# Why is a lower Noise Figure considered better than a higher Noise Figure?

I'm trying to understand why a smaller Noise Figure is supposed to be better. The conventional definition for N.F. is the ratio of SNR(in) to SNR(out). This can further be broke down as follows:

\begin{align} N.F. = \frac{SNR_{in}}{SNR_{out}} = \frac{\frac{P_{sig,in}}{P_{noise,in}}}{\frac{P_{sig,out}}{P_{noise,out}}} = \frac{P_{sig,in}}{P_{sig,out}}\cdot \frac{P_{noise,out}}{P_{noise,in}} \end{align}

If we want a low noise figure, that means we need a low SNR(in) and a high SNR(out). So does this mean our final objective is to always try to make our SNR(out) as high as we can so that our signal is amplified much more than our noise?

• yes, you want signal, you don't care about the noise. Remember: what you're trying to do is extract information that was sent somewhere else from your output signal, and noise contains no clue on that original information – Marcus Müller Mar 21 '17 at 21:15
• The SNR of the input is always higher than the output as the gain of both input signal and noise is the same plus added noise of the amplifier. So a low noise factor adds as little noise as possible to get as close to ratio=1 as possible. Noise Figure is the 10*log version of the linear Noise Factor. SNR is then increased by matching filter bandwidth to the signal bandwidth and thus rejecting noise. – Tony Stewart Sunnyskyguy EE75 Mar 21 '17 at 21:48
• Your thinking is backwards when you say "we need low SNR(in)...". You never need low SNR(in); you have to get by with a given (low) SNR(in) and that is the reason why you need low NF to reach a given (minimum) SNR(out). – Curd Mar 22 '17 at 0:09

o does this mean our final objective is to always try to make our SNR(out) as high as we can

Yes, we want the output SNR as high as possible, because that means the best chance of recovering the message signal accurately.

so that our signal is amplified much more than our noise?

This is not possible.

The input noise will be amplified just as much as the signal.

So the overall effect is the output SNR is lower than the input SNR. (This is why the NF is positive when expressed in dB)

But we want the SNR to be reduced by as little as possible.

Noise Figure is a measure of how much the Signal-to-Noise ratio has degraded after going through a receiver. The following picture illustrates this effect:

Source of the image: this site

Because we can always amplify almost as much as we need, the limiting factor isn't having an extremely weak signal level, but the presence of noise when we receive the signal - plus the noise added by the system.

A low Noise Figure is key to have the best possible sensitivity, that is, to keep as low as possible the signal power needed at the input of the receiver to successfully demodulate the signal.

This enhanced sensitivity relaxes the required $SNR_{in}$, which can, in turn, extend the effective range of our communication link.

Example: if we can reduce NF by 3 dB, then we will need 3 dB less of signal power at the input of the receiver in order to have the same $SNR_{out}$, and our range will increase a hefty +40%.

• Thanks for your insightful answer. Can the Noise Figure ever be lower than 0 dB i.e. lower than 1? – ragzputin Mar 24 '17 at 4:47
• No, it can't. That would mean the internal noise of the receiver can somehow cancel out the external noise, which is impossible. – Enric Blanco Mar 24 '17 at 8:21

Why is a lower Noise Figure considered better than a higher Noise Figure?

that's not universally true. there are applications where noises are desired. in those cases, higher noise figures are helpful.

in most applications, you want to process a signal, not the noise so a lower noise figure is better.

In a channel-rich environment (WiFI, cellphones), you need to consider SPFR --- the spurious free dynamic range --- because a lower noise transistor may or may not have acceptable IP3 performance (important in channelized systems). And IP2 cannot be ignored.

Summary: having cross products fall onto top of your signal, or fall so close you cannot easily reject the cross products with filter (Intermediate Frequency), has the same (or worse) impact as higher random noise. Cross products may be deterministic, and thus really degrade the dataeye.

• I don't see how this answers the question that was asked. – The Photon Apr 19 '17 at 15:51