Impedance
Understanding Impedance in RF Systems
Impedance is the single most important concept in RF engineering. Every component, every transmission line, every connector has a characteristic impedance. When impedances are mismatched, reflections occur, power is lost, and standing waves form on the transmission line.
Complex Impedance
Impedance has two components:
- Resistance (R): The real part, representing energy dissipation. Frequency-independent in ideal resistors.
- Reactance (X): The imaginary part, representing energy storage. Inductive reactance (X_L = 2 pi f L) is positive; capacitive reactance (X_C = -1/(2 pi f C)) is negative.
At resonance, inductive and capacitive reactances cancel, leaving only resistance. This is exploited in resonant circuits, filters, and matching networks.
Characteristic Impedance
Transmission lines have a characteristic impedance (Z0) determined by their geometry and dielectric material. For coaxial cable: Z0 = (138/sqrt(er)) x log10(D/d), where D is the outer conductor diameter and d is the inner conductor diameter. This impedance is independent of cable length.
Why 50 Ohms?
The 50-ohm standard is a compromise. For air-filled coaxial cable, minimum attenuation occurs at 77 ohms and maximum power handling at 30 ohms. The geometric mean (sqrt(77 x 30) = 48 ohms, rounded to 50) provides a practical balance between low loss and high power capacity.
Impedance Mismatch Effects
- Reflections: Power bounces back toward the source, reducing delivered power.
- Standing waves: Voltage and current vary along the line, creating peaks that can cause breakdown.
- Gain ripple: Multiple reflections create frequency-dependent amplitude variations.
- Phase distortion: Reflections add out-of-phase components, distorting wideband signals.
Z = R + jX (ohms)
Magnitude: |Z| = √(R² + X²)
Phase: θ = arctan(X / R)
Coaxial cable Z0:
Z0 = (138 / √εr) × log10(D/d)
Reflection coefficient:
Γ = (Z_L - Z0) / (Z_L + Z0)
VSWR = (1 + |Γ|) / (1 - |Γ|)
Standard Impedance Values
| Impedance | Standard | Application |
|---|---|---|
| 50 Ω | RF/Microwave | Test equipment, military, telecom, most RF systems |
| 75 Ω | Video/Broadcast | Cable TV, satellite IF, broadcast antenna feeds |
| 93 Ω | Legacy data | IBM mainframe networks (historical) |
| 100 Ω | Differential | Ethernet, USB, LVDS differential pairs |
| 300 Ω | Balanced | Folded dipole antennas, twin-lead feedline |
| 377 Ω | Free space | Intrinsic impedance of vacuum/air |
Frequently Asked Questions
What is impedance in RF?
Impedance is the total opposition to AC current flow, expressed in ohms as a complex number Z = R + jX. The real part (R) is resistance, and the imaginary part (X) is reactance from inductors and capacitors. In RF systems, impedance matching between components is critical for maximum power transfer.
Why is 50 ohms the standard RF impedance?
50 ohms is a compromise between minimum loss (77 ohms) and maximum power handling (30 ohms) in air-filled coaxial cable. The geometric mean of these two values is approximately 48 ohms, rounded to 50. This provides a practical balance for most RF applications.
What happens when impedance is mismatched?
When source and load impedances differ, some signal power reflects back toward the source instead of being delivered to the load. This creates standing waves on the transmission line (measured as VSWR), reduces power transfer efficiency, and can cause voltage peaks that damage components.