Measuring noise: The Y-method

Fig.1: Measurement setup for Y-method

Fig.2: Input referred noise voltage vs. Y factor

The Y method of measuring the input referred noise level of an amplifier (Device Under Test, DUT) consists of alternately connecting two different noise sources with known output levels, measuring the change of output noise, and deducing from that the noise of the DUT proper [1]. This description assumes a matched system: source resistance equals amplifier input resistance.

The noise sources are actually 50Ω coaxial termination resistors. The sources' output levels are set by keeping them at two well defined temperatures. For example, the 'hot' noise source may be at room temperature (296K) and the 'cold' source immersed in liquid N₂ at 77K (Fig.1). Either can be connected to the amplifier input using a high-quality coaxial relay.

In this setup, a hypothetical perfect amplifier, contributing no noise of its own, would have a Y-factor of 296/77, corresponding to 10*log₁₀(296/77)=5.85dB. Noise contributed by the DUT will tend to mask the source noise and will thus reduce this value. For a good low-noise amplifier, the Y-factor will be somewhere from 2 to 5 dB (Fig.2).

Finding the amplifier noise contribution

Let P_a be the input noise power density of the amplifier proper, P_h the noise power density of the 'hot' source, and P_c that of the 'cold' source. The two equations below (1) then give the total equivalent noise power density at the amplifier input with the hot, respectively, cold source connected.

(1)

It's not easy to accurately measure absolute noise power levels. However, measuring the ratio of two such powers is rather simple. It requires neither an accurate absolute calibration of the measuring instrument, nor exact knowledge of the DUT gain. A spectrum analyser can easily detect the change in signal level due to a switch from the hot to the cold source, provided the DUT gain is high enough to make the spectrum analyser's noise contribution negligible. Note that the noise figure of spectrum analysers is often in the 25dB ballpark, requiring at least 30dB of DUT gain to fulfil this condition.

So let's define the Y-factor as the ratio of the power values defined in (1).

(2)

Solving for P_a yields:

(3)

Note that exactly the same reasoning holds for noise temperatures instead of noise powers, because the available noise power density from a resistor is simply proportional to its absolute temperature (in kelvin).

(4)

In which k is Boltzmann's constant (k=1.38⋅10^-23 J/K). Finally, the noise voltage can be found using equation (5):

(5)

Note that connections in this test setup are critical. Use only semirigid coax of excellent quality, and keep the connections short. Any loss in the connections will increase the apparent noise level of the cold source and bias the results to make the amplifier look worse than it really is.

References

1. A.H. Haus et al, "Description of the noise performance of amplifiers and receiving systems", Proc. IEEE, Vol.51, March 1963, pp436-442