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Formula Reference
Electronics, RF, and communications formulas for aviation, marine, and telecommunications professionals.
Ohm's Law & Power
| Formula | Expression | Variables |
|---|---|---|
| Voltage | V = I × R | V = volts, I = current (A), R = resistance (Ω) |
| Current | I = V / R | I = amps, V = volts, R = resistance (Ω) |
| Resistance | R = V / I | R = ohms, V = volts, I = current (A) |
| Power (basic) | P = V × I | P = watts, V = volts, I = current (A) |
| Power (from R) | P = I² × R | P = watts, I = amps, R = resistance (Ω) |
| Power (from V) | P = V² / R | P = watts, V = volts, R = resistance (Ω) |
Wavelength & Antenna
| Formula | Expression | Variables |
|---|---|---|
| Wavelength | λ = 300 / f | λ = wavelength (m), f = frequency (MHz) |
| Wavelength (precise) | λ = c / f | λ = wavelength (m), c = 3×10⁸ m/s, f = frequency (Hz) |
| Half-wave dipole length | L = 142.5 / f | L = length (m), f = frequency (MHz) |
| Quarter-wave vertical | L = 71.25 / f | L = length (m), f = frequency (MHz) |
| Antenna length (with VF) | L = (142.5 / f) × VF | VF = velocity factor (0–1), f = MHz |
| Quarter-wave stub length in coax | L = (λ / 4) × VF | λ = free space wavelength, VF = velocity factor of the coax |
Reactance & Impedance
| Formula | Expression | Variables |
|---|---|---|
| Capacitive reactance | Xc = 1 / (2π × f × C) | Xc = ohms, f = Hz, C = farads |
| Inductive reactance | XL = 2π × f × L | XL = ohms, f = Hz, L = henries |
| Resonant frequency | f = 1 / (2π × √(L × C)) | f = Hz, L = henries, C = farads |
| Impedance (series RLC) | Z = √(R² + (XL − Xc)²) | Z = ohms, R = resistance, XL, Xc = reactances |
| Q factor | Q = XL / R = f₀ / BW | Q = quality factor, f₀ = resonant freq, BW = bandwidth |
| Bandwidth from Q | BW = f₀ / Q | BW = −3dB bandwidth (Hz), f₀ = center frequency |
Decibels & Power Ratios
| Formula | Expression | Variables |
|---|---|---|
| Power ratio to dB | dB = 10 × log₁₀(P₂ / P₁) | P₁ = reference power, P₂ = measured power |
| Voltage ratio to dB | dB = 20 × log₁₀(V₂ / V₁) | V₁ = reference voltage, V₂ = measured voltage |
| dB to power ratio | P₂ / P₁ = 10^(dB/10) | dB = decibel value |
| dBm to watts | P(W) = 10^((dBm − 30) / 10) | dBm = power in dBm, P = power in watts |
| Watts to dBm | dBm = 10 × log₁₀(P × 1000) | P = power in watts |
| dBi to dBd | dBd = dBi − 2.15 | dBi = gain over isotropic, dBd = gain over dipole |
| ERP | ERP = P(W) × G(linear) | P = power at the antenna, G = gain over a dipole (dBd) as a ratio |
| EIRP (dBm) | EIRP = P(dBm) + G(dBi) − L(dB) | P = power, G = gain, L = feedline loss |
Time Constants
| Formula | Expression | Variables |
|---|---|---|
| RC time constant | τ = R × C | τ = seconds, R = ohms, C = farads |
| RL time constant | τ = L / R | τ = seconds, L = henries, R = ohms |
| Voltage at time t (charging) | V(t) = Vs × (1 − e^(−t/τ)) | Vs = supply voltage, t = time, τ = time constant |
| Voltage at time t (discharging) | V(t) = V₀ × e^(−t/τ) | V₀ = initial voltage, t = time, τ = time constant |
| Time to charge to 63.2% | t = τ | One time constant = 63.2% of supply voltage |
| Time to charge to 99.3% | t = 5τ | Five time constants = effectively fully charged |
Power Factor & True Power
| Formula | Expression | Variables |
|---|---|---|
| True power (W) | P = V × I × cos(θ) | θ = phase angle between V and I |
| Apparent power (VA) | S = V × I | S = volt-amperes, V = volts, I = amps |
| Reactive power (VAR) | Q = V × I × sin(θ) | Q = volt-amperes reactive |
| Power factor | PF = P / S = cos(θ) | PF = 0 to 1, 1 = unity (purely resistive) |
| Power triangle | S² = P² + Q² | S = apparent, P = true, Q = reactive power |
RADAR
| Formula | Expression | Variables |
|---|---|---|
| Radar range | R = (c × t) / 2 | R = range (m), c = 3×10⁸ m/s, t = round-trip time (s) |
| Range in nautical miles | R(nm) = t(μs) × 0.0810 | t = pulse round-trip time in microseconds |
| PRF to max unambiguous range | R_max = c / (2 × PRF) | PRF = pulse repetition frequency (Hz) |
| Range resolution | ΔR = (c × τ) / 2 | τ = pulse width (s), c = speed of light |
| Radar equation (basic) | P_r = (P_t × G² × λ² × σ) / ((4π)³ × R⁴) | P_t = TX power, G = antenna gain, σ = RCS, R = range |
Batteries & Motors
| Formula | Expression | Variables |
|---|---|---|
| Battery runtime | t = C / I | t = hours, C = capacity (Ah), I = current draw (A) |
| C rating current | I = C_rating × Capacity(Ah) | I = max current (A), e.g. 50C × 1.5Ah = 75A |
| Watt-hours | Wh = V × Ah | Wh = energy, V = voltage, Ah = amp-hour capacity |
| Motor RPM (no load) | RPM = KV × V | KV = motor constant (RPM/volt), V = battery voltage — loaded RPM is lower |
| Drone flight time (est.) | t ≈ (Capacity(mAh) × 0.8) / Current(mA) × 60 | 0.8 = 80% usable capacity factor, result in minutes |
| Joules stored | E = 0.5 × C × V² | E = energy (J), C = capacitance (F), V = voltage |
FM Modulation
| Formula | Expression | Variables |
|---|---|---|
| Frequency deviation | Δf = kf × m(t) | kf = frequency sensitivity (Hz/V), m(t) = modulating signal |
| Modulation index | mf = Δf / fm | Δf = peak deviation, fm = modulating frequency (Hz) |
| Carson's rule (bandwidth) | BW = 2 × (Δf + fm) | BW = approximate FM bandwidth, Δf = peak deviation |
| Land mobile FM deviation | Δf = ±2.5 kHz (12.5 kHz channels), ±5 kHz (25 kHz channels) | Narrowband vs wideband FM. (VHF aviation voice is AM, not FM.) |
SSB & AM Power
| Formula | Expression | Variables |
|---|---|---|
| AM total power | P_total = P_c × (1 + m²/2) | P_c = carrier power, m = modulation index (0–1) |
| AM sideband power (each) | P_sb = P_c × m²/4 | P_c = carrier power, m = modulation index |
| PEP to average power (SSB) | P_avg = P_PEP / 3 (approx) | For typical voice modulation |
| Modulation percentage | m% = (V_max − V_min) / (V_max + V_min) × 100 | Measured from AM envelope on oscilloscope |
AC Voltage Conversions
| Formula | Expression | Variables |
|---|---|---|
| RMS to peak | V_peak = V_RMS × √2 | √2 ≈ 1.414 |
| Peak to RMS | V_RMS = V_peak / √2 | V_RMS = V_peak × 0.707 |
| Peak to peak | V_pp = 2 × V_peak | Full swing from positive to negative peak |
| Average (full-wave rectified) | V_avg = V_peak × 0.637 | Half-wave rectified average is V_peak × 0.318 |
| Form factor | FF = V_RMS / V_avg = 1.11 | Ratio of RMS to average for sine wave |
Transformer & Turns Ratio
| Formula | Expression | Variables |
|---|---|---|
| Turns ratio | N₁/N₂ = V₁/V₂ | N = turns, V = voltage, subscripts 1=primary 2=secondary |
| Current ratio | I₁/I₂ = N₂/N₁ | Current is inverse of turns ratio |
| Impedance transformation | Z₁/Z₂ = (N₁/N₂)² | Impedance transforms as square of turns ratio |
| Efficiency | η = P_out / P_in × 100% | Typical transformer efficiency: 95–99% |
Filter Design
| Formula | Expression | Variables |
|---|---|---|
| RC low-pass cutoff frequency | fc = 1 / (2π × R × C) | fc = −3dB frequency (Hz), R = ohms, C = farads |
| RL low-pass cutoff frequency | fc = R / (2π × L) | fc = Hz, R = ohms, L = henries |
| LC low-pass cutoff frequency | fc = 1 / (2π × √(L × C)) | fc = Hz, L = henries, C = farads |
| Filter rolloff (nth order) | −20n dB/decade (−6n dB/octave) | n = filter order; 1st order = −20 dB/decade |
| Band-pass bandwidth | BW = f_upper − f_lower | Between the −3 dB points |
| Notch filter Q | Q = f₀ / BW | Higher Q = narrower notch width |
Transmission Line
| Formula | Expression | Variables |
|---|---|---|
| Characteristic impedance (coax) | Z₀ = (138 / √εr) × log₁₀(D/d) | D = outer conductor ID, d = inner conductor OD, εr = dielectric constant |
| Velocity factor | VF = 1 / √εr | εr = relative permittivity of dielectric |
| Electrical length | θ = 360° × (l / λ) × (1/VF) | l = physical length, λ = free space wavelength |
| VSWR from reflection coefficient | VSWR = (1 + |Γ|) / (1 − |Γ|) | |Γ| = magnitude of reflection coefficient (0–1) |
| Reflection coefficient | Γ = (ZL − Z₀) / (ZL + Z₀) | ZL = load impedance, Z₀ = line impedance |
| Return loss | RL = −20 × log₁₀(|Γ|) | RL = return loss (dB), |Γ| = reflection coefficient magnitude |
| Mismatch loss | ML = −10 × log₁₀(1 − |Γ|²) | Power lost due to mismatch (dB) |
Propagation & Link Budget
| Formula | Expression | Variables |
|---|---|---|
| Free space path loss | FSPL(dB) = 20×log₁₀(d) + 20×log₁₀(f) + 20×log₁₀(4π/c) | d = distance (m), f = frequency (Hz), c = 3×10⁸ |
| FSPL simplified (MHz/km) | FSPL(dB) = 32.44 + 20×log₁₀(f_MHz) + 20×log₁₀(d_km) | f_MHz = frequency in MHz, d_km = distance in km |
| Received power | P_r(dBm) = P_t(dBm) + G_t(dBi) − FSPL(dB) + G_r(dBi) | P_t = TX power, G_t = TX gain, G_r = RX gain |
| Link margin | LM = P_r − P_min | P_r = received power (dBm), P_min = receiver sensitivity (dBm) |
| Friis transmission equation | P_r = P_t × G_t × G_r × (λ / 4πd)² | Linear power ratios, λ = wavelength, d = distance |
| Noise figure | NF(dB) = 10 × log₁₀(F) | F = noise factor = SNR_in / SNR_out |
| Thermal noise floor | N = −174 + 10×log₁₀(BW) | N = noise power (dBm), BW = bandwidth (Hz), at 290K |
Digital & Sampling
| Formula | Expression | Variables |
|---|---|---|
| Nyquist sampling theorem | fs ≥ 2 × fmax | fs = sample rate, fmax = highest signal frequency |
| ADC resolution | ΔV = V_ref / 2^n | ΔV = LSB voltage, V_ref = reference voltage, n = bit depth |
| ADC SNR (theoretical) | SNR = 6.02n + 1.76 dB | n = number of ADC bits |
| Nyquist maximum bit rate | R = 2 × BW × log₂(M) | Noiseless channel; R = bits/sec, BW = bandwidth (Hz), M = number of symbol levels |
| Shannon capacity | C = BW × log₂(1 + SNR) | C = max channel capacity (bits/s), SNR = linear ratio |
| Baud rate vs bit rate | Bit rate = Baud rate × log₂(M) | M = number of modulation states (e.g. QPSK: M=4) |