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Desired Signal. Thermal Noise. Contained within bandwidth “B”. Ideal Components. Equipment Noise Characterization. N TH (W) = kTB. P s (W). G 1. G N. B. Noise Ratio. P S1 (mW) + N TH (mW). G 1. G 1 (P S1 (mW) + N TH (mW) + N 1 (mW)). + +. N 1 (mW). Definition:

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Equipment noise characterization

Desired Signal

Thermal Noise

Contained within bandwidth “B”

Ideal Components

Equipment Noise Characterization

NTH(W) = kTB





Noise ratio
Noise Ratio

PS1(mW) + NTH(mW)


G1(PS1(mW) + NTH(mW) + N1(mW))





A measure of how much a system degrades SNR.

If NR is given, then we can compute

Ratio of noise added to thermal noise

T0is ALWAYS 290 K for Noise Ratio Computations

Equipment noise characterization1

Practical Components

Noise spectral density out of any device can never be less than kT.

Desired Signal

Thermal Noise

Equipment Noise Characterization

NTH(dBm) = 10 log10(kT0B) + 30 dB

Because kTB is in Watts!







Shot noise contribution of first amp.

We model the noise contribution as being added at the amp input, and amplified by the amp’s gain.


Since noise power is being added, we must use mW, NOT dBm.

Cascade noise ratio
Cascade Noise Ratio

G1 , NR1

G2 , NR2







G1(PS1 + kT0B+ N1)

G2(G1(PS1 + kT0B + N1)+N2)

Which can be Generalized to N Stages: Friis’ Formula

Noise ratio with preceding insertion loss
Noise Ratio with Preceding Insertion Loss


G1 , NR1





G1(a1 PS1 + kT0B + N1)

a1PS1 + kT0B

Since the effects of preceding loss are multiplicative w.r.t. both noise ratio and gain, it makes sense to deal with losses using dB units . . .

Noise figure db
Noise Figure (dB)

Noise Figure, NF(dB), is Noise Ratio expressed in dB:

Noise characteristics for devices are usually published/specified by Noise Figure (dB).

When a device with specified Gain and Noise Figure (G, NF; both in dB) is preceded by one or more passive devices with specified total insertion loss (LI in dB), they can be combined into a single stage having

GT (dB) = G (dB) – LI (dB) and NFT(dB) = NF (dB) + LI (dB)




System noise figure
System Noise Figure

The overall noise figure for a system containing both active gain stages and passive loss stages is computed as follows:

  • Combine all passive losses with their succeeding gain stages using

    • GT (dB) = G (dB) – LI (dB) and NFT(dB) = NF (dB) + LI (dB)

  • 2. The sum of the resulting gains (in dB) is total system gain, GSYS(dB)

  • Convert all resulting gains and noise figures to their ratio metric (non-dB) values

  • Apply Friis’ formula using the resulting Gains and Noise Ratios to obtain overall Noise Ratio for the system.

  • Convert overall Noise Ratio back into dB’s : NFSYS(dB)

System noise temperature
System Noise Temperature

Concepts of Noise Figure and Noise Ratio were developed when virtually all communications system were terrestrially based, hence the implicit use of T0 = 290 K (the mean blackbody temperature of the earth). No one ever aimed an antenna up at the sky and expected to receive anything meaningful.

With the advent of space communication and radio astronomy, an equivalent concept of noise temperature was developed which seemed to make more sense in that context:

If we subtract one from each side of Friis’ formula and then multiply both sides by T0, we have:

Substituting the definition of equivalent noise temperature from above,


Consider Friis’ Formula:

The Noise Ratio contributions of all but the first stage are reduced by the gains of preceding stages.

The gain of the first stage should be high, to reduce the contributions of succeeding stages.

The Noise Ratio of the first stage should be as low as possible, since it contributes directly to the system noise ratio.

Any passive losses prior to the first gain stage should be minimized, as it detracts from 1 and 2 above.


G1 = 15 dB

NF1 = 6 dB

G2 = 10 dB

NF2 = 12 dB

G3 = 25 dB

NF3 = 16 dB

G4 = 18 dB

NF4 = 12 dB

L1 = 2 dB

L2 = 5 dB

G2 = 10 dB

NF2 = 12 dB

G3 = 20 dB

NF3 = 21 dB

G4 = 18 dB

NF4 = 12 dB

G1 = 13 dB

NF1 = 8 dB

G2 = 10

NR2 = 16

G3 = 100

NR3 = 128

G4 = 64

NR4 = 16

G1 = 20

NR1 = 6.4

Step 2: Convert Gains and Noise Figures ratio-metric Forms

Step 3: Combine Gains and Noise Ratios Using Friis’ Formula

Step 4: Convert overall Gain and Noise Ratio Back to dB

Step 1: Combine all passive losses with succeeding gain stages.