Electronic – Johnson–Nyquist noise contribution Antenna noise temperatures

antennanoisetemperature

I understand that for an antenna the greatest contribution to the noise comes from the noise that the antenna captures from the environment, not the "internal" thermal noise of the antenna. But I do not know how to calculate this myself (and prove to myself that the Johnson-Nyquist noise is negligible).

I am imagining a 50 Ohm antenna in a room at temperature \$ T \$, receiving \$ P_{noise} \$ over bandwidth \$ B \$, matched to a 50 Ohm receiver. Hence the noise temperature will be \$ T_n = \frac{P_{noise}}{k_bB} \ne T \$.

However, if the wire making up the antenna has resistance \$ R=1\Omega\$, what happens to the thermal noise power \$P_{Johnson}=k_bTB\$? Is it just mismatched because \$ R \ll 50\Omega\$, and hence not delivered to the receiver?

Similarly, is there a way to express the antenna noise temperature as the sum of a component due to noise received from the environment and intrinsic thermal Johnson-Nyquist noise?

Best Answer

It depends on the ambient noise & stray signal in each band but I know LNA's are essential for Sat. Rx and GPS Rx as well for VLF global Rx. The Tx levels, Friis path loss, antennae gains and noise figure and BW of Preamp all are included in C/N ratios and with demodulation gains to S/R ratios.

So it is not universally true that Johnson-Nyquist Noise is negligible and depends on background interference and Rx threshold & acceptable BER.

\$P_\mathrm{dBm} = 10\ \log_{10}(k_\text{B} T \times 1000) + 10\ \log_{10}(\Delta f)\$

which is more commonly seen approximated for room temperature (T = 300K) as:

\$P_\mathrm{dBm} = -174 + 10\ \mathrm\log_{10} \ (\Delta f)\$

  • for 0dBm= 1mW

e.g. for \$(\Delta f)\$

  • 1 MHz −114 dBm Bluetooth channel ( well below ambient noise)
  • 20 MHz −101 dBm WLAN 802.11 channel ( >-80 dBm signal min. typical needed)
  • 80 MHz −95 dBm WLAN 802.11ac 80 MHz channel (>-65 dBm often needed )

Even small Capacitors have thermal noise due to V and C and those not using NP0 material are even microphonic.

\$v_{n} = \sqrt{ k_\text{B} T / C }\$

  • e.g. 1pF 64µV, 1nF 2µV

Then we have \$1/f\$ pink solid-state noise for the spectrum of pink noise in one-dimensional signals and for 2D signals (e.g., images) the power spectrum is \$1/f^2\$.

The most common units of measure for noise is \$dB/\sqrt{Hz}\$.

The understanding of threshold noise depends on many factors including Shannon's Law for SNR vs BER and non-"matched receivers" that match the signal BW and non-ideal discriminators and Ricean Fading loss (phase cancelling reflections) and many other factors.

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