Thévenin Equivalents in Receive Systems
Thévenin Equivalents in Receive Systems
A receiving antenna does not hand the receiver a magic “signal level.” At a declared frequency and reference plane, it presents an open-circuit voltage and a complex source impedance. The Thévenin model keeps those two facts together—and makes the consequences of loading, matching, loss and noise visible.
RF.Guru working definition: Common-mode current is the non-cancelling phasor-sum current in a specified set of conductors, evaluated at a defined cross-section and using a declared current-direction convention. In the intended differential transmission-line mode, the outgoing and return currents are equal and opposite, so their phasor sum is zero. When they do not cancel, the remaining current must close through another reference or return path—such as the outside of a coax shield, a mast, equipment chassis, station wiring, nearby structures, earth, the operator, or distributed coupling through the environment.
This broader working definition is especially useful in practical antenna systems. On transmit, non-cancelling current on the outside of the coax can make the feedline and connected structures part of the radiating antenna system unless that path is intentional, clearly defined and properly controlled—for example by providing the required return path and placing a suitable common-mode choke at the correct boundary.
Thévenin does not make the antenna frequency-independent, linear under every field strength or immune to its environment. It gives us a clean local model: one frequency, one operating condition, one mode and one reference plane at a time.
The Antenna Port Becomes a Source and an Impedance
For small-signal receive analysis, a linear antenna system viewed from a two-terminal port can be represented by an RMS phasor voltage Voc in series with its complex impedance:
ZA = RA + jXA
VL = Voc · ZL / (ZA + ZL)
Voc is the open-circuit voltage induced by the incident field for the stated direction, polarization, frequency and environment. ZA is the antenna impedance at the same port. The load ZL may be a feedline, transformer, matching network, LNA or receiver input.
The Norton form is exactly equivalent: Isc = Voc/ZA in parallel with ZA. Use the representation that makes the next stage easiest to analyze. A voltage-input front end often reads naturally in Thévenin form; a current-sensing or shunt-input front end may be clearer in Norton form.
Available Power Requires a Conjugate Match
With RMS phasors and RA > 0, the maximum available power occurs when the load is the complex conjugate of the source impedance:
ZL = ZA*
Pav = |Voc|² / (4RA)
A 50 Ω label does not guarantee that condition. Antenna impedance changes with frequency, installation, nearby conductors and common-mode current. Receiver inputs also depart from an ideal broadband 50 Ω termination. Define the plane where impedance and power are stated before comparing numbers.
From Field Strength to Available Power
For a far-field plane wave, matched polarization and RMS electric-field strength E, the average power density is E²/η0, where η0 is approximately 377 Ω in free space. The antenna's effective aperture in the arrival direction is related to gain:
Ae = λ²G / (4π)
Pav = (E²/η0)Ae
|Voc| = 2√(PavRA)
Those equations are not a near-field shortcut. Polarization mismatch, arrival angle, multipath, ground, loss and the installed gain pattern change the result. The field-strength-to-voltage conversion is only as good as the antenna factor and reference conditions behind it.
| Illustrative case | At E = 1 µV/m | Boundary |
|---|---|---|
| 40 m half-wave dipole, λ ≈ 42.9 m, G ≈ 1.64, RA ≈ 73 Ω | Ae ≈ 240 m²; Pav ≈ −92 dBm; Voc ≈ 13.6 µV RMS | Ideal far field, matched polarization and conjugate match |
| 2 m antenna, λ ≈ 2.08 m, G = 12 dBi, RA ≈ 50 Ω | Ae ≈ 5.46 m²; Pav ≈ −108.4 dBm; Voc ≈ 1.70 µV RMS | Same stated ideal conditions |
The Noise Source Belongs in the Same Model
The real part of a passive source impedance at physical temperature T has Johnson–Nyquist noise. In the classical RF range, its open-circuit mean-square voltage in equivalent noise bandwidth B is 4kTRB. Under a conjugate match, the available thermal-noise power is kTB.
An antenna also receives external atmospheric, galactic and man-made noise. We can refer that received noise to an antenna noise temperature TA, but it is not automatically the antenna's physical temperature. ITU-R P.372 treats those external sources separately and makes the environment, frequency, direction and antenna response part of the receiving problem.
That distinction is why a receive mismatch does not have one universal SNR penalty. If wanted signal and dominant external noise arrive through the same antenna mode, a lossless mismatch may attenuate both similarly. Receiver-generated noise does not receive the same attenuation, and the LNA's noise parameters depend on source impedance. Once internal noise matters, mismatch and pre-LNA loss reduce SNR.
Power Match and Noise Match Are Different Questions
A conjugate power match maximizes power delivered from the stated source. A transistor or MMIC reaches its minimum noise figure at a particular complex source impedance Zopt, which need not be 50 Ω or ZA*. Front-end design therefore trades noise figure, gain, input match, stability, linearity and bandwidth.
On noisy HF bands, the useful design may deliberately accept some mismatch while preserving enough external-noise margin and strong-signal headroom. On a quiet VHF or microwave link, the same loss ahead of the LNA may be decisive. “Put an LNA at every antenna” and “HF never needs an LNA” are both incomplete rules.
Loss Before the LNA Has a Reference-Plane Cost
For a passive loss L expressed as a power ratio at physical temperature Tp, its equivalent input noise temperature is (L−1)Tp. With an LNA noise temperature Te after that loss, the receiver contribution referred to the loss input becomes:
Trx,input = (L−1)Tp + L·Te
The equation does not say every decibel of cable always costs one decibel of received SNR. Add the antenna noise temperature and compare the total. When TA is very high, a modest loss can leave the system externally noise-dominated. When TA is low, loss directly consumes sensitivity.
A Receive-Chain Workflow That Keeps the Planes Straight
- Define frequency, bandwidth, direction, polarization and the antenna terminal reference plane.
- Measure or model ZA(f) in the installed geometry, including the intended common-mode condition.
- Establish Voc, antenna factor or available power under stated field conditions.
- Refer feedline loss, matching networks and front-end noise to the same plane.
- Decide whether external noise, receiver noise or strong-signal linearity is the limiting condition.
- Choose the match for the declared objective: delivered power, noise, bandwidth, stability or a compromise.
- Verify gain compression, intermodulation and overload as well as small-signal noise.
Bottom line: Thévenin is valuable on receive because it prevents voltage, impedance, power and noise from being discussed as separate folklore. It does not replace the antenna pattern or receiver noise model. It connects them at a port.
Primary sources checked
Mini-FAQ
- Is a Thévenin model valid for a broadband antenna? Yes, frequency by frequency and for a defined operating condition. Voc and ZA generally vary across the band.
- Can I use the Norton equivalent instead? Yes. It contains the same port information and may be clearer for current-mode front ends.
- Does a 50 Ω receiver always receive maximum power? No. Maximum available power requires a conjugate match to the actual complex antenna source impedance at the stated plane.
- Does mismatch always reduce receive SNR by the mismatch loss? No. The result depends on how wanted signal, external noise and receiver noise are transferred and on the LNA's source-dependent noise behaviour.
- Is antenna noise temperature the antenna's physical temperature? Not generally. It represents received noise weighted by the antenna pattern and environment.
- Where should an LNA go? Where the full noise, loss and linearity budget says it belongs—often near the antenna when receiver noise matters, but not as an automatic rule.