Thermal Noise
Every resistor in your radio — in the antenna, in the coaxial cable, in the preamplifier input network — is constantly generating a tiny random voltage. You cannot hear it as a separate signal. You cannot switch it off. It is an unavoidable consequence of the fact that electrons in any conductor above absolute zero temperature are in constant, random thermal motion. This random motion produces random voltage fluctuations: thermal noise, also called Johnson noise or Johnson-Nyquist noise. It sets the absolute lower limit on how sensitive any receiver can ever be.
Understanding thermal noise from first principles is the foundation of everything else in this module. Once you understand where noise comes from and how to calculate how much of it any circuit element generates, you can understand noise figure, noise floor, dynamic range, and the many ways that your receiving system can be optimized to work closer to that fundamental physical limit.
Thermal noise has a flat power spectral density from DC to extremely high frequencies. The total noise power available in any bandwidth B is simply P = kTB. The narrower the bandwidth, the less total noise power — which is why narrower filters improve reception.
View LargerThe Physical Origin of Thermal Noise
Thermal noise originates in the thermal (heat) energy stored in a material. All matter above absolute zero (0 K or −273.15 °C) contains thermal energy — the kinetic energy of atoms and electrons in random motion. In a conductor, the free electrons that carry current are not stationary between uses. They are constantly moving at high velocities in random directions, colliding with the crystal lattice of the conductor billions of times per second. This is true even with no external voltage applied and no current flowing through the circuit.
Each random collision and each segment of random electron motion involves a small displacement of charge. A displacement of charge is the definition of a current, and a current through a resistance produces a voltage. Because the motion is random, the resulting voltage is also random — it has no specific frequency, no specific phase, and averages to zero over any long period of time. But it is not zero at any given instant. It fluctuates continuously around zero, and that fluctuation is what we call thermal noise.
The key insight is that this process is driven entirely by temperature. Hotter conductors have more energetic electrons, more violent random motion, and therefore more noise. Colder conductors have less. At absolute zero, the random thermal motion would stop and so would the thermal noise — but absolute zero is physically unreachable, so some thermal noise is always present in any practical circuit.
This phenomenon was first measured experimentally by John B. Johnson at Bell Labs in 1928, and the theoretical explanation was provided almost simultaneously by Harry Nyquist. Their names are attached to the effect: Johnson noise or Johnson-Nyquist noise. The terms thermal noise, resistor noise, and thermal agitation noise all refer to the same thing.
Noise Power: P = kTB
Nyquist derived the fundamental formula for the available noise power from any resistor at temperature T, measured over a bandwidth B:
Where:
P = available noise power (watts)
k = Boltzmann's constant = 1.38 × 10−23 joules per kelvin (J/K)
T = absolute temperature of the resistor in kelvins (K)
B = noise bandwidth in hertz (Hz)
This formula has several remarkable properties that are worth understanding fully.
It does not depend on the resistance value. A 1 Ω resistor and a 1 MΩ resistor at the same temperature generate the same available noise power in the same bandwidth. The resistance affects the noise voltage (more resistance, more voltage) but the available power is the same. This is a consequence of thermodynamics: a resistor at temperature T in thermal equilibrium with a matched load delivers exactly P = kTB to that load, regardless of the resistance value. If the power depended on resistance, you could extract net energy from a thermal equilibrium system, violating the second law of thermodynamics.
It depends linearly on temperature. Double the temperature in kelvins, and you double the noise power. Room temperature (around 17 °C) is approximately 290 K. A cryogenically cooled low-noise amplifier at 77 K (liquid nitrogen temperature) generates only 77/290 = 0.27 times as much thermal noise as one at room temperature — which is why astronomers use cryogenic cooling to achieve very low noise in radio telescope receivers.
It depends linearly on bandwidth. Double the bandwidth, and you double the noise power. This is the practical implication that most affects amateur radio: narrow filters mean less noise. A 200 Hz CW filter passes much less noise than a 2.4 kHz SSB filter — exactly 2400/200 = 12 times less, or about 10.8 dB less noise. That is why CW operators can hear signals in noise that would be completely unreadable on SSB with the same transmit power.
Worked Example: Noise Power at Room Temperature
Solution:
P = kTB
P = (1.38 × 10−23) × 290 × 2400
P = (1.38 × 10−23) × 696,000
P = 9.60 × 10−18 watts
P = 9.60 × 10−15 milliwatts
Converting to dBm: P(dBm) = 10 × log10(9.60 × 10−15)
P = 10 × (−14.02)
P = −140.2 dBm
Result: The noise floor in a 2.4 kHz SSB bandwidth at room temperature (with a perfectly noiseless receiver) is approximately −140 dBm. Any signal weaker than this cannot be received, even with a perfect receiver.
Noise Voltage and Noise Current
The formula P = kTB gives the available noise power. For circuit design purposes, it is often more useful to think in terms of the equivalent noise voltage or noise current produced by a resistor. The Thevenin equivalent circuit of a noisy resistor is a noiseless resistor of the same value in series with a noise voltage source. The Norton equivalent is a noiseless resistor in parallel with a noise current source.
Noise Current (RMS): In = √(4kTB/R)
Where R is the resistance in ohms.
Notice that unlike the noise power (which is independent of R), the noise voltage increases with the square root of resistance, and the noise current decreases with the square root of resistance. A high-resistance source generates more noise voltage but less noise current than a low-resistance source of the same temperature. The available noise power remains P = kTB regardless.
Worked Example: Noise Voltage of an Antenna
Solution:
Vn = √(4kTBR)
Vn = √(4 × 1.38 × 10−23 × 290 × 2400 × 50)
Vn = √(4 × 9.60 × 10−18 × 50)
Vn = √(1.92 × 10−15)
Vn = 4.38 × 10−8 V
Vn = 43.8 nanovolts (nV) RMS
Result: About 44 nanovolts RMS of random noise voltage appears across the antenna terminals in a 2.4 kHz bandwidth. Any received signal must produce more than this to be detectable. This is why a good LNA or preamplifier connected directly to the antenna makes such a dramatic difference on HF weak-signal work.
Noise Temperature
Noise temperature is an alternative way to express the noise contribution of a component or system. Instead of specifying noise in dB or in noise power, you express it as the temperature (in kelvins) of a resistor that would produce the same amount of noise power.
The concept is particularly useful in two contexts. First, real antennas do not simply present a resistive source impedance with a pure thermal noise of 290 K. An antenna pointed at the sky picks up background radiation from space, galactic noise, and any local noise sources. The effective noise temperature of an antenna might be anywhere from a few kelvins (a highly directive dish pointing at cold sky) to tens of thousands of kelvins (an antenna near power lines). Second, noise temperature allows the noise contribution of an amplifier to be expressed independently of any reference temperature, making it easier to apply the Friis formula for cascaded stages.
The relationship between noise factor F (a dimensionless ratio, covered in the next lesson) and noise temperature Te is:
where T0 = 290 K (the standard reference temperature)
and F = SNRin / SNRout (the noise factor of the amplifier)
A perfectly noiseless amplifier has F = 1 and Te = 0 K. A preamplifier with a noise figure of 1 dB has F = 1.259, giving Te = (1.259 − 1) × 290 = 75 K. This means it adds noise equivalent to a 75 K resistor at its input — far less than room temperature, which is why 1 dB NF preamplifiers are considered very good for HF weak-signal work.
The Noise Spectrum: White Noise
One of the most useful properties of thermal noise is that its power spectral density — the noise power per unit bandwidth — is essentially constant across all frequencies from DC to several hundred gigahertz. This flat spectrum is the defining characteristic of what engineers call white noise, by analogy with white light that contains all visible wavelengths equally.
Why is thermal noise white? Because the random collisions between electrons and the crystal lattice are extremely short events — much shorter than the period of any radio frequency. A very short, sharp impulse in the time domain corresponds to a very flat, broad spectrum in the frequency domain. The collision events are so brief that the noise they generate is flat across all frequencies that matter for radio communications, from VLF to millimeter-wave.
The practical consequence is that the P = kTB formula can be applied to any bandwidth, anywhere in the frequency spectrum, and gives the correct result. Whether your receiver's bandwidth is centered at 3.5 MHz or 144 MHz, the noise power in a 2.4 kHz bandwidth at 290 K is the same: approximately −140 dBm.
This flatness does eventually break down at very high frequencies (above about 10 THz) where quantum mechanical effects become important. But for all practical radio work, thermal noise is perfectly white.
The −174 dBm/Hz Reference
The most important single number in receiver noise analysis is −174 dBm/Hz, the thermal noise power density at room temperature (290 K). This comes directly from the P = kTB formula with T = 290 K and B = 1 Hz:
P0(dBm) = 10 × log10(4.00 × 10−18) = −173.98 ≈ −174 dBm/Hz
This is the starting point for all noise floor calculations. To find the noise floor in any bandwidth B (in Hz), simply add 10 × log10(B) to −174 dBm:
For common amateur radio bandwidths:
| Bandwidth | Mode | 10·log₁₀(BW) | Noise Floor (perfect receiver) |
|---|---|---|---|
| 200 Hz | CW narrow | +23 dB | −151 dBm |
| 500 Hz | CW wide | +27 dB | −147 dBm |
| 2400 Hz | SSB | +33.8 dB | −140 dBm |
| 8000 Hz | AM audio | +39 dB | −135 dBm |
| 15 kHz | FM wide | +41.8 dB | −132 dBm |
| 3.84 MHz | LTE 5 MHz channel | +65.8 dB | −108 dBm |
These are the noise floors of a perfectly noiseless receiver. Every real receiver adds additional noise on top of this, characterized by its noise figure (covered in the next lesson). The actual noise floor is always worse than these values by an amount equal to the noise figure in dB.
Thermal Noise in Your Station
Understanding thermal noise has direct practical consequences for every aspect of your receiving setup.
Coaxial Cable Is a Noise Source
Any lossy component — including coaxial feedline — generates thermal noise. A length of coaxial cable with 3 dB of loss at room temperature introduces 3 dB of noise in addition to losing half the signal power. The signal is halved, the noise floor stays approximately the same (because the cable generates its own thermal noise to replace what it absorbs), and the result is a 3 dB degradation in sensitivity. This is why minimizing feedline loss is important for receiving, not just transmitting.
The Low-Noise Amplifier (LNA) at the Antenna
Placing a low-noise amplifier at the antenna, before any feedline loss, dramatically improves receiver sensitivity on VHF and UHF. If the LNA has 20 dB of gain and 1 dB noise figure, it amplifies the signal by a factor of 100 before any feedline attenuation occurs. The subsequent noise contribution of the feedline is divided by the LNA gain of 100 and becomes insignificant. This is the fundamental reason why tower-mounted or mast-mounted preamplifiers with short feedlines to the LNA are used on EME (Earth-Moon-Earth) and other weak-signal VHF/UHF work.
Temperature and Sensitivity
Most amateur radio work at HF takes place in an environment where the external noise received by the antenna (galactic noise, man-made noise, atmospheric noise) is much greater than the receiver's internal thermal noise floor. In this situation, improving the receiver's noise figure below about 10 dB makes little practical difference — you are limited by the external noise, not the receiver's internal noise. This is not true at VHF and above, where the external noise environment is much quieter and receiver noise figure becomes the dominant factor in sensitivity.
Cooling for Extreme Sensitivity
Some specialized amateur applications — EME, meteor scatter, and moonbounce — use cryogenically cooled preamplifiers to achieve noise temperatures below 50 K. By cooling the amplifier to near liquid helium temperature (4 K), the thermal noise is reduced by a factor of 290/4 = 72.5, or about 18.6 dB, compared to room temperature operation. For most HF work, this level of effort is not warranted, but it demonstrates that thermal noise is a physical phenomenon that can be reduced by reducing temperature.
⚖ Experiment: Observe Thermal Noise with an SDR
This experiment makes thermal noise visible on a spectrum display, demonstrating the flat noise floor and how bandwidth changes the measured noise power.
- RTL-SDR dongle or similar SDR receiver
- SDR# or GNU Radio or similar SDR software
- A 50 Ω SMA terminator (dummy load, available for under $2)
- A short SMA-to-SMA cable or direct connection
- Connect the 50 Ω terminator directly to the SDR input. This replaces the antenna with a resistor at room temperature — pure thermal noise with no external signals.
- Open your SDR software and tune to 100 MHz. Set the gain to maximum. Set the bandwidth to 2 MHz.
- Observe the spectrum. You will see a flat, noisy baseline — this is the combination of the SDR's own internal noise and the thermal noise from the 50 Ω terminator.
- Note the approximate noise level in dBm. Write it down.
- Now change the SDR sample rate (bandwidth) from 2 MHz to 250 kHz. What happens to the displayed noise level?
- The noise level should drop by approximately 10 × log10(2,000,000 / 250,000) = 9 dB. This directly demonstrates that noise power is proportional to bandwidth.
- Now connect a real antenna instead of the terminator and compare. You will see the noise floor rise as the antenna picks up thermal and man-made noise from the environment.
The 50 Ω terminator produces a flat noise floor with no signal peaks. Reducing bandwidth reduces the displayed noise level by exactly the amount the formula predicts. This confirms that noise power is proportional to bandwidth (P = kTB) and that the noise is spectrally flat (white noise). The difference between the terminator noise floor and the antenna noise floor shows you the external noise arriving from the environment.
Frequently Asked Questions
Why can't we filter out thermal noise the way we filter out interference?
Interference has a specific frequency, so a filter can remove it without affecting the desired signal. Thermal noise is spectrally white — it has equal power at every frequency. A filter does reduce thermal noise, but it reduces the signal by exactly the same fraction. The only way to improve the signal-to-noise ratio against thermal noise is to either increase the signal (more transmit power, better antenna, lower feedline loss) or reduce the bandwidth — which you can only do if the signal itself is narrowband enough to fit in the narrower bandwidth.
Does the noise power really not depend on the resistance value?
Correct — the available noise power P = kTB is independent of resistance. This can seem counterintuitive because a higher resistance produces a higher noise voltage (Vn = √(4kTBR)). However, when you connect that higher-resistance source to a load, the load must be matched to the source (same resistance) to extract maximum power. A high-resistance source needs a high-resistance load, and the current through that load is correspondingly smaller. The extra voltage and the smaller current cancel out, leaving the same available power regardless of resistance value. This is required by thermodynamics.
Is the noise floor of −174 dBm/Hz an absolute limit that cannot be beaten?
−174 dBm/Hz is the thermal noise floor at 290 K (approximately room temperature). It can be beaten by cooling the receiving system to a lower temperature. At 29 K (one-tenth of 290 K), the thermal noise floor is −184 dBm/Hz. At liquid helium temperature (4 K), it is approximately −197 dBm/Hz. These very low noise temperatures are used in specialized weak-signal work such as deep-space communication, radio astronomy, and high-performance EME stations. For practical amateur radio, treating −174 dBm/Hz as a floor is appropriate.
Why does my receiver still pick up signals weaker than the noise floor?
The noise floor is the level below which a signal cannot be detected using simple amplitude measurement in a single bandwidth. Signals below the noise floor can still be recovered using techniques that average or correlate over time. WSPR, JT65, and other digital weak-signal modes take many seconds or minutes of data and use sophisticated signal processing to detect signals 20 to 30 dB below the instantaneous noise floor. These modes exploit the fact that the signal is coherent (consistent, predictable) while the noise is random, so averaging over time pulls the signal up relative to the noise.
Test Your Knowledge
Answer the questions below to check your understanding. Every answer can be found in the lesson above.