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Cascaded Noise Figure & Noise Temperature

Noise figure (NF) is the increase in noise power of a device from the input to the output that is greater than the signal gain. In effect, it is the amount of decrease of the signal-to-noise ratio. Like gain, noise figure can be expressed either as a ratio or in decibels (dB). Note: NF is not a power level, so it never has units of dBm.

As the following equation shows, cascaded noise figure is affected most profoundly by the noise figure of components closest to the input of the system as long as some positive gain exists in the cascade. If only loss exists in the cascade, then the cascaded noise figure equals the magnitude of the total loss.

 

Cascading Noise Figure Values in a Chain of Components

Example cascaded system - RF Cafe

Click here to view an example of a cascaded system.
Calculating the cascaded values for noise figure (NF) for the system budget requires the following operation based upon ratios for gain and noise figure (do not use decibel values). The standard format for indicating decibel values is to use upper case letters, i.e., G and NF for units of dB; the standard format for indicating ratio values is to use lower case letters, i.e., g and nf.

Conversions:   nf = 10NF/10  ↔  NF (dB) = 10 * log10 (nf)

where nf is a unitless ratio and NF has units of dB

Cascaded components for calculating IP2 - RF Cafe

A Typical Chain of Cascaded Components

 Cascading receiver transmitter stages two at a time - RF Cafe

Combining 2 Stages at a Time for Calculations

See cascade calculations for NF, IP2, IP3, and P1dB.

This equation gives the method for calculating cascaded NF (nf) values based on the nf and gain of each stage. When using the formula in a software program or in a spreadsheet, it is more convenient and efficient to calculate each successive cascaded stage with the one preceding it using the following format, per the drawing (above-right).

Cascaded noise figure (NF) formula - RF Cafe     Cascaded receiver transmitter stage notation - RF Cafe

- RF Cafe

Click here to see Agilent's App Note 1303 on using a spectrum analyzer to measure noise figure.

 

Conversion Between Noise Figure and Noise Temperature

Noise Temperature (K) = Noise figure to noise temperature conversion equation formula - RF Cafe

Noise Figure (dB) = Noise temperature to noise figure conversion equation - RF Cafe

These equations assume a room temperature reference (290 K). If applicable, use whatever your reference temperature is in place of the 290K shown.

Cascaded Noise Temperature Calculation

Cascaded noise temperature equation - RF Cafe

 

The following table lists a few conversions. See the Noise Power Calculator online calculator for calculating other values.

NF(dB) TN (°K)   NF(dB) TN (°K)
0.1 7 2.1 180
0.2 14 2.2 191
0.3 21 2.3 202
0.4 28 2.4 214
0.5 35 2.5 226
0.6 43 2.6 238
0.7 51 2.7 250
0.8 59 2.8 263
0.9 67 2.9 275
1.0 75 3.0 289
1.1 84 3.1 302
1.2 92 3.2 316
1.3 101 3.3 330
1.4 110 3.4 344
1.5 120 3.5 359
1.6 129 3.6 374
1.7 139 3.7 390
1.8 149 3.8 406
1.9 159 3.9 422
2.0 170 4.0 438
Noise figure equation - RF Cafe

Related Pages on RF Cafe

- Noise Figure <--> Noise Temperature Calculator

- Noise Power and Voltage

- Cascaded Noise Figure

- Noise Figure Meters & Noise Generators

- Noise Sources

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