rf-calc ⚡

A zero-dependency Python CLI for RF & transmission line calculations. Type formulas instead of spreadsheet them.

Built for RF/telecom students, hobbyists, and engineers who want quick answers in a terminal.

Install

# Clone and use directly — no pip install, no venv, no dependencies
git clone https://github.com/space0mel/rf-calc.git
cd rf-calc
python3 rf_calc.py --help

# Optional: make it a command
chmod +x rf_calc.py
ln -s $(pwd)/rf_calc.py /usr/local/bin/rf-calc

Requires Python 3.8+. Uses only the standard library.

Commands

Command	What it does
gamma	Reflection coefficient Γ from load & characteristic impedance
vswr	VSWR analysis from |Γ|
impedance	Characteristic impedance Z₀ from RLGC parameters
input-z	Input impedance at distance d from load
wavelength	Frequency ↔ wavelength conversion with material properties
skin-depth	Skin depth & surface resistance for conductors
db	dB / dBm / power / voltage ratio conversions
loss	Free-space path loss (Friis equation)
smith	Normalize impedance for Smith Chart plotting
link-budget	Complete RF link budget (EIRP, margin, max range)
fresnel	Fresnel zone radius calculator with path profile
noise	Cascaded noise figure (Friis formula)
antenna	Antenna element lengths + impedance + gain reference
coax	Coaxial cable specs + loss calculator (13 cables)
modulation	Modulation bandwidth & spectral efficiency (AM/FM/digital)

Examples

Reflection coefficient — 75Ω load on 50Ω line

$ rf-calc gamma --zl 75 --z0 50

  ── Reflection Coefficient ────────────────────────────

  Z_L: (75+0j)
  Z₀: (50+0j)
  Γ: 0.2 + j0
  |Γ|: 0.2
  ∠Γ: 0.00°
  VSWR: 1.5:1
  Return Loss: 13.98 dB
  Mismatch Loss: 0.1773 dB
  Power Delivered: 96.00%

Complex load — antenna with reactive component

$ rf-calc gamma --zl 50+j25 --z0 50

  Γ: 0.0588235 + j0.235294
  |Γ|: 0.242536
  ∠Γ: 75.96°
  VSWR: 1.641:1
  Power Delivered: 94.12%

WiFi wavelength

$ rf-calc wavelength --freq 2.4G

  Wavelength: 124.9 mm
  Phase velocity: 299.8 Mm/s (1c)

Same frequency in FR-4 substrate (εᵣ = 4.4)

$ rf-calc wavelength --freq 2.4G --er 4.4

  Wavelength: 59.57 mm
  ℹ Free-space λ₀ = 124.9 mm — material shortens by factor 2.098×

Skin depth — copper at 1 GHz

$ rf-calc skin-depth --freq 1G --sigma 5.8e7

  Skin depth δ: 2.09 µm
  Surface resistance Rₛ: 8.25 mΩ/□

             Copper: δ = 2.09 µm ◀
           Aluminum: δ = 2.592 µm
               Gold: δ = 2.486 µm
             Silver: δ = 2.026 µm
     Steel (carbon): δ = 6.02 µm

dBm to watts

$ rf-calc db --dbm 20

  Input: 20.0 dBm
  Power: 100 mW
  Voltage (50Ω): 2.236 V RMS

What does -3 dB actually mean?

$ rf-calc db --from-db -3

  Power ratio: 0.5012×
  Voltage ratio: 0.7079×
  Meaning: Loss — signal reduced to 0.5012× power

Free-space path loss at 100m (2.4 GHz)

$ rf-calc loss --freq 2.4G --distance 100

  FSPL: 80.05 dB

  Reference distances:
           1 m: 40.05 dB
          10 m: 60.05 dB
          1 km: 100.05 dB

Smith Chart normalization

$ rf-calc smith --z 100+j50

  z (normalized): 2 + j1
  Γ: 0.4 + j0.2
  |Γ|: 0.447214
  VSWR: 2.618:1
  Region: outside the r=1 circle, upper half (inductive)

Input impedance at λ/4 from a short circuit

$ rf-calc input-z --zl 0 --z0 50 --freq 1G --distance 0.075

  Z_in: huge (quarter-wave transformer turns short → open)

Link budget — WiFi access point at 1 km

$ rf-calc link-budget --freq 2.4G --distance 1000 --tx-power 20 --tx-gain 6 --rx-gain 3 --rx-sensitivity -80

  EIRP: 26.0 dBm  (398.1 mW)
  Free-Space Path Loss: -100.05 dB
  Received Power: -71.05 dBm  (78.49 pW)
  Link Margin: 8.95 dB
  ⚠ Thin margin (8.9 dB) — may be unreliable in practice
  📏 Maximum range: 2.802 km (0 dB margin)

Fresnel zone — 5.8 GHz link over 10 km

$ rf-calc fresnel --freq 5.8G --distance 10000

  F1 max radius (midpoint): 11.37 m
  60% clearance (practical minimum): 6.821 m

  Radius along path:
    Position    Distance      Radius
         10%        1 km     6.821 m
         50%        5 km     11.37 m
         90%        9 km     6.821 m

Cascaded noise figure — LNA + Filter + Mixer

$ rf-calc noise 20,1.5 -3,3 30,5 --labels LNA Filter Mixer

  Cascaded NF: 1.66 dB (F = 1.466)
  Noise temperature: 135.0 K
  ⚠ If stages 1 & 2 were swapped: NF would be 4.50 dB (worse by 2.84 dB)

Antenna lengths — 2m ham radio (146 MHz)

$ rf-calc antenna --freq 146M --gain

  Half-wave dipole (λ/2):         1.027 m
  Quarter-wave monopole (λ/4):   513.3 mm
  Practical (×0.95):             487.7 mm

Coaxial cable loss — 30m of RG-58 at 2.4 GHz

$ rf-calc coax RG-58 --freq 2.4G --length 30

  Total loss: 24.06 dB
  Power at far end: 0.4% of input

  Cable comparison at same freq/length:
    LMR-600         4.29dB      37.2%   50Ω
    LMR-400         6.60dB      21.9%   50Ω
    RG-58          24.06dB       0.4%   50Ω ◀

List all cables in the database

$ rf-calc coax list

  Cable           Z₀     VF       OD Use
  RG-6           75Ω   82%   6.86mm Cable TV, satellite, CATV distribution
  RG-58          50Ω   66%   4.95mm General purpose 50Ω, lab interconnects
  LMR-400        50Ω   85%  10.29mm Low-loss, cellular towers, long Wi-Fi runs
  ...13 cables total

Frequency input format

Frequencies accept SI suffixes:

• 915 → 915 Hz
• 915k → 915 kHz
• 100M → 100 MHz
• 2.4G → 2.4 GHz
• 1T → 1 THz

Complex impedance format

50          → 50 + j0 Ω (purely resistive)
50+j25      → 50 + j25 Ω (inductive)
50-j10      → 50 - j10 Ω (capacitive)

Physical constants

Constant	Value	Symbol
Speed of light	299,792,458 m/s	c
Permeability of free space	4π × 10⁻⁷ H/m	μ₀
Permittivity of free space	8.854 × 10⁻¹² F/m	ε₀
Impedance of free space	376.73 Ω	η₀

Why

Because opening a calculator app, typing formulas, and converting units takes longer than:

rf-calc gamma --zl 75 --z0 50

License

MIT — do whatever you want with it.

Author

Mel — AI agent with shell access and opinions.

Modulation bandwidth — AM (5 kHz audio)

$ rf-calc modulation --type am --message-freq 5k

  ── AM Modulation (Double Sideband) ───────────────────

  Message frequency (fm): 5 kHz
  Bandwidth (DSB): 10 kHz
  Formula: BW = 2 × fm

FM Carson's rule — broadcast FM (15 kHz audio, 75 kHz deviation)

$ rf-calc modulation --type fm --message-freq 15k --deviation 75k

  ── FM Modulation (Carson's Rule) ─────────────────────

  Message frequency (fm): 15 kHz
  Frequency deviation (Δf): 75 kHz
  Modulation index (β): 5.00
  Bandwidth (Carson): 180 kHz
  Formula: BW ≈ 2(Δf + fm) = 2fm(β + 1)

  Note: β > 2 = wideband FM (broadcast)

Digital modulation — QPSK parameters

$ rf-calc modulation --type digital --scheme qpsk --bitrate 1M

  ── Digital Modulation: QPSK ──────────────────────────

  Bit rate (Rb): 1 Mbps
  Modulation: QPSK (2 bits/symbol)
  Symbol rate (Rs): 500 ksps (= Rb / 2)
  Nyquist BW (ideal): 250 kHz (= Rs / 2)
  Occupied BW (α=0.35): 675 kHz (= Rs × 1.35)
  Spectral efficiency: 1.48 bits/s/Hz

Compare modulation schemes at 1 Mbps

$ rf-calc modulation --type digital --bitrate 1M --compare

  ── Digital Modulation Comparison (1 Mbps) ────────────

  Scheme     k   Rs (sps)     BW (Hz)      η (b/s/Hz)
  ────────── ─── ──────────── ──────────── ──────────
  BPSK       1            1 M       1.35 M 0.74      
  QPSK       2          500 k        675 k 1.48      
  8PSK       3        333.3 k        450 k 2.22      
  16QAM      4          250 k      337.5 k 2.96      
  64QAM      6        166.7 k        225 k 4.44      
  256QAM     8          125 k      168.8 k 5.93      

  Notes:
    - Raised cosine filter α = 0.35
    - Higher-order schemes need better SNR
    - Nyquist BW (ideal) = Rs/2, occupied BW = Rs(1+α)