Relation between noise level and noise figure NF

For example, the input signal is amplified 20dB whe n it passes an amplifier of 20dB gain. This is understandable.
How about a noise ?  This cannot be understood well.

That is, the appearance of signal is same if a noise is also amplified 20dB when a signal is amplified 20dB?

Figure: How the signal looks

It’s wrong. Let’s consider the definition of noise figure NF.

NF is a ratio of input S/N to output S/N.
NF(dB)=20log[(Si/Ni)/(So/No)]
  • Si,So:signal level of input and output
  • Ni,No:noise level of input and output

<Meaning of NF>

  1. A ratio of input S/N to output S/N.
  2. Output S/N is reduced only NF(dB) from input S/N.
  3. Output noise No = Ni + G + NF …… G,NF and Ni should be dB.

Let’s explain concretely.

  • Input signal level Si=-100dBm
  • Input noise level Ni=-150dBm
  • Amplifier gain =20dB
  • NF of amplifier=3.5dB

With the above conditions, the output will be as sh own in the figure below because of <Meaning of NF>3mentioned above.

Figure: The meaning of NF $$ \begin{cases} \text{Input}~S/N=-100-(-150)=50dB\\ \text{Output}~S/N=-80-(-126.5)=46.5dB \end{cases} $$ $$ \begin{align} ∴NF&=(\text{Input}~S/N~50dB)-(\text^{Output}~S/N~46.5dB)\\ &=3.5dB ← \text{Indeed, <Meaning of NF>2 is established.} \end{align} $$

Output S/N is reduced only NF(dB) from input S/N.This’s an important point.

Then, the signal and noise at input and output shall be observed with a spectrum analyzer.
The noise level of a spectrum analyzer assumes -110dBm.

  • Relation between noise level and noise figure NF
  • Although the input S/N is 50dB, S/N gets worese to 10dB when observed with a spectrum analyzer.
    Only 10dB from noise level is visible.
  • Relation between noise level and noise figure NF
  • Although the output S/N is 46.5dB, S/N gets worse to 30dB when observed with a spectrum analyzer.
    However, it’s 20dB better than input S/N.

When observed with a spectrum analyzer, the appearance of spectrum is related greatly to that noise level.

Case Study:

To verify the effect of the pre-amplifier, following connection of the signal generator, the pre-amplifier MAP301/302 and signal analyzer MSA538 is established. We made the measurement of the signal to noise ration and gain for each signal path. The setting of equipments is as follows.

  • Signal Generator
    • Frequency:100MHz
    • Output Level:-92dBm
  • Signal Analyzer
    • Center Frequency:100MHz
    • Span:20MHz
    • Reference Level:-30dBm
    • RBW : 100kHz
    • VBW : 30kHz
Relation between noise level and noise figure NF

The measurement results are shown in bellow.

Connection Gain [dB] S/N Ratio [dB]
No Amplifier 0 10
MAP301 52 27
MAP302 21 21

No Amplifier

No Amplifier

MAP301

MAP301

MAP302

MAP302

It is confirmed that we can improve the S/N ratio by using appropriate pre-amplifier.

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