ACMA Advanced Amateur Radio Theory cheat sheet

Power ratios in decibels: dB = 10 log10(P2/P1); voltage or current ratios across equal impedance use dB = 20 log10(V2/V1).

+3 dB doubles power, +10 dB multiplies power by ten, -6 dB quarters power; a 1 S-unit on HF is conventionally 6 dB.

Ohm's law and power: V = IR, P = VI = I^2R = V^2/R; series resistances add, parallel conductances add.

Capacitive reactance Xc = 1/(2pifC) falls with frequency; inductive reactance Xl = 2pifL rises with frequency.

Series resonance occurs when Xl = Xc, giving f = 1/(2pisqrt(L*C)) and minimum impedance in a series tuned circuit.

Loaded Q of a resonant circuit equals f0 divided by the -3 dB bandwidth; higher Q gives narrower bandwidth and slower transient response.

RC low-pass corner frequency is f = 1/(2piR*C); a first-order filter rolls off 6 dB per octave (20 dB per decade).

Peak, peak-to-peak and RMS for a sine wave: Vrms = 0.707Vpeak, Vpp = 2Vpeak; RMS heating equals the equivalent DC value.

Silicon PN junction forward drop is about 0.6-0.7 V; a germanium junction drops about 0.3 V; a reverse-biased junction blocks current until breakdown.

Bipolar transistor regions: cutoff (no base current), active (current source, IC = beta*IB), saturation (VCE near 0.2 V, behaves as a closed switch).

MOSFET gate draws essentially no DC current; it is controlled by gate-source voltage and is vulnerable to electrostatic discharge.

Class A conducts 360 degrees (low distortion, poor efficiency); Class B 180 degrees per device; Class AB reduces crossover distortion; Class C is used for efficient RF output stages.

Gain in dB: voltage gain = 20 log10(Vout/Vin); cascaded stages add their dB gains rather than multiplying ratios.

Oscillator conditions: loop gain of at least unity and total loop phase shift of 360 degrees; crystal resonators give the highest frequency stability.

Half-wave rectifier ripple frequency equals the mains frequency; full-wave and bridge rectifiers give twice the mains frequency.

Linear regulators dissipate (Vin - Vout)*I as heat; switch-mode supplies achieve higher efficiency by rapidly switching a storage inductor.

Receiver sensitivity is set by front-end noise figure and bandwidth; minimum detectable signal rises with noise figure and with wider bandwidth.

The dynamic range and third-order intercept (IP3) describe large-signal handling; a strong signal can cause desensitization or intermodulation products.

A superheterodyne receiver converts to an intermediate frequency; the image frequency is separated from the wanted signal by twice the IF.

An IF filter sets selectivity; a narrow CW or SSB filter improves rejection of nearby strong signals.

Automatic gain control reduces gain on strong signals; too-fast AGC causes pumping on voice peaks.

A product detector mixes the received signal with a local carrier to recover SSB or CW audio; an envelope detector suits AM only.

Transmitter spurious and harmonic outputs are reduced by low-pass or band-pass filters after the final amplifier.

Digital signal processing enables noise reduction, notch filtering and demodulation of digital modes, limited by ADC dynamic range and processing artifacts.

Characteristic impedance of a coaxial or parallel line depends on conductor geometry and dielectric; common values are 50 ohms and 75 ohms.

Reflection coefficient magnitude is |(Zl - Zo)/(Zl + Zo)|; VSWR = (1 + |rho|)/(1 - |rho|), and return loss in dB = -20 log10(|rho|).

A half-wavelength line repeats the load impedance; a quarter-wavelength line transforms impedance by Zo^2/Zl and inverts reactance.

Velocity factor equals the wave speed on the line divided by the speed of light; physical length = electrical length * velocity factor.

A half-wave dipole in free space has about 2.15 dBi gain and a nominal 73-ohm feedpoint impedance; a quarter-wave vertical needs a ground plane.

Antenna gain and effective aperture are related: effective aperture = gain * lambda^2/(4*pi); shorter wavelength means smaller aperture for the same gain.

Free-space path loss in dB = 32.44 + 20 log10(f in MHz) + 20 log10(d in km); doubling distance adds about 6 dB.

HF skywave depends on ionospheric F-layer refraction; the maximum usable frequency rises with solar activity and is lower at night.

VHF/UHF propagation is mostly line of sight; tropospheric ducting and sporadic E can extend range well beyond the radio horizon.

AM double-sideband full carrier wastes power in the carrier; total power = carrier power * (1 + m^2/2) for modulation index m.

SSB transmits one sideband with suppressed carrier, giving roughly 3 dB advantage over AM per unit of peak envelope power and a 2.7-3 kHz bandwidth.

FM deviation and modulating frequency determine the modulation index; Carson's rule estimates bandwidth as 2*(deviation + highest modulating frequency).

Narrowband FM uses about 2.5-5 kHz deviation; wideband FM broadcast uses 75 kHz deviation.

CW is on-off keyed carrier; bandwidth is set mainly by keying rise and fall times, so hard keying causes clicks and keying sidebands.

Frequency-shift keying such as RTTY shifts the carrier between two tones; phase-shift keying such as PSK31 carries data in phase changes and is more bandwidth-efficient.

Digital modes use error detection or forward error correction; weak-signal modes trade bandwidth for processing gain.

Frequency modulation is demodulated by a discriminator or a phase-locked loop; phase noise and residual FM limit weak-signal reception.

A directional wattmeter reads forward and reflected power; VSWR can be computed from those readings as (sqrt(Pf) + sqrt(Pr))/(sqrt(Pf) - sqrt(Pr)).

An oscilloscope probe should be compensated and rated for the circuit voltage; bandwidth must exceed the highest frequency component of interest.

A dummy load must present 50 ohms and dissipate the full transmitter power; a 2:1 VSWR corresponds to about 11 percent reflected power.

Frequency counters need adequate sensitivity and timebase accuracy; a GPS-disciplined reference gives traceable frequency measurement.

Spectrum analyzers display amplitude versus frequency; resolution bandwidth affects noise floor and the ability to resolve close signals.

Common-mode choke baluns suppress feedline radiation and received common-mode noise on coaxial feedlines.

Ferrite beads and clamp-on chokes attenuate RF currents on cables; the ferrite mix must suit the frequency band.

Interference from a nearby transmitter may enter through the antenna, the mains wiring, or by direct pickup; identify the path before applying filters.

RF exposure limits are averaged over time and frequency; the controlled environment limit is higher than the uncontrolled (general public) limit.

Power density in the far field is S = EIRP/(4pid^2); near-field evaluation requires measurement or modelling rather than this formula alone.

Electric field strength E in V/m relates to power density by S = E^2/377; magnetic field H relates by S = 377*H^2.

The near-field/far-field boundary is approximately 2*D^2/lambda for an antenna of largest dimension D.

Duty cycle reduces average exposure; a transmitter operating 50 percent of the time halves the time-averaged power density.

Grounding and bonding of station equipment reduces common-mode currents and conducted interference; a single-point ground avoids ground loops.

Filtering at the equipment boundary and shielding of cables are the primary tools against conducted and radiated emissions.

Exceeding exposure limits requires reducing power, increasing distance, raising antenna height, or restricting access to the area.

The amateur service is defined internationally by the ITU Radio Regulations; national administrations issue licences and set privilege classes.

An amateur licence authorizes two-way communication for self-training and technical investigation, not commercial or broadcast use.

Callsigns identify the station; identification is required at the start, end, and at intervals during a contact as national rules specify.

Third-party traffic rules restrict messages on behalf of others; international third-party traffic requires the relevant administrations to permit it.

Frequency allocations and power limits vary by band and licence class; the national band plan and licence conditions take precedence over informal practice.

Harmful interference must be avoided and, when reported, resolved cooperatively; deliberate interference is an offence.

Emergency communications may use any available means when normal systems fail, within national rules for emergency declarations.

Logging, QSL and contest operation are governed by licence conditions and the rules of the sponsoring organization.