Noise measurement system verification includes the following two methods:
1. Verification of exraction math using matched standards, such as passive 3-, 6-, and 9-dB attenuators; and
2. System accuracy is verified using mismatched standards, such as passive bandpass filters.
Noise measurements are dispersive. This is essentially due to the small power levels being measured compared with environmental spurious levels. Because of this dispersion, four source impedance data points are never enough for any measurement. Typically, a higher number of data points are measured and noise-parameter extractions are effectuated, often yielding slightly dispersive results.
Mathematical and statistical methods, such as singular value decomposition (SVD) are applied to extract the correct information from the dispersive raw data.3,4 The comparison of noise parameters extracted from measured dispersive data points using SVD with theoretically known results shows that the math is capable of extracting the correct information (even if at first view the data seem random).
In general, the SVD method computes a least-squaressolution of an over-defined, linear system of equations. As such, this method computes the pseudo-inverse of the corresponding matrix (which represents the aforementioned system of equations) and uses this result to produce a solution. The Focus Microwaves standard noise parameter extraction method uses SVD analysis of the measured noise-figure data (produced by noise-figure measurements under various source impedances) to determine the noise parameters.
The disadvantage of the SVD method (and matrix inversion operations in general) is that a few incorrect data points can cause the final solution to vary wildly, or even fail completely. This can occur in noise-figure measurements, particularly if the DUT oscillates, or if the linearity of the noise receiver is somehow compromised in a few of the measured data points. This can occur if a noise receiver is operating under compression or if the power density level is too low to be distinguished from the thermal noise floor.
The solution in these cases is to measure more points and remove their effects on the final noise parameter solution. This is accomplished in the Focus Microwaves software by using a “statistical extraction” method. Specifically, the software selects many different subsets of the measured data and performs an extraction (i.e., determines a set of noise parameters) on each subset. Mathematically, these subsets correspond to the selection of many “combinations without repetition” of the measured data points. This produces several million solutions (sets of noise parameters). These solutions are then filtered, ranked, and statistically analyzed to determine the final set of noise parameters. In this way, the effects of a few incorrect data points on the overall solution are minimized.5,6
Noise standards provide an independent verification tool for noise system calibration and measurement accuracy. Noise parameters produced from noise standards are easily verified, both via measurements and mathematical calculations of the noise parameters for passive components. Matched attenuators are straightforward to measure; there are no noise power reflections created between the DUT (the attenuator) and the receiver, reducing the requirements for receiver dynamics. If the extracted noise parameters based on measured data correspond to the noise parameters calculated for the DUT’s S-parameters, the system is considered accurate under matched conditions.
Figure 1 illustrates the experimental setup of a noise parameter measurement. This setup performs both S-parameter and noise-parameter measurements of a DUT, without removing and/or reconnecting any component, by configuring the input and output switches in the correct paths. For the measurements, the DUTs were a set of passive, 50-Ω matched attenuators with values of 3, 6, and 9 dB. Figures 2-4 show theoretical and measured noise-parameter results for the attenuators.
Multiple measurement samples were taken consecutively for each DUT to evaluate the repeatability of the noise test system. As the test results show, the maximum variation of Fmin is 0.16 dB or ±0.08 dB, occurring at the highest frequency (26.5 GHz). The variation is due to the uncertainty in reading the noise power from the power detector of the noise figure meter.
For the Agilent PNA-X VNA with noise option used for this testing, the measured variation is comparable with the dynamic accuracy of the noise receiver over an 8-MHz bandwidth. The variation of noise resistance is well within 2.5%. The repeatability and accuracy of Γopt are excellent in all cases. Since these attenuators are well matched (25 dB or better return loss), the Γopt points are all in the center of the Smith chart. While it is difficult to find the correct phase for Φopt, Focus’ extraction math accurately predicts the values of Φopt in all cases.