Amateur Extra Quick Formula Sheet

Ohm’s Law

V = I · R
I = V / R
R = V / I

Power

P = V · I
P = V² / R
P = I² · R

Series / Parallel

R_series = R₁ + R₂ + …
1/R_parallel = 1/R₁ + 1/R₂ + …

C_series:   1/C_eq = 1/C₁ + 1/C₂ + …
C_parallel: C_eq = C₁ + C₂ + …

L_series:   L_eq = L₁ + L₂ + …
L_parallel: 1/L_eq = 1/L₁ + 1/L₂ + …

Reactance

X_L = 2π f L
X_C = 1 / (2π f C)

Impedance (series RLC)

Z = √( R² + (X_L − X_C)² )

Phase Angle

φ = arctan( (X_L − X_C) / R )

Resonance (LC)

f₀ = 1 / (2π √(L C))

Q Factor

Q = X / R   (at resonance)
Bandwidth:  BW = f₀ / Q

RC / RL Time Constant

τ_RC = R · C
τ_RL = L / R

Wavelength

λ (m) = c / f
≈ 300 / f_MHz

Half‑Wave Dipole Length

L_total (ft) ≈ 468 / f_MHz
L_total (m)  ≈ 143 / f_MHz

Cut each leg ≈ L_total / 2. Adjust for wire diameter & environment.

Quarter‑Wave Vertical

L (m) ≈ 71.5 / f_MHz

Free‑Space Path Loss (FSPL)

FSPL(dB) = 32.44 + 20·log₁₀(f_MHz) + 20·log₁₀(d_km)

Friis Transmission (link budget)

P_r(dBm) = P_t(dBm) + G_t(dBi) + G_r(dBi) − L_path(dB) − L_misc(dB)

Field Strength (far field)

E ≈ √(30 · P · G) / r   (V/m)

Power & Voltage Ratios

ΔdB_power   = 10 · log₁₀(P₂ / P₁)
ΔdB_voltage = 20 · log₁₀(V₂ / V₁)

Handy dB Values

• +3 dB ≈ ×2 power
• +10 dB = ×10 power
• −3 dB ≈ ×0.5 power
• +6 dB ≈ ×2 voltage (×4 power)

dBm / dBW

P(dBm) = 10 · log₁₀( P(mW) )
P(dBW) = 10 · log₁₀( P(W) )
dBm = dBW + 30

Gain & Loss Chaining

Total(dB) = Σ Gains(dB) − Σ Losses(dB)

Reflection & SWR

Γ = (Z_L − Z₀) / (Z_L + Z₀)           (complex in general)
SWR = (1 + |Γ|) / (1 − |Γ|)

Return Loss & Mismatch Loss

RL(dB) = −20 · log₁₀(|Γ|)
ML(dB) = −10 · log₁₀( 1 − |Γ|² )

Line Input Impedance (lossless)

Z_in = Z₀ · ( Z_L + j Z₀ tan βl ) / ( Z₀ + j Z_L tan βl )
β = 2π / λ

Velocity & Electrical Length

v_p = VF · c
l_elec (λ) = physical_length / λ_medium

Quarter‑Wave Transformer

Z_match = √( Z_S · Z_L )       (use 90° section, lossless)

L‑Network (lossless)

Let R_H be larger, R_L smaller.
Q = √(R_H/R_L − 1)
If series with R_L:
  X_series = Q · R_L
  X_shunt  = R_H / Q
Choose +jX (inductor) or −jX (capacitor) per needed reactance.

Cutoff / Corner

RC low/high‑pass: f_c = 1 / (2π R C)
RL low/high‑pass: f_c = R / (2π L)

Series RLC (near f₀)

Q_series = ω₀ L / R = 1 / (ω₀ R C)
BW = f₀ / Q_series

Parallel RLC (near f₀)

Q_parallel = R / (ω₀ L) = R · ω₀ C
BW = f₀ / Q_parallel

Quality Factor Identities

ω₀ = 2π f₀
Stored Energy / Cycle Loss = Q / (2π)

Skin Depth (good conductor)

δ = √( 2 / ( ω μ σ ) )

ω = 2πf, μ ≈ μ₀ for copper, σ = conductivity.

Thermal Noise (kTB)

N = k T B   (W)
N(dBm) ≈ −174 dBm/Hz + 10·log₁₀(B_Hz) + NF(dB)

Smith Chart Quickies

• Normalize impedances: z = Z / Z₀
• Admittance is 180° rotation on the chart
• Quarter‑wave (λ/4) transforms z → 1/z

Power Density (far field)

S ≈ P · G / (4π r²)     (W/m²)

Common Prefixes

• p (10⁻¹²), n (10⁻⁹), µ (10⁻⁶), m (10⁻³)
• k (10³), M (10⁶), G (10⁹)

Frequency

• 1 MHz = 10⁶ Hz
• 1 kHz = 10³ Hz

Constants

• c ≈ 3.00×10⁸ m/s
• μ₀ = 4π×10⁻⁷ H/m
• ε₀ ≈ 8.854×10⁻¹² F/m
• k (Boltzmann) = 1.38×10⁻²³ J/K

Dipole Length @ 7.2 MHz

L_total ≈ 468 / 7.2 ≈ 65.0 ft
Each leg ≈ 32.5 ft

SWR from Return Loss

RL = 20 dB → |Γ| = 10^(−20/20) = 0.1
SWR = (1 + 0.1) / (1 − 0.1) = 1.22:1