Thevenin Equivalents in Receive Systems

—Why They Matter More on RX Than TX

Thevenin is especially handy on the receive (Rx) side. On transmit (Tx) we care about power capability, efficiency, and non-linear behavior of PAs. On receive, signals are tiny, everything is linear, and noise + impedance dominate — exactly where the Thevenin model shines.

The One-Port That Rules Your RX Front End

Any antenna feedpoint can be modeled as:

[V_ant]──[Z_ant]──► (feedline / LNA / receiver)

• V_ant ≡ antenna’s open-circuit RF voltage from the incident field.
• Z_ant ≡ antenna feedpoint impedance = R + jX.

The Norton equivalent (a current source in parallel with Z_ant) is interchangeable, but the Thevenin form suits voltage-input LNAs and receivers best.

The Norton equivalent (a current source in parallel with Z is fully interchangeable with the Thevenin form. We often present receivers in Thevenin form because many LNA inputs are voltage‑sensing and 50‑Ω test gear is naturally series‑resistance based. That said, the Norton picture absolutely still applies—especially for current‑mode RX front ends—and remains highly relevant on the TX side, where PA devices, current‑steering DACs, and mixer outputs are well modeled as current sources feeding a load network. Choose the representation that matches what the next stage senses; the underlying match and delivered power are unchanged.

Why it matters: the entire RX chain can be reduced to two parameters — V_ant and Z_ant — making it easy to compute delivered signal, noise, and SNR.

From Field Strength to Microvolts and dBm

A plane wave of field E (V/m) delivers power to the antenna through its effective aperture A_e = λ²G / (4π).

Power flux: S = E² / η (η ≈ 377 Ω).
Available power: P_avail = S A_e = E² A_e/η.

In Thevenin form:

P_avail = V_ant² / (4 R_ant) → V_ant = 2√(P_availR_ant) = E·h_eff, where h_eff = 2√(R_antA_e/η).

Example 1 — HF 40 m Dipole:
G ≈ 1.64 (2.15 dBi), R_ant ≈ 73 Ω, λ ≈ 42.9 m → A_e ≈ 239 m². For E = 1 µV/m: P_avail ≈ 6.3×10⁻¹³ W = −92 dBm, V_ant ≈ 13.6 µV RMS.

Example 2 — VHF 2 m Yagi (12 dBi):
G = 15.85, R ≈ 50 Ω, λ ≈ 2.08 m → A_e ≈ 5.5 m². For E = 1 µV/m: P_avail ≈ 1.4×10⁻¹⁴ W = −108 dBm, V_ant ≈ 1.7 µV RMS.

RX work lives in microvolts and −90 to −130 dBm. Thevenin turns that into a solvable two-number problem.

Noise and SNR — Why Thevenin Shines on RX

Any resistive source at T produces thermal noise power Pₙ = kTB and open-circuit noise voltage eₙ = √(4kTRB). At 290 K, the baseline is −174 dBm/Hz.

Antenna SNR = P_signal,avail / (k T_ant B). Two key regimes:

• External-noise-dominated (HF & below) — T_ant ≫ T_rx; lossless mismatch barely affects SNR.
• Receiver-noise-dominated (VHF/SHF) — T_ant ≈ few hundred K; feedline loss before LNA directly costs SNR.

Loss placement rule (Friis simplified):
T_sys ≈ T_ant + (L−1)·290 + L·T_LNA + … → Place the LNA at the antenna when you’re not external-noise-limited.

Matching: Power vs Noise

• Power match (Z_L = Z_S*) maximizes delivered power.
• Noise match sets Z_S = Z_opt of the LNA for minimum NF (often ≠ 50 Ω).
• Lossless networks preserve SNR; resistive ones reduce it if receiver noise matters.

Mismatch factor τ = 1 − |Γ|². Signal and external noise scale with τ, internal noise does not — so mismatch hurts only in quiet, receiver-noise-dominated bands.

Designing a Better RX Chain (Step-by-Step)

1. Measure Z_ant(f) with a VNA → that’s your Thevenin impedance.
2. Estimate field → A_e → P_avail → V_ant.
3. Determine noise regime (HF vs VHF/SHF).
4. Minimize loss before LNA if receiver-noise-limited.
5. Choose matching goal (50 Ω power match or Z_opt noise match).
6. Use lossless L/π/T networks or transformers.
7. Verify voltages and currents so the LNA is not overdriven.

Mini-Example — HF 40 m Dipole: ~73 Ω → 1:1 balun + coax → receiver; no LNA needed. Mini-Example — VHF 2 m Yagi: ~50 Ω → match to LNA’s Z_opt with low-loss L-network at antenna.

What About Transmit?

The same equations predict delivered power and SWR, but transmit adds non-linearity and efficiency limits. On TX we’re power-limited, not noise-limited — so Thevenin is useful for matching and reflection math, not as a daily design tool.

Quick RX Cheat Sheet

• P_avail = (E²/η)A_e, A_e = λ²G/(4π).
• V_ant = 2√(P_availR_ant) = E h_eff, h_eff = 2√(R_antA_e/η).
• Thermal noise = kTB (−174 dBm/Hz at 290 K).
• Loss before LNA adds T_loss = (L−1)·290 K.
• Mismatch factor τ = 1 − |Γ|².

Common Pitfalls

• Ignoring frequency dependence of Z_ant(f) and G(f).
• Neglecting common-mode currents on coax — use baluns/chokes.
• Using lossy pads in quiet bands where NF matters.
• Assuming 50 Ω is always optimal on RX — it isn’t when noise matching rules.

Bottom Line

Thevenin modeling is most valuable on receive: it quantifies signal, noise, and SNR at the antenna port and guides where to place loss and how to match impedances. On transmit it still applies mathematically but efficiency and linearity take over as the dominant constraints.

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