RF Fundamentals

Radio-frequency engineering deals with signals whose wavelength is comparable to circuit dimensions. Learn frequency bands, wavelength, dB/dBm/dBi, free-space path loss and the Friis link budget, impedance matching, reflection coefficient, VSWR and return loss, and the building blocks of RF transceivers.

Above a few tens of MHz, wires become antennas, PCB traces become transmission lines and every mismatch reflects power. RF engineers think in dB, impedance and wavelength to design Wi-Fi, cellular, GPS and radar hardware.

An analogy

An RF mismatch is like a wave in a rope hitting a knot: part of the energy reflects back instead of continuing to the end.

Why RF is different

When line length exceeds ≈ λ/10, voltage and current vary along the line; lumped circuit theory fails. Standard impedance (50 Ω for most RF, 75 Ω for video/cable) lets components connect without reflections.

Link budgets

Start with transmit power, add antenna gains, subtract path and cable losses, compare with receiver sensitivity; the difference is the fade margin. Path loss rises 6 dB per doubling of distance or frequency in free space.

Matching

Maximum power transfer and minimal reflection require Z_L = Z₀ (or conjugate match). L-networks, stubs and quarter-wave transformers match impedances; the Smith chart is the graphical tool.

Transceiver chain

Transmitter: DAC → mixer/upconverter → PA → filter → antenna. Receiver: antenna → filter → LNA → mixer → IF/baseband → ADC. Key specs: noise figure, gain, P1dB, IP3 linearity, phase noise and spurious emissions.

Formulas

• Reflection coefficient: Γ = (Z_L − Z₀)/(Z_L + Z₀)
• VSWR & return loss: VSWR = (1 + |Γ|)/(1 − |Γ|), RL = −20 log|Γ|
• Free-space path loss: FSPL = 20 log d_km + 20 log f_MHz + 32.44
• Link budget (Friis): P_r = P_t + G_t + G_r − FSPL − losses (dB)
• Mismatch loss: ML = −10 log(1 − |Γ|²)

Worked example: Wi-Fi link budget

Given: 20 dBm Tx, 2 dBi antennas each end; 2.4 GHz, 100 m

Find: Received power.

• FSPL = −20 + 67.6 + 32.44 = 80.0 dB
• P_r = 20 + 2 + 2 − 80 = −56 dBm

Answer: −56 dBm (plenty above −85 dBm sensitivity)

Worked example: Mismatch

Given: 75 Ω load on 50 Ω line

Find: Γ, VSWR, return loss.

• Γ = 25/125 = 0.2
• VSWR = 1.5, RL = 14 dB
• Mismatch loss = 0.18 dB

Answer: VSWR 1.5:1 — acceptable for most systems

Common mistakes

• Wrong: Ignoring cable and connector losses. — Right: Include every loss in the budget.
• Wrong: Long unmatched traces at GHz. — Right: Design controlled-impedance lines.

Applications

• Wireless links: Wi-Fi, LoRa, point-to-point microwave.
• Antenna matching: Phone and IoT antenna tuning.
• Test & measurement: VNAs measure S-parameters and VSWR.

Key takeaways

• Γ = (Z_L − Z₀)/(Z_L + Z₀).
• FSPL = 20 log d + 20 log f + 32.44.
• P_r = P_t + G_t + G_r − losses.
• Match to 50 Ω; LNA first.

Going further

• S-parameters: S11, S21 for multiport networks.
• Smith chart: Graphical impedance matching.
• Linearity: P1dB and IP3 specifications.