## Review of noise

Let’s review of the concepts of noise figure, equivalent noise temperature and measurement.

Firstly let’s consider the nature of noise. The noise we are discussing is dominated by thermal noise, the noise due to random thermal agitation of charge carriers in conductors. Johnson noise (as it is known) has a uniform spectral power density, ie a uniform power/bandwidth. The maximum thermal noise power density available from a resistor at temperature T is given by \(NPD=k_B T\) where Boltzmann’s constant k_{B}=1.38064852e-23 (and of course the load must be matched to obtain that maximum noise power density). Temperature is absolute temperature, it is measured in Kelvins and 0°C≅273K.

## Noise Figure

Noise Figure NF by definition is the reduction in S/N ratio (in dB) across a system component. So, we can write \(NF=10 log \frac{S_{in}}{N_{in}}- 10 log \frac{S_{out}}{N_{out}}\).

### Equivalent noise temperature

One of the many methods of characterising the internal noise contribution of an amplifier is to treat it as noiseless and derive an equivalent temperature of a matched input resistor that delivers equivalent noise, this temperature is known as the equivalent noise temperature Te of the amplifier.

So for example, if we were to place a 50Ω resistor on the input of a nominally 50Ω input amplifier, and raised its temperature from 0K to the point T where the noise output power of the amplifier doubled, would could infer that the internal noise of the amplifier could be represented by an input resistor at temperature T. Fine in concept, but not very practical.

### Y factor method

Applying a little maths, we do have a practical measurement method which is known as the Y factor method. It involves measuring the ratio of noise power output (Y) for two different source resistor temperatures, Tc and Th. We can say that \(NF=10 log \frac{(\frac{T_h}{290}-1)-Y(\frac{T_c}{290}-1)}{Y-1}\).

AN 57-1 contains a detailed mathematical explanation / proof of the Y factor method.

We can buy a noise source off the shelf, they come in a range of hot and cold temperatures. For example, one with specified Excess Noise Ratio (a common method of specifying them) has Th=9461K and Tc=290K. If we measured a DUT and observed that Y=3 (4.77dB) we could calculate that NF=12dB. Continue reading Noise figure of active loop amplifiers – some thoughts