#### What is in this article?:

- Measure Noise Without A Calibrated Source
- Making a noise-figure measurement
- Determine the change in ENR at a DUT’s input

It is possible to measure the noise figure of a component or DUT without a calibrated noise source by using a source capable of generated two different input noise levels to the DUT.

## Making a noise-figure measurement

Spectrum analyzers usually have a large noise figure in the 20-to-30-dB range or, for more sophisticated instruments with an internal preamplifier, the noise figure may be reduced to the 10-to-15-dB range. The typical procedure for making a noise-figure measurement is to first measure the noise figure of the spectrum analyzer by placing the noise source directly on the analyzer’s input port. A measurement is then made with the DUT placed between the noise source and the input to the spectrum analyzer, as shown in** Fig. 2**. Once the two measurements have been made, the noise figure of the device is calculated from the following equations:

Noise factor of spectrum analyzer = ENR/(Y_{SA} - 1) = NFac_{SA} (3)

Total noise factor of the DUT plus the spectrum analyzer:

NFac_{TOTAL} = ENR/(Y_{TOTAL} - 1) (4)

Noise factor of the DUT = NFac_{TOTAL} - (NFac_{SA} - 1)/G_{DUT} (5)

where G_{DUT} is the gain of the DUT.

The novel noise-measurement approach about to be described follows the procedure for first characterizing the noise figure of a spectrum analyzer, and then evaluating the noise of a DUT in cascade with the analyzer. One important difference is that results with the new method are obtained by means of the derivative of the Y-factor. Measurements are independent of the absolute value of the input excess noise level to the DUT and eliminate the need for a calibrated noise source.

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The new method begins with the standard equation for the noise factor of a DUT, given the ENR of the noise source and a Y-factor measurement as detailed in Eq. 6:

NFac = ENR/(Y - 1) (6)

Rearranging terms results in Eq. 7:

Y = ENR/NFac + 1 (7)

Taking the derivative of each side with respect to the ENR yields Eq. 8:

dY/dENR = 1/NFac (8)

This results in Eq. 9:

NFac = 1/(dY/dENR) (9)

What this shows is that the noise factor can be determined without knowing the absolute ENR; only the difference in ENR, which results in a difference of the Y-factor measurement, is needed for the calculation. This new noise factor approach consists of making two Y-factor measurements at two different noise power levels at the input of the DUT. These two Y-factor values, along with the corresponding source noise power values, provide the information needed to construct the ΔY and ΔENR values. These will produce the slope or dY/dENR, and in turn produce the noise factor result according to Eq. 9.

The method used to vary the ENR involved using an arbitrary source of noise power (e.g., a high-gain amplifier) with its noise output level controlled by a step attenuator. This produces a range of ENR values based on the setting of the step attenuator. This method does not require knowledge of how much noise power is being generated, nor details about the attenuation characteristics of the step attenuator. The only purpose of the noise source/attenuator is to provide two different levels of noise power. This also means that a cable with unknown loss characteristics can be used to connect the noise source/attenuator to the DUT without impacting the noise-figure calculations.

*3. A spectrum analyzer can also be used when measuring the change in ENR of an uncalibrated noise source to check the noise figure of a DUT. *