Section 5.3: Noise and Sensitivity #

Tune to an empty spot on the band, and you still hear a soft hiss. Part of that noise comes in through the antenna, and the receiver itself generates the rest. A weak station is readable only if it stands out above that background. More gain lifts the hiss along with the signal, so judging a receiver means measuring its noise.

Power in dBm #

Decibels compare two powers, using $10\log_{10}(P_2/P_1)$ . Give the ratio a fixed reference, and the same scale measures actual power levels. For dBm, that reference is 1 milliwatt: 0 dBm equals 1 mW. Thus $-10$ dBm is 0.1 mW and $-20$ dBm is 0.01 mW. Every 30 dB down divides power by another 1,000: $-30$ dBm is 1 microwatt (µW), $-60$ dBm is 1 nanowatt, and $-90$ dBm is 1 picowatt (pW), a trillionth of a watt.

Noise in Each Hertz #

Even a resistor at room temperature generates thermal noise. Its power depends only on temperature and bandwidth, so it is usually quoted for a 1 Hz bandwidth. Because the noise spreads evenly across the band, its power grows in proportion to bandwidth. Widening the filter from 50 Hz to 1,000 Hz admits $1{,}000/50=20$ times as much noise. In decibels, that’s $10\log_{10}(20)\approx13$ dB. Without a calculator: 10 times is 10 dB and 2 times is 3 dB, so 20 times is 13 dB.

Key Information:

• A receiver noise floor of $-174$ dBm represents the theoretical noise in a 1 Hz bandwidth at the input of a perfect receiver at room temperature.
• Increasing a receiver’s bandwidth from 50 Hz to 1,000 Hz increases the receiver’s noise floor by 13 dB.

What the Receiver Adds #

A real receiver adds noise of its own. With no signal present, the noise it produces at its output is the amplified thermal noise plus that addition. A perfect receiver would produce only the thermal part, the theoretical minimum. Both amplify a signal equally, so comparing their noise shows how much the real receiver worsens the signal-to-noise ratio. A receiver that adds as much noise as the thermal minimum produces twice the minimum: a ratio of 2, or 3 dB. The comparison ignores whatever atmospheric noise reaches the antenna.

Key Information: The noise figure of a receiver is the ratio in dB of the noise generated by the receiver to the theoretical minimum noise.

At room temperature, a useful estimate of a real receiver’s noise floor is

where bandwidth $B$ is in hertz and noise figure $NF$ is in dB. In a 1,000 Hz bandwidth with a 3 dB noise figure, the estimate is $-174+30+3=-141$ dBm.

A low-noise preamplifier can lower the overall noise figure. It adds little noise of its own, and its gain makes the noise of later stages less important. This matters most where outside noise is low, as it often is at VHF and UHF. Mounted at the antenna, a preamplifier also keeps feed-line loss from adding directly to the noise figure.

Because noise figure is a ratio, it uses dB, never dBm. Zero would mean no added noise, and a negative value would mean the amplifier removed noise, which it can’t do.

Key Information: A noise figure of 0.5 dB is typical of a low-noise UHF preamplifier.

Finding the Smallest Signal #

The $-141$ dBm estimate also predicts sensitivity, often quoted as the smallest signal a receiver can distinguish under stated test conditions. One common test finds the signal that raises the receiver’s output 3 dB above its noise alone. That signal’s power equals the noise power in the test bandwidth, so the receiver above could just distinguish about $-141$ dBm through a 1 kHz filter. Filter width matters, so compare only figures measured in the same bandwidth.

A level of $-100$ dBm is 10 dB below $-90$ dBm (1 pW), so it is one-tenth of a picowatt: 0.1 pW.

Key Information:

• The MDS of a receiver represents the minimum discernible signal.
• A receiver minimum discernible signal of $-100$ dBm represents 0.1 picowatts.

A direct-sampling receiver has one more limit: the size of its ADC’s steps. The reference voltage sets the full-scale range, and the sample width in bits divides that range into codes. With no noise at all, a signal smaller than one step might never change the output code. In practice, noise or added dither moves the input across step boundaries, so processing can find signals smaller than one step.

Key Information: In the absence of atmospheric or thermal noise, reference voltage level and sample width in bits set the minimum detectable signal level for a direct-sampling software defined receiver.