Understanding impedance matching
Impedance matching is the practice of making a load's impedance equal (or as close as practical) to the impedance of the source or transmission line feeding it, so that a signal or power source delivers its energy to the load instead of bouncing part of it back where it came from. It matters anywhere a signal travels along a defined-impedance path — coaxial cable feeding an antenna, a transmission line feeding an amplifier, audio gear, or high-speed digital traces — because any mismatch reflects a portion of the incident wave back toward the source.
The formulas
For a source or line impedance Z0 (assumed real) driving a load impedance Z_L = R_L + jX_L, four values describe the match:
- Reflection coefficient: Γ = (Z_L − Z0) / (Z_L + Z0). Its magnitude |Γ| runs from 0 (perfect match) to 1 (total reflection, as with an open or short circuit).
- VSWR (voltage standing wave ratio): VSWR = (1 + |Γ|) / (1 − |Γ|). A perfect match gives VSWR = 1:1; VSWR grows without bound as |Γ| approaches 1.
- Return loss: Return loss (dB) = −20 × log10(|Γ|). Unlike most "loss" figures, bigger is better here — it means less power came back.
- Power delivered: the fraction of incident power that reaches the load is 1 − |Γ|², so delivered power = incident power × (1 − |Γ|²); the rest is reflected.
Maximum power transfer
The maximum power transfer theorem states that a source delivers the most power to a load when the load impedance equals the complex conjugate of the source impedance (Z_L = Z0*). For the common case of a purely resistive source or transmission line (Z0 real, no reactance), that condition simplifies to Z_L = Z0 with X_L = 0 — a purely resistive load equal to the line impedance. This calculator assumes a real Z0, which covers the vast majority of coax, cable, and line-driver situations; if the source itself has significant reactance, use its full complex conjugate as the matching target instead.
Common reference impedances
- 50 Ω — the standard for most RF equipment, Wi-Fi hardware, and general-purpose coaxial cable.
- 75 Ω — the standard for video, cable TV, and satellite feeds; it minimizes loss for that application but is not directly compatible with 50 Ω gear without a matching pad or transformer.
- 300 Ω — classic twin-lead television antenna feedline, now largely obsolete.
- 600 Ω — a traditional reference impedance for telephone and audio transmission lines.
Frequently Asked Questions
What is the reflection coefficient?
What is VSWR and how does it relate to the reflection coefficient?
What is return loss?
How much power actually reaches the load?
Common Tip Percentages
| Service | Typical Tip Range | Notes |
|---|---|---|
| Restaurant (sit-down) | 15–20% | 20%+ for exceptional service |
| Food delivery | 10–20% | Consider extra for long distances |
| Taxi / rideshare | 10–20% | More for assistance with luggage |
| Hotel housekeeping | $2–5/night | Leave daily, not just at checkout |
| Barber / hair salon | 15–20% | On pre-discount total |
| Pizza delivery | 10–15% or $3–5 minimum | Higher in bad weather |
General Household Budget Ratios (50/30/20 Rule)
| Category | % of Net Income | Examples |
|---|---|---|
| Needs | 50% | Rent, groceries, utilities, insurance |
| Wants | 30% | Dining out, entertainment, hobbies |
| Savings / Debt | 20% | Emergency fund, retirement, extra payments |
Common Measurement Conversions for Everyday Use
| Quantity | US / Imperial | Metric Equivalent |
|---|---|---|
| 1 cup | 8 fl oz | 237 mL |
| 1 pint | 16 fl oz | 473 mL |
| 1 quart | 32 fl oz | 946 mL |
| 1 gallon | 128 fl oz | 3.785 L |
| 1 lb | 16 oz | 453.6 g |
| 1 ft | 12 in | 30.48 cm |