#### 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.

## Determine the change in ENR at a DUT’s input

The key to this new noise measurement approach is to determine the change in ENR at a DUT’s input, using power readings from the spectrum analyzer translated to the input plane of the DUT. For example, if the spectrum analyzer reads -121 dBm, and the gain between the input to the DUT and the input to the spectrum analyzer is 15 dB, then the translated noise power at the input reference plane of the DUT would be -136 dBm. The noise temperature model of** Fig. 3** shows how the internal noise power generated by the analyzer can be translated to the input reference plane of the DUT as an effective input noise temperature. The effective input noise power at the input to the DUT is a composite of three sources:

1. The input noise power (generated by the noise source);

2. The effective input noise power of the DUT (related to the noise figure of the DUT); and

3. The effective input noise power of the spectrum analyzer translated to the input of the DUT (related to the noise figure of the spectrum analyzer).

This can be written as:

P_{n1} = KB(T_{H1} + T_{DUT} + T_{SA}) (A)

and

P_{n2} = KB(T_{H2} + T_{DUT} + T_{SA}) (B)

where P(p)_{n1} is defined as the effective input noise power into the DUT for different values of hot input temperature, T_{Hi}, and is determined from the measurements by the simple equality

P(p)_{ni} = 10[(P_{dB MEASURED} - Gain_{dB})/10]

and where parameter Gain_{dB} represents the small-signal gain (in dB) from the input of the DUT to the input of the spectrum analyzer.

Taking the difference of the two noise powers, P(p)_{n2} - P(p)_{n1}, yields Eq. 10:

ΔP_{n} = KB(T_{H2} - T_{H1}) → (T_{H2} - T_{H1} = ΔP_{n}/KB) (10)

At this point, it is necessary to solve for ΔENR by means of Eq. 11:

ENR_{1} = (T_{H1} - 290)/290

and

ENR_{2} = (T_{H2} - 290)/290 → ΔENR = ENR_{2} - ENR_{1} = (T_{H2} - T_{H1})/290

and from Eq. 10,

→ ΔENR = ΔP_{n}/(290KB) (11)

Parameter dY can be calculated from Eq. 12:

Y_{1} = 10^{(Pn1 - Pn0)}/10)

and

Y_{2} = 10^{(Pn2 - Pn0)}/10)

where P_{n} is in dBm (12)

where P_{n0} is the noise power measured on the spectrum analyzer with an input noise power to the DUT of 290 K (the input of DUT terminated with a matched load at 290 K):

→ ΔY = Y_{2} - Y_{1} (13)

The first set of data appearing in **Table 1 **is the measurement of the spectrum analyzer’s noise figure (with the preamplifier turned on) using two calibrated noise sources. The last column shows the result of using the standard Y-factor method for the two different ENR noise heads. The next-to-last column shows the result using the method described in this article. The set of data shown in **Table 2** shows the result of using the new method with dENR determined by taking the difference in ENR of the calibrated noise sources. **Table 3** shows the results for the spectrum analyzer’s noise figure for different values of ENR obtained from an uncalibrated noise source (about a 22-dB-gain amplifier). This is obtained by using a variable attenuator whose output is connected to the spectrum analyzer through a test cable.

The remaining data show the results for two amplifiers with noise figures measured at 1.62 GHz with a model HP 8970A noise figure test set from Hewlett-Packard (now Agilent Technologies). The two amplifiers yielded a noise figure of 2.60 dB and gain of 11.6 dB for amplifier A1 and a noise figure of 0.55 dB and gain of 22.2 dB for amplifier A2. **Table 4** shows the total noise figure of amplifier A2 together with the spectrum analyzer. By applying Eq. 5, the actual noise figure of amplifier A2, NFac_{A2}, can be calculated as:

NFac_{A2} = 1.25 - (20.75 - 1)/165.96 = 0.54 dB

**Table 5** shows the total noise figure of amplifier A1 together with the spectrum analyzer. By applying Eq. 5, the actual noise figure of amplifier A1, NFac_{A1}, can be calculated as:

NFac_{A1} = 3.14 - (20.75 - 1)/14.45 = 2.50 dB

In summary, a manual noise figure test method has been presented which eliminates the need for a calibrated noise source. The method is as accurate as the previous Y-factor method, while eliminating the expense and calibration routine associated with a calibrated noise source. The method allows the use of a lossy test cable to connect the noise source to the DUT without any need to account for the cable’s loss in the noise figure calculations. As with the standard Y-factor method, the accuracy of this method will also depend upon such parameters as measured gain accuracy, ambient room temperature, and VSWR of the DUT and other interconnecting components. The effect of these parameters is beyond the scope of this article, but can be researched in the multitude of articles written about the standard Y-factor method.

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