ACMA Standard Theory Exam cheat sheet

Ohm's law: V = I × R; power P = V × I = I²R = V²/R.

Series resistances add (Rt = R1 + R2 + ...); parallel conductances add, so 1/Rt = 1/R1 + 1/R2 + ...

For two resistors in parallel, Rt = (R1 × R2)/(R1 + R2).

Capacitive reactance Xc = 1/(2πfC); inductive reactance Xl = 2πfL.

Capacitors in parallel add; capacitors in series combine reciprocally, the opposite of resistors.

A sine wave's RMS value is peak/√2 (0.707 × peak); peak-to-peak is twice the peak.

Frequency and period are reciprocal: f = 1/T; free-space wavelength λ(m) = 300/f(MHz).

Decibels: dB = 10 log10(P2/P1) = 20 log10(V2/V1); +3 dB doubles power, +6 dB doubles voltage.

Silicon diodes drop about 0.6–0.7 V in forward conduction; germanium about 0.3 V; LEDs higher.

Kirchhoff's current law: sum of currents entering a node equals sum leaving; voltage law: sum of voltages around a closed loop is zero.

Thevenin equivalent: any linear network can be represented by Vth in series with Rth; Norton uses In = Vth/Rth in parallel with the same Rth.

Series LC resonance: f0 = 1/(2π√(LC)); at resonance Xl = Xc.

At series resonance impedance is minimum and current maximum; at parallel resonance impedance is maximum.

Quality factor Q = f0/bandwidth; for a series resonant circuit Q = Xl/R.

RC time constant τ = RC; RL time constant τ = L/R; one τ reaches about 63%, five τ about 99%.

A capacitor blocks DC and passes high frequencies; an inductor passes DC and blocks high frequencies.

Transformer voltage ratio Vs/Vp = Ns/Np; impedance transforms by (Np/Ns)².

Resistor colour code: black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, grey 8, white 9; gold ±5%, silver ±10%.

Superheterodyne receiver: mixer output IF = |fRF − fLO|; high-side injection gives image at fRF + 2IF.

AM sidebands are at fc ± fm; total bandwidth is 2fm; modulation index m = Em/Ec; m > 1 causes splatter.

FM bandwidth by Carson's rule: BW ≈ 2(Δf + fm), where Δf is peak deviation and fm is highest modulating frequency.

SSB transmits one sideband and suppresses the carrier; voice bandwidth is about 3 kHz; a BFO or product detector restores audio.

Sensitivity is the minimum signal needed for usable output; selectivity is the ability to reject adjacent-channel signals.

AGC reduces gain on strong signals to keep audio output roughly constant; squelch mutes receiver output when no signal is present.

Transmitter chain: oscillator, buffer, driver, power amplifier, harmonic filter; the filter reduces spurious harmonics.

A mixer multiplies two signals and produces sum and difference frequencies; unwanted mixing products cause intermodulation interference.

Free-space wavelength λ(m) = 300/f(MHz); a practical half-wave dipole is about 143/f(MHz) metres long.

A half-wave dipole has a figure-eight radiation pattern and a feedpoint impedance near 73 Ω at resonance.

Reflection coefficient Γ = (ZL − Z0)/(ZL + Z0); VSWR = (1 + |Γ|)/(1 − |Γ|).

VSWR 1:1 transfers all available power; 2:1 reflects about 11% of incident power; mismatch loss = −10 log10(1 − |Γ|²).

Coaxial cable is unbalanced and commonly 50 Ω or 75 Ω; ladder line is balanced and commonly 300 Ω or 450 Ω.

A balun connects a balanced antenna to an unbalanced feedline and reduces common-mode current on the coax.

Velocity factor vf is the fraction of light speed in a line; electrical length = physical length × vf.

Antenna gain in dBd equals gain in dBi minus 2.15 dB; an isotropic radiator is the dBi reference.

Reciprocity: an antenna's transmitting and receiving radiation patterns and impedance are the same.

Ground-wave propagation supports LF and MF vertically polarised signals beyond the horizon; loss increases with frequency.

Sky-wave HF propagation refracts from the ionosphere; the F2 layer usually supports the longest distances.

D, E, F1 and F2 layers: D absorbs daytime HF; E and F layers refract; ionisation varies with solar activity and time of day.

Maximum usable frequency (MUF) is the highest frequency returned by the ionosphere for a given path; above it the signal escapes.

Skip distance is the shortest distance reached by a sky wave for a given frequency; between ground wave and skip is the skip zone.

Sporadic E and auroral ionisation can extend VHF range or cause flutter and distortion; solar flares can cause HF blackouts.

Line-of-sight radio horizon is about 3.57√h kilometres for antenna height h in metres; combined path is the sum for both antennas.

Tropospheric refraction and ducting bend VHF/UHF signals beyond the geometric horizon; multipath causes fading.

A voltmeter is connected in parallel and should have high resistance; an ammeter is connected in series and should have low resistance.

0 dBm = 1 mW into 50 Ω ≈ 0.224 V RMS; dBm = 10 log10(P/1 mW).

A 10× oscilloscope probe divides voltage by 10, raises input impedance, and reduces circuit loading.

Oscilloscope bandwidth should be at least 3–5 times the highest signal frequency for accurate amplitude display.

A frequency counter's resolution is approximately 1/(gate time); longer gates give finer resolution but slower readings.

A dummy load absorbs transmitter power for testing; an SWR meter or directional coupler measures forward and reflected power.

Spectrum analyzer resolution bandwidth affects the noise floor and ability to separate close signals; narrower RBW shows lower noise but sweeps slower.

True-RMS meters are required for non-sinusoidal waveforms; average-responding meters are calibrated for sine waves and read low on distorted signals.

EMI couples by conduction along cables or radiation through space; suppression addresses the source, coupling path, or victim.

Common-mode currents flow in the same direction on both conductors and return via earth; differential-mode currents flow in opposite directions.

Ferrite beads, common-mode chokes, bypass capacitors, shielding and twisted pairs reduce unwanted RF coupling.

Shield effectiveness depends on material, seams and apertures; gaps larger than about one-twentieth wavelength leak significantly.

Nonlinear stages create intermodulation products such as 2f1 − f2 and f1 + f2, which may fall on a victim frequency.

Ground loops form when equipment is earthed at multiple points; they cause hum and RF interference and are broken by single-point grounding or isolation.

Filter types: low-pass passes below cutoff, high-pass above, band-pass a range, notch rejects a narrow band; insertion loss is the loss in the passband.

Strong nearby signals can block or desensitise a receiver, reducing sensitivity even when the interfering frequency is not on channel.

RF exposure: far-field power density S ≈ PG/(4πd²); limits vary with frequency, and antennas should be kept clear of people.

High-voltage capacitors can retain charge after power-off; discharge through a resistor and confirm zero volts before touching.

Mains work requires isolation, fuses or circuit breakers, earth connection and an RCD; never work alone on live equipment.

Antenna and tower work requires fall protection, hard hat, and checking for overhead power lines before raising a mast.

Lightning protection: bond antenna structures to earth, use surge arrestors, and disconnect feedlines during storms.

Soldering produces fumes and burns; use ventilation, eye protection, and a stand; lead-free solder needs higher tip temperature.

Lithium batteries can catch fire if shorted, crushed or overcharged; use the correct charger and isolate damaged cells.

Batteries can release hydrogen when charging; avoid sparks and ensure ventilation, especially with lead-acid cells.

First aid for electric shock: isolate the supply before touching the casualty, then call emergency services and begin CPR if trained.