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Electronics & Antennas for Ham Radio

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Reciprocity Is a Mathematical Theorem

Related Reading:
The Limitations of NEC
The Ham’s Obsession with Resonance
SkyTracer — Technical Overview
TerraBooster — Technical Overview
OctaLoop — Technical Overview
EchoTracer — Technical Overview
VerticalVortex — Technical Overview
Pulseroot — Technical Overview

Reciprocity in antenna theory says transmit and receive patterns are the same under linear, time‑invariant, reciprocal media. If an antenna radiates strongly at an angle, it will also hear from that angle equally well.

But reality is not a theorem.

Real HF stations aren’t ideal LTI systems. The environment, feedline, grounding, and local noise field introduce asymmetries the theorem doesn’t cover—so receive‑only antennas often beat shared TX/RX systems in practice.

Reciprocity Is a Mathematical Theorem — roast comic illustration
Reciprocity Is a Mathematical Theorem — but your backyard isn’t.

Return Currents vs. Common‑Mode: Not the Same Thing

Return‑current path issues arise from imbalance, opening a path on the outside of the coax and structures. That path then allows common‑mode pickup (ambient noise flowing on the cable assembly). They’re related—but not identical:

  • Return currents (cause): due to imbalance; they seek any available return path, often the coax exterior.
  • Common‑mode pickup (effect): the noise that rides those exterior paths into the receiver.

Fix balance and add high‑CM choking → you suppress both the return‑current path and the common‑mode noise it invites.

The Hidden Asymmetries

  • Feedline return currents: Tolerable on TX; on RX they import household RFI as unintended antennas.
  • Local noise fields: TX can punch through S7 noise; RX can’t. Switchers, PLC/Ethernet leakage, MW overload dominate.
  • Ground/structure coupling: Poor decoupling turns masts, gutters, shack wiring into noise antennas.
  • Imbalance & pattern distortion: Small unbalances warp the practical RX pattern and raise noise while TX seems “fine.”

Why RX Antennas Win

Receive‑only designs—Beverages, phased loops, K9AY, and active E/H probes—prioritize high CMRR, controlled patterns, overload immunity, and clean grounding. Reciprocity still holds for the ideal radiator; it’s the system that breaks symmetry by letting noise in asymmetrically.

RDF: Why Receive‑Only Antennas Shine
Antenna (typical) RDF (dB) Notes
Low horizontal dipole (≤0.25λ) ~0–2 Strong high‑angle pickup; poor DX RX
Small passive magnetic loop ~4–7 Good local noise rejection when nulled
K9AY / pennant / flag ~6–9 Compact directional RX with deep nulls
Beverage (single longwire) ~8–10 Excellent low‑angle, low‑noise DX RX
4‑square (receive‑configured) ~10–11 Switchable directivity with F/B
Optimized phased loops / arrays ~11–13+ Tight beam + strong nulls

RDF (Reception Directivity Factor) ≈ forward gain − average hemispherical gain. Higher RDF ⇒ better RX SNR via noise rejection, more valuable than raw gain.

RF.Guru RX Antennas — CMRR‑First Design

Our receive antennas are engineered for maximum CMRR and system immunity first, then pattern/array performance. Typical CMRR figures exceed what most hams are used to.

Model Type / Band Focus CMRR Key Technical Notes
SkyTracer Dual‑leg active E‑field dipole, 50 kHz–30 MHz >55 dB High‑IP3 differential front‑end; FM notch 88–108 MHz; Standard (cap hats) & Maxi (1 m legs); cardioid null; PolarFlip‑ready
TerraBooster Medi Shielded H‑field ground loop, 160–10 m >60 dB 32 m loop; ground‑level; broad cardioid; LPF ~32 MHz; high‑linearity push‑pull
OctaLoop 1.2 m active magnetic loop, 1–30 MHz >50 dB Shielded H‑field; true differential push‑pull; LPF ~41–46 MHz; high IP3; phased‑array friendly
EchoTracer Active E‑probe, ~10 kHz–200 MHz ≥45 dB (min) FM notch; surge/ESD stack; high linearity; 75 Ω output; height guidance per band
VerticalVortex 6 m active E‑probe, low‑band RX (160/80/60/40) ≥50 dB (min) Broadband LF/MW notch ~1.46 MHz; FM trap ~130 MHz; fast TX mute (hard short); LPF 30 MHz
Pulseroot Active Beverage‑on‑Ground (BoG) >50 dB 4:1 front‑end → LF/MW notch + FM & airband notch; GALI‑74+ LNA → 30 MHz LPF; DR311‑474BE choke

CMRR values are typical and installation‑dependent. Always add a high‑CM choke at the shack entry to keep the entire system quiet.

Indicative RDF by Model (Conservative)
Model 160 m 80 m 40 m 20 m Notes
SkyTracer — Standard 6–8 6–8 6–7 5–7 Broad cardioid; aim null toward QTH noise
SkyTracer — Maxi 7–9 7–9 6–8 5–7 Longer legs give a small low‑band edge
TerraBooster Medi 8–10 8–10 7–9 6–8 Ground‑hugging H‑loop is inherently quiet
OctaLoop 1.2 m 6–8 6–8 6–8 5–7 Single loop; phased pairs reach 11–13+
EchoTracer 3–5 3–5 3–5 2–4 Honest omni; high CMRR helps SNR
VerticalVortex 6–8 6–8 5–7 4–6 Vertical E‑probe + quiet counterpoise
Pulseroot (BoG) 8–10 8–10 7–9 6–8 Length & soil drive RDF; directional

These RDF figures are indicative and conservative, assuming average soil, quiet site, and the placements noted in each overview. Arrays (phased loops, dual SkyTracers with PolarFlip, multiple BoGs) typically reach 11–13 dB+ RDF with deeper nulls.

The Shift to RDF

Reception Directivity Factor (RDF)—popularized for hams by ON4UN—is the RX metric that really matters. It quantifies noise rejection from unwanted directions. For RX, RDF beats raw gain because SNR—not absolute level—sets copy.

Others Who Address the Gap

  • N6LF (Rudy Severns): Radials, soil, and asymmetry affect TX vs RX differently.
  • W8JI (Tom Rauch): Poor choking/grounding & return currents clobber RX long before TX.
  • Eric E. Johnson (N5FDL): Patterns are reciprocal; SNR is not in noise‑dominated RX environments.

Conclusion

Reciprocity stands—mathematically. But real stations are not ideal LTI systems. It’s the complete RF system that breaks symmetry by admitting noise via return‑current paths and common‑mode pickup. High‑CMRR hardware, correct choking, and antennas with strong RDF deliver the RX edge.

“When you can’t change the world, design to hear around it.”

Mini-FAQ

  • Are return currents the same as common‑mode? — No. Imbalance opens a return‑current path; common‑mode is the noise riding that path. Fix balance + add high‑CM chokes to suppress both.
  • Why do RX antennas outperform TX antennas? — They prioritize CMRR, clean grounding, and RDF, which directly improve SNR in noise‑dominated environments.
  • What should I optimize first? — Balance and choking (high CMRR), then pattern/RDF. Add a high‑CM choke at the shack entry even with quiet antennas.

Interested in more technical content? Subscribe to our updates for deep‑dive RF articles and lab notes.

Questions or experiences to share? Contact RF.Guru.

Joeri Van Dooren, ON6URE – RF engineer, antenna designer, and founder of RF.Guru, specializing in high‑performance HF/VHF antennas and RF components.

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