

  Also proved

  • 10*log(V2**2/R / (V1**2/R), 10) = 20*log(V2/V1, 10)

    The 20 in the voltage form is the exponent in P = V^2/R, which is why it is only valid when the two voltages share an impedance.

  • 10*log(2, 10) = 10*log(2, 10)

    3.0103 dB is exactly a factor of two in power, not approximately.

  Every line above is re-proved by SymPy on each build; a wrong step fails make check.

  Taught in: decibels

• Deviation ratio

  formulaadvanced

  ratio = maximum deviation / maximum modulating frequency

  Taught in: modulation index and multiplexing

• Deviation through a frequency multiplier

  formulaadvanced

  oscillator deviation = output deviation / multiplier ratio

  Taught in: frequency changing

• Digital Coded Squelch

  DCStermintro

  A digital equivalent of CTCSS: a continuous low-rate data pattern that a receiver checks before opening its squelch. Same purpose, same non-privacy, different encoding.

  Do not confuse with: ctcss

  Taught in: repeaters and tones

• Duty Cycle

  termunit: %core

  The percentage of time a transmitter is actually transmitting at full power during a defined averaging period.

  More

  RF exposure limits are averaged over time, so duty cycle scales what is permitted: halving the duty cycle from 100% to 50% doubles the allowable power density. It is why SSB voice, which transmits only on syllables, is far less demanding than a carrier-continuous digital mode at the same peak power.

  Taught in: rf exposure

• Effective Radiated Power

  ERPtermunit: Wcore

  Transmitter power adjusted for feed-line loss and antenna gain — what the antenna effectively radiates in its favoured direction, referenced to a dipole (ERP) or an isotropic radiator (EIRP).

  Taught in: antenna parameters

• Emergency traffic outranks every other rule about who may use a channel

  conceptintro

  In an emergency, the ordinary restrictions on channel use, station type, and even service boundaries give way. Operators must give priority to emergency communications at all times and on all channels.

  Why it matters. Hesitating over whether a channel is "yours" while someone needs help is both wrong and unnecessary. Knowing that the rules already permit the call removes the hesitation.

  Common mistakes (2)

  • ✗ You must not transmit outside your licensed service, ever.
    ✓ Section 97.403 says no provision of the amateur rules prevents using any means of radiocommunication at your disposal for the immediate safety of life or protection of property *when normal communication systems are not available*. That last clause is part of the rule: it is a genuine exception, not a general licence to ignore service boundaries because a situation feels urgent.
  • ✗ Emergency priority means I can interrupt anyone for anything urgent to me.
    ✓ Priority attaches to emergency communications, which the rules tie to immediate safety of life and protection of property. A late dinner is not one.

  Taught in: nets and emergency operating, what you may and may not say

• Equipment Certification

  termcore

  FCC approval of a transmitter type for a specific radio service. Part 95 services require it; the Amateur Radio Service largely does not.

  More

  This is why an inexpensive programmable handheld is a legal problem on GMRS even when it can tune the frequencies: certification attaches to the radio, not to the operator's licence, and §95.1761 explicitly bars certifying a GMRS transmitter that can also operate in a service which needs no certification.

  Taught in: frs gmrs murs

• ERP or EIRP from a station budget

  formulaadvanced

  ERP = transmitter power * 10^((gain - total losses)/10)

  Derivation · machine-proved

  1. $$G_{\text{net}} = G - L$$

     gains and losses in decibels add, because they multiply as ratios

  2. $$\frac{P_{ERP}}{P_{tx}} = 10^{(G-L)/10}$$

     undo the decibel: a power ratio in dB is $10\log_{10}$ of the ratio

  3. $$P_{ERP} = P_{tx}\,10^{(G-L)/10}$$

     multiply through

  4. $$G_{dBi} = G_{dBd} + 2.15$$

     a lossless half-wave dipole has 2.15 dBi of gain over isotropic, so EIRP exceeds ERP by that much for the same antenna

  Also proved

  • 10**((G - L)/10) * 10**(L/10) = 10**(G/10)

    Removing a loss and adding it back returns the bare antenna gain — the dB bookkeeping is consistent.

  • log(10**((G-L)/10), 10)*10 = G - L

    Decibels really are logarithms: the round trip is exact, not approximate.

  Every line above is re-proved by SymPy on each build; a wrong step fails make check.

  Taught in: antenna parameters

• Exposure limits are strictest where the body absorbs best

  conceptcore

  Maximum permissible exposure varies with frequency because human tissue absorbs RF energy most efficiently in the VHF range, roughly 30 to 300 MHz. Limits are correspondingly lowest there.

  Why it matters. It explains why 50 MHz is the most demanding amateur band for exposure evaluation while HF and microwave are more forgiving at the same power — an ordering that looks arbitrary until you know the reason.

  Common mistakes (1)

  • ✗ Higher frequency always means more hazardous.
    ✓ The limit is lowest in VHF, where the body is near resonant and absorbs most efficiently. Above and below that range the limits relax.

  Taught in: rf exposure

• Family Radio Service

  FRStermintro

  An unlicensed personal radio service sharing all 22 channel frequencies with GMRS, limited to 2 W ERP on most channels, 0.5 W on channels 8-14, and permanently attached antennas.

  Do not confuse with: murs

  Taught in: frs gmrs murs

• Feed Line

  termintro

  The cable carrying RF between transmitter and antenna, characterised by its impedance, loss per unit length, and velocity factor.

  Taught in: feed lines

• FM bandwidth (Carson's rule)

  formulacore

  BW = 2 * (deviation + highest modulating frequency)

  Taught in: frequency changing

• Frequency

  ftermunit: Hzintro

  The number of complete cycles per second of a periodic signal, measured in hertz.

  Do not confuse with: wavelength

  Taught in: alternating current, metric prefixes

• GMRS Repeater

  termcore

  A station that receives on a 467 MHz main channel and simultaneously retransmits on the paired 462 MHz main channel 5.000 MHz below, extending the range of hand-held and mobile stations.

  Taught in: repeaters and tones

• Half-power bandwidth of a resonant circuit

  formulaadvanced

  bandwidth = resonant frequency / Q

  Derivation · machine-proved

  1. $$Q = \dfrac{2\pi f_0 L}{R} = \dfrac{1}{R}\sqrt{\dfrac{L}{C}}$$

     reactance at resonance over series resistance, using $f_0 = 1/2\pi\sqrt{LC}$

  2. $$|Z(f)| = \sqrt{R^2 + \left(2\pi f L - \tfrac{1}{2\pi f C}\right)^2}$$

     series impedance magnitude away from resonance

  3. $$\left|2\pi f L - \tfrac{1}{2\pi f C}\right| = R$$

     half power means $|Z| = R\sqrt{2}$, so the net reactance equals $R$

  4. $$BW = f_2 - f_1 = \dfrac{R}{2\pi L} = \dfrac{f_0}{Q}$$

     solving both roots and subtracting; the $\sqrt{LC}$ terms cancel

  Also proved

  • (2*pi*(1/(2*pi*sqrt(L*C)))*L)/R = sqrt(L/C)/R

    The two standard expressions for Q at resonance are the same expression.

  • (1/(2*pi*sqrt(L*C)))/(sqrt(L/C)/R) = R/(2*pi*L)

    f0/Q reduces to R/(2*pi*L) — the bandwidth is set by loss alone, not by f0.

  Every line above is re-proved by SymPy on each build; a wrong step fails make check.

  Taught in: resonance and q

• Half-wave dipole length

  formulacore

  length (feet) = 468 / frequency (MHz)

  Taught in: dipoles and verticals

• Harmful Interference

  termcore

  Interference that endangers the functioning of a radionavigation or other safety service, or that seriously degrades, obstructs, or repeatedly interrupts a radiocommunication service operating in accordance with the regulations.

  More

  The definition is doing real work: it is not "anything I find annoying". It requires a service operating lawfully, and either a safety impact or serious degradation. It is also the hinge of every secondary allocation — a secondary user must not cause harmful interference to a primary user, and must accept it from them.

  Taught in: station restrictions and zoning

• Impedance

  Ztermunit: ohmcore

  Total opposition to alternating current, combining resistance and reactance. Because reactance shifts phase, impedance has both a magnitude and an angle.

  More

  Written Z = R + jX, where R dissipates and X stores. A "50 ohm" feed line means 50 ohms resistive with no reactance — the condition that lets power transfer without reflection.

  Do not confuse with: resistance

  Taught in: capacitance and inductance

• Inductance

  Ltermunit: Hintro

  The ability to store energy in a magnetic field around a conductor, measured in henries. An inductor opposes a change in current.

  Do not confuse with: capacitance

  Taught in: capacitance and inductance

• Inductive reactance

  formulacore

  XL = 2 * pi * f * L

  Taught in: reactance and impedance

• Interstitial Channel

  termintro

  In GMRS, one of the 14 channels sitting halfway between the main channels, sharply limited in power and, at 467 MHz, restricted to hand-held units.

  More

  462 MHz interstitials are capped at 5 W ERP; 467 MHz interstitials at 0.5 W ERP and hand-held units only. These are the channels FRS radios share, which is why a GMRS handheld talking to an FRS radio is on low power whether or not it says so.

  Do not confuse with: main channel

  Taught in: the thirty channels

• Inverting op-amp voltage gain

  formulaadvanced

  gain = -RF / R1

  Taught in: operational amplifiers

• Ionizing Radiation

  termintro

  Radiation energetic enough to remove electrons from atoms, such as X-rays, gamma rays, and the emissions of radioactive decay.

  Do not confuse with: non ionizing radiation

  Taught in: rf exposure

• Lightning Arrester

  termcore

  A device in a feed line that shunts high-voltage surges to ground, installed on a grounded panel where feed lines enter the building.

  More

  Placement is the whole point: an arrester at the antenna end protects nothing inside. The surge has to be diverted before it reaches the building, at a single grounded entry panel where every feed line, control cable, and ground bonds together.

  Taught in: electrical safety

• Main Channel

  termintro

  In GMRS, one of the 16 channels at 462 or 467 MHz on 25 kHz spacing that carry the highest power limits and, at 467 MHz, serve as repeater inputs.

  More

  Main channels take up to 50 W from mobile, repeater, and base stations, and 15 W from fixed stations. The 467 MHz main channels may be used by mobile, hand-held, and control stations only through a repeater or for brief test transmissions.

  Do not confuse with: interstitial channel

  Taught in: the thirty channels

• Maximum Permissible Exposure

  MPEtermcore

  The FCC's limit on human exposure to radiofrequency fields, expressed as power density or field strength, varying with frequency and with whether the exposure is controlled or uncontrolled.

  More

  Limits are lowest — that is, strictest — in the VHF range around 30 to 300 MHz, because that is where the human body most efficiently absorbs RF energy. A body is roughly resonant at those wavelengths.

  Taught in: rf exposure

• Modulation index

  formulaadvanced

  index = deviation / modulating frequency

  Taught in: modulation index and multiplexing

• Multi-Use Radio Service

  MURStermintro

  An unlicensed service of five VHF channels near 151 and 154 MHz, limited to 2 W transmitter output, with repeaters prohibited but external antennas allowed.

  More

  MURS is the only one of the three unlicensed-ish services that permits a removable, gain, or elevated antenna — which at VHF can beat a 5 W GMRS handheld outdoors despite the lower power.

  Do not confuse with: frs

  Taught in: frs gmrs murs

• Non-Ionizing Radiation

  termintro

  Electromagnetic radiation without enough energy per photon to strip electrons from atoms. Radio signals, including every amateur and GMRS transmission, are non-ionizing.

  More

  The distinction is not a reassurance that RF is harmless — it heats tissue, and enough of it burns. It is a statement that the mechanism differs from that of X-rays or gamma rays, which break chemical bonds directly.

  Do not confuse with: ionizing radiation

  Taught in: rf exposure

• Ohm's law

  formulaintro

  E = I * RI = E / RR = E / I

  Taught in: ohms law

• One bonded ground system, entered at one point

  conceptcore

  Every ground rod, equipment ground, and the electrical service ground must be bonded together with heavy conductor, and every feed line should enter the building through a single grounded panel carrying arresters.

  Why it matters. Two unbonded grounds are more dangerous than one, because a surge lifts one relative to the other and the difference appears across whatever equipment bridges them — usually the radio, usually with you touching it.

  Common mistakes (2)

  • ✗ A separate ground rod for the radio keeps station noise off the house wiring.
    ✓ An unbonded rod creates a potential difference during a surge. Bond it to the service ground; solve noise with common-mode chokes and shielding instead.
  • ✗ Sharp bends in a grounding conductor are fine if the wire is heavy enough.
    ✓ A lightning surge is a fast transient, and a sharp bend presents inductance that it will jump rather than follow. Keep runs short, direct, and gently curved.

  Taught in: electrical safety, antennas and towers

• Peak Envelope Power

  PEPtermunit: Wcore

  The average power supplied during one complete RF cycle at the crest of the modulation envelope. It is the measure the FCC uses to set amateur power limits.

  More

  PEP matters because SSB power varies constantly with the voice. A radio rated "100 W PEP" delivers 100 W only on syllable peaks; its average output during speech is a fraction of that. Section 97.313 caps transmitter power in PEP, not average.

  Taught in: power rms and decibels

• Peak Voltage

  termunit: Vcore

  The maximum instantaneous voltage a waveform reaches, measured from the zero line to the crest.

  Do not confuse with: rms

  Taught in: reading a waveform

• Peak-to-Peak Voltage

  Vpptermunit: Vcore

  The full swing of a waveform from its most negative to its most positive point — for a symmetrical wave, twice the peak voltage.

  More

  This is what an oscilloscope shows you most directly, which is why scope readings and meter readings of the same signal disagree by a factor of about 2.8 unless you convert.

  Taught in: reading a waveform

• Pecuniary Interest

  termcore

  A financial stake in the content of a communication. Amateur stations may not transmit communications in which the control operator or their employer has one.

  More

  The test is the financial stake, not the identity of the other party. It is why ordering a pizza on the air is legal and calling in a delivery for your employer is not, and why being paid to operate is prohibited apart from the narrow exceptions Part 97 names.

  Taught in: amplifiers line a and prohibited traffic

• PEP from peak-to-peak voltage

  formulacore

  P = (Vpp / 2.828)^2 / R

  Derivation · machine-proved

  1. $$V_{peak} = \dfrac{V_{pp}}{2}$$

     peak-to-peak spans both half-cycles

  2. $$V_{RMS} = \dfrac{V_{peak}}{\sqrt{2}} = \dfrac{V_{pp}}{2\sqrt{2}}$$

     for a sine wave, RMS is peak over root two

  3. $$P = \dfrac{V_{RMS}^2}{R} = \dfrac{V_{pp}^2}{8R}$$

     $(2\sqrt{2})^2 = 8$ — where the 8 comes from

  Also proved

  • (2*sqrt(2))**2 = 8

    The 8 in the shortcut is the square of 2*sqrt(2), nothing more.

  • ((Vpp/2)/sqrt(2))**2 / R = Vpp**2/(8*R)

    The two-step and one-step forms are the same expression.

  Every line above is re-proved by SymPy on each build; a wrong step fails make check.

  Taught in: power rms and decibels

• Phase angle of a series RLC circuit

  formulaadvanced

  theta = atan((XL - XC) / R)

  Taught in: time constants and phase

• Power

  Ptermunit: Wintro

  The rate of energy transfer, measured in watts. In a DC circuit it is simply voltage times current.

  More

  Radio makes several distinct power measurements and the exams care which one you mean: PEP (peak envelope power) is what the FCC limits, average power is what heats a dummy load, and ERP or EIRP fold in antenna gain.

  Taught in: charge current voltage, power and heat

• Power from resistance

  formulacore

  P = I^2 * R = E^2 / R

  Taught in: power and heat

• Power transfers best when impedances match

  conceptcore

  Maximum power reaches a load when the load impedance equals the source impedance. A mismatch reflects part of the wave back toward the source instead of delivering it.

  Why it matters. This is why everything in a station is nominally 50 ohms, why an antenna tuner exists, and why SWR is worth reading. It is also why a tuner at the radio end does not fix a bad antenna: it hides the mismatch from the transmitter, leaving the loss out on the feed line.

  Common mistakes (2)

  • ✗ An antenna tuner tunes the antenna.
    ✓ It transforms the impedance the transmitter sees at the tuner. The standing wave between the tuner and the antenna is unchanged, and any feed-line loss it causes is unchanged too.
  • ✗ A 1:1 SWR means the antenna is working well.
    ✓ It means the transmitter sees a matched load. A 50 ohm dummy load shows a perfect 1:1 and radiates almost nothing.

  Taught in: resonance

• Q of a parallel resonant circuit

  formulaadvanced

  Q = resistance / reactance

  Taught in: resonance and q

• Q of a series resonant circuit

  formulaadvanced

  Q = reactance / resistance

  Taught in: resonance and q

• Quarter-wave monopole length

  formulacore

  length (feet) = 234 / frequency (MHz)

  Taught in: dipoles and verticals

• RC time constant

  formulaadvanced

  tau = R * C

  Taught in: time constants and phase

• Reactance

  Xtermunit: ohmcore

  Opposition to alternating current from capacitance or inductance. It stores energy and returns it rather than dissipating it as heat, and it changes with frequency.

  More

  Inductive reactance rises with frequency (XL = 2*pi*f*L); capacitive reactance falls with it (XC = 1/(2*pi*f*C)). At one frequency the two cancel — that is resonance, and it underpins every tuned circuit, filter, and resonant antenna.

  Do not confuse with: resistance

  Taught in: capacitance and inductance

• Reflection Coefficient

  Γtermadvanced

  The fraction of an incident wave's voltage that is reflected by a mismatched load, from 0 (perfect match) to 1 (total reflection).

  More

  Power reflected is the square of the voltage reflection coefficient, which is why a 2:1 SWR (Γ = 1/3) sends back about 11% of the power rather than 33%.

  Taught in: measurement technique

• Repeater Offset

  termintro

  The fixed frequency difference between a repeater's input and output. GMRS uses +5.000 MHz; the 2 metre amateur band conventionally uses ±600 kHz and 70 cm ±5 MHz.

  Taught in: making contact, repeaters and tones

• Resistance

  Rtermunit: ohmintro

  Opposition to current flow that converts electrical energy into heat, measured in ohms. Unlike reactance, it dissipates power rather than storing and returning it.

  Do not confuse with: reactance, impedance

  Taught in: charge current voltage

• Resistors in parallel

  formulacore

  1/R_total = 1/R1 + 1/R2 + ...

  Taught in: series and parallel

• Resistors in series

  formulaintro

  R_total = R1 + R2 + ... + Rn

  Taught in: series and parallel

• Resonance

  termcore

  The frequency at which inductive and capacitive reactance are equal and cancel, leaving a purely resistive impedance.

  More

  In a series circuit that means minimum impedance and maximum current; in a parallel circuit, maximum impedance and minimum line current. Exams ask the difference constantly, and the two behave oppositely.

  Taught in: resonance

• Resonance is two opposite reactances cancelling

  conceptcore

  Inductive reactance rises with frequency and capacitive reactance falls with it. At exactly one frequency they are equal and opposite, so they cancel and the circuit looks purely resistive.

  Why it matters. Resonance is the single idea behind tuned circuits, filters, traps, and antennas. An antenna that is "resonant" is not magic — it is a circuit whose reactance happens to cancel at the frequency you want to use.

  Common mistakes (2)

  • ✗ At resonance the reactances disappear.
    ✓ Both are still there and can be enormous. They cancel each other in the total, which is why the voltage across a coil or capacitor in a high-Q series circuit can far exceed the applied voltage.
  • ✗ Series and parallel resonant circuits behave the same way.
    ✓ They are opposites. Series resonance gives minimum impedance and maximum current; parallel resonance gives maximum impedance and minimum line current.

  Taught in: resonance

• Resonant frequency

  formulacore

  f = 1 / (2 * pi * sqrt(L * C))

  Derivation · machine-proved

  1. $$X_L = 2\pi f L, \quad X_C = \dfrac{1}{2\pi f C}$$

     the two reactances, each a function of frequency

  2. $$2\pi f L = \dfrac{1}{2\pi f C}$$

     resonance is defined as the frequency where they are equal

  3. $$4\pi^2 f^2 LC = 1$$

     multiply both sides by $2\pi f C$

  4. $$f^2 = \dfrac{1}{4\pi^2 LC}$$

     isolate $f^2$

  5. $$f = \dfrac{1}{2\pi\sqrt{LC}}$$

     take the positive root; frequency is a magnitude

  Also proved

  • 2*pi*(1/(2*pi*sqrt(L*C)))*L = sqrt(L/C)

    At resonance the common reactance is the characteristic impedance sqrt(L/C), which is why a high-L low-C tank is a high-impedance one.

  Every line above is re-proved by SymPy on each build; a wrong step fails make check.

  Taught in: reactance and impedance

• Return Loss

  termunit: dBadvanced

  The reflected power expressed in decibels below the forward power. Higher return loss means a better match — the opposite direction from SWR.

  Do not confuse with: swr

  Taught in: measurement technique

• RF Burn

  termintro

  A skin burn caused by touching a conductor carrying radio-frequency current — typically an antenna element while transmitting.

  More

  RF burns are characteristically deep and slow to heal, because the current heats tissue directly rather than only the surface. They occur at power levels that feel unremarkable.

  Taught in: rf exposure

• RF exposure limits are averaged over time, not instantaneous

  conceptcore

  The FCC's exposure limits apply to average power density over a defined averaging period. Duty cycle therefore scales what is permitted: halve the time spent transmitting and the allowable power density doubles.

  Why it matters. It changes which stations need to worry. A 1500 W station running SSB with long listening periods can present less average exposure than a 100 W station holding a continuous carrier. Evaluating peak power alone gives the wrong answer in both directions.

  Common mistakes (2)

  • ✗ More power always means a bigger RF exposure problem.
    ✓ Average exposure is what the limits address. Power, duty cycle, antenna gain, and distance all enter; a high-power intermittent station can be well inside limits where a modest continuous one is not.
  • ✗ RF radiation is radioactive.
    ✓ Radio signals are non-ionizing: individual photons lack the energy to strip electrons from atoms. The hazard is heating, not ionisation.

  Taught in: rf exposure

• RL time constant

  formulaadvanced

  tau = L / R

  Taught in: time constants and phase

• RMS from peak (sine wave)

  formulacore

  V_RMS = 0.707 * V_peakV_peak = 1.414 * V_RMS

  Taught in: reading a waveform

• Root Mean Square

  RMStermunit: Vcore

  The equivalent DC value of an AC waveform — the value that would produce the same heating in a resistor. For a sine wave, RMS = 0.707 x peak.

  Do not confuse with: peak voltage, peak to peak voltage

  Taught in: reading a waveform

• Series shares current; parallel shares voltage

  conceptintro

  Elements in series carry the same current and divide the voltage. Elements in parallel see the same voltage and divide the current. Every combination formula follows from those two sentences.

  Why it matters. You can derive the resistance rules instead of memorising them, and the derivation transfers to capacitors and inductors — where the series and parallel rules swap over for capacitors, which is exactly the trap the exams set.

  Common mistakes (2)

  • ✗ Capacitors combine the same way resistors do.
    ✓ They combine the opposite way. Capacitors in parallel add; capacitors in series combine by the reciprocal rule. Inductors follow the resistor pattern; capacitors do not.
  • ✗ Adding a resistor in parallel increases total resistance.
    ✓ It always decreases it, because you have added another path for current. The total is always less than the smallest branch.

  Taught in: series and parallel

• Standing Wave Ratio

  SWRtermcore

  The ratio of maximum to minimum voltage along a feed line, caused by reflection from a mismatched load. A perfectly matched line shows 1:1.

  More

  SWR is a symptom, not a fault. It tells you that the impedance at the far end differs from the line's characteristic impedance — it does not tell you why, and it does not tell you whether the antenna radiates. High SWR matters mostly because reflected power stresses a solid-state final and because it multiplies loss in a lossy line.

  Do not confuse with: return loss

  Taught in: feed lines, resonance

• Station Identification

  termintro

  Transmitting your assigned call sign so that transmissions can be attributed to a licensee. Required in every licensed radio service, with the timing set by that service's rules.

  More

  GMRS: at the end of a transmission or series, and at least every 15 minutes during a long series. Amateur: at the end and at least every 10 minutes. The two are close enough to confuse and different enough to matter.

  Taught in: identification and repeaters, who may hold and operate

• SWR from a resistive mismatch

  formulacore

  SWR = larger impedance / smaller impedance

  Derivation · machine-proved

  1. $$\Gamma = \dfrac{Z_L - Z_0}{Z_L + Z_0}$$

     the reflection coefficient of a load $Z_L$ on a line of impedance $Z_0$

  2. $$\mathrm{SWR} = \dfrac{1 + |\Gamma|}{1 - |\Gamma|}$$

     standing-wave ratio is the envelope maximum over the minimum

  3. $$\mathrm{SWR} = \dfrac{1 + \frac{Z_h - Z_l}{Z_h + Z_l}}{1 - \frac{Z_h - Z_l}{Z_h + Z_l}} = \dfrac{2Z_h}{2Z_l}$$

     substitute and clear the common denominator $Z_h + Z_l$

  4. $$\mathrm{SWR} = \dfrac{Z_h}{Z_l}$$

     the twos cancel — the ratio rule is not a shortcut, it is exact for a resistive load

  Also proved

  • (1 + (Z_higher - Z_lower)/(Z_higher + Z_lower))/(1 - (Z_higher - Z_lower)/(Z_higher + Z_lower)) = Z_higher/Z_lower

    The ratio rule is the reflection-coefficient formula in disguise.

  • Abs((2*Z_lower - Z_lower)/(2*Z_lower + Z_lower)) = Abs((Z_lower/2 - Z_lower)/(Z_lower/2 + Z_lower))

    A load twice the line impedance and one half of it give the same magnitude of reflection, hence the same SWR. Symmetry in the ratio, not a coincidence.

  Every line above is re-proved by SymPy on each build; a wrong step fails make check.

  Taught in: feed lines and swr

• Telemetry

  termcore

  A one-way transmission of measurements at a distance from the measuring instrument.

  More

  Telemetry travels down from a balloon or satellite; telecommand travels up to control it. Telemetry is one of the narrow exceptions to the general prohibition on one-way amateur transmissions, and it still identifies with the station's call sign like anything else.

  Taught in: space telecommand and telemetry

• Transformer impedance ratio

  formulacore

  Zp / Zs = (Np / Ns)^2

  Derivation · machine-proved

  1. $$\frac{V_p}{V_s} = \frac{N_p}{N_s}$$

     voltage follows the turns ratio directly

  2. $$\frac{I_p}{I_s} = \frac{N_s}{N_p}$$

     an ideal transformer conserves power, so current goes the other way

  3. $$\frac{Z_p}{Z_s} = \frac{V_p/I_p}{V_s/I_s} = \frac{V_p}{V_s}\cdot\frac{I_s}{I_p}$$

     impedance is voltage over current, on each side

  4. $$= \frac{N_p}{N_s}\cdot\frac{N_p}{N_s} = \left(\frac{N_p}{N_s}\right)^{2}$$

     both ratios are the turns ratio, so it appears twice — that is the square

  Also proved

  • (Np/Ns)*(Np/Ns) = (Np/Ns)**2

    The square is not a rule to memorise: voltage and current each scale, so the ratio scales twice.

  • sqrt((Np/Ns)**2) = Np/Ns

    Hence the turns ratio for a wanted impedance transformation is the square root of it.

  Every line above is re-proved by SymPy on each build; a wrong step fails make check.

  Taught in: combining components

• Transformer turns ratio

  formulacore

  Vs / Vp = Ns / Np

  Taught in: combining components

• Velocity Factor

  VFtermcore

  The speed of a signal in a feed line as a fraction of its speed in free space, typically 0.66 for solid-dielectric coax and up to 0.95 for open-wire line.

  More

  It matters whenever length matters: a half-wave matching stub or a quarter-wave transformer must be cut to the electrical length, which is the free-space length multiplied by the velocity factor.

  Taught in: transmission lines

• Voltage

  Etermunit: Vintro

  The difference in electrical potential between two points — the pressure that pushes charge around a circuit. Always measured between two points, never at one.

  More

  Amateur exam material writes voltage as E (for electromotive force) while most datasheets write V. They mean the same quantity. The "between two points" part is not pedantry: a voltmeter with one lead in the air reads nothing meaningful, and "the voltage at the antenna" is shorthand for "relative to the chassis ground".

  Do not confuse with: current

  Taught in: charge current voltage

• Volunteer Examiner Coordinator (VEC)

  termcore

  An organisation that has entered into an agreement with the FCC to coordinate, prepare, and administer amateur operator licence examinations, and that accredits the individual Volunteer Examiners who run sessions.

  More

  Part 97 tasks the VECs — not the FCC — with maintaining the question pools for every US amateur licence examination. That is why the pools are published in full, with answers, on a four-year cycle, and why this courseware can be built from them at all.

  Taught in: the volunteer examiner system

• Wavelength

  lambdatermunit: mintro

  The physical distance a radio wave travels during one complete cycle. Inversely proportional to frequency.

  More

  Amateur bands are named by wavelength (2 metres, 20 metres) while radios are tuned by frequency, so fluency in converting between them is day-to-day vocabulary rather than exam trivia.

  Do not confuse with: frequency

  Taught in: frequency and wavelength

• Wavelength from frequency

  formulaintro

  wavelength (m) = 300 / frequency (MHz)f (MHz) = 300 / wavelength (m)

  Taught in: what a radio wave is, frequency and wavelength