## Relationship between Teq and Noise Figure

In the last part, the meaning of the equivalent noise temperature of an amplifier was given.

Whilst you will find that working in Teq has advantages for this analysis, amplifier specifications may not give Teq, but may give Noise Figure.

Teq can be calculated from Noise figure.

**Teq=(10^(NF/10)-1)*290 K** where:

NF is Noise Figure in dB

Be rearranging the terms, NF can be calculated from Teq.

**NF=10*log(1+Teq/290)**

Note that since Teq implies a Noise Power Density (W/Hz) of noise, Teq from two sources can simply be added (whereas Noise Figures cannot).

The Noise Figure of an attenuator is simply equal to it attenuation in dB (proof left as an exercise for the reader).

## A cascade of two stages

If two amplifiers of known PowerGain (PowerOut/PowerIn) and Teq are cascaded, a simple single stage equivalent can be calculated.

The PowerGain of the cascade is simply the PowerGain of stage 1 multiplied by the PowerGain of stage 2.

**PowerGain=PowerGain1*PowerGain2**

The second stage can be replaced by a noiseless second stage by referring its Teq to the input of the first stage by dividing it by the PowerGain of the first stage.

**Teq=Teq1+Teq2/PowerGain1**

You will see some pretty complicated formulas for multiple stages, but remember that any pair of adjacent stages can be converted to a single equivalent… and taking hamburger size bites lets you eat the elephant.

Remember that the PowerGain of an attenuator or any purely passive network or device (like a transmission line) is less than 1, a 3dB attenuator has a PowerGain of 0.5.

A simple cascade could be a feed line and a receiver.

Lets work a simple example. What is Teq of a feed line with 1dB of loss followed by a receiver with NF=6dB.

First step, convert the receiver NF to Teq2. Teq2=865K

Now calculate the PowerGain of the feed line. PowerGain1=10^(-1/10)=0.794.

Now calculate NF of the feed line as 1dB (equal to its attenuation in dB), and Teq1 as 75.1K.

Calculate Teq as Teq1+Teq2/PowerGain1=75.1+865/0.794=1165K.

## More complex networks

More complex networks are analysed by applying these simple rules consistently and reducing the multi stage networks to a single stage equivalent.

## References

- Terman 1955. Electronic and Radio Engineering: McGraw-Hill New York.

Designing high performance VHF/UHF receive systems – Part 4

More installments to come…