Will the Receiver Read Zero?

  • Connect a room-temperature noise source (290 K) to a receiver with noise bandwidth 𝐵 and a power meter; no transmitted signal
  • Thermal motion creates random electrical fluctuations — so no, the receiver does not read zero
  • Assumes a matched connection: the receiver accepts the source’s available noise power

Random Fluctuations Carry Real Power

  • Noise voltage vs. time: no repeating cycle; mean voltage ≈ 0
  • But the squared fluctuations have a positive average: the noise power is real
  • Noise density vs. frequency: flat at height 𝑁0=𝑘𝑇 over a width of 𝐵 hertz
    • The collected “area” is the total noise power 𝑁=𝑘𝑇𝐵

Thermal Noise Density

Thermal Noise

  • 𝑁0=𝑘𝑇,𝑁=𝑁0𝐵=𝑘𝑇𝐵
  • 𝑁0 in W/Hz; 𝑘 = Boltzmann’s constant (1.380649⋅10−23 J/K)
  • In dB:
    • [𝑁0]=−228.6+10log10(𝑇/K)dBW/Hz
    • [𝑘]=−228.6dBW/(Hz K)
  • At 290 K:
    • [𝑁0]=−204.0dBWHz−1=−174.0dBm/Hz
  • Doubling 𝑇 raises the noise density by 3.0 dB
  • For a receiving system, 𝑇 becomes the system noise temperature 𝑇sys