Noise limits the sensitivity of a receiver and degrades the performance of a transmitter.Both R&D and production environments rely on several time-honored approaches to evaluate component noise in terms of noise figure. They now have an additional option in the form of single-connection, source-corrected noise-figure measurements through 26.5 GHz using the Agilent PNA-X vector network analyzer (VNA) from Agilent Technologies (www.agilent.com).Using an ECal calibration module and vector error correction,the PNA-X VNA delivers noise-figure measurements with high accuracy by minimizing the effects of imperfect source impedances.

Noise comes in many forms. Noise-figure measurements are usually concerned with shot and thermal noise. Shot noise is generally associated with semiconductor junctions and caused by the random nature of current flow. Thermal noise is due to the effects of temperature on electron motion, and can be defined by the equation for available power, Pa :

where:
Pa = the available power (in J/s or W),
k = Boltzmann's constant (1.38 1023 J/K)
T = the absolute temperature (in degrees K), and
B = the bandwidth of the device, circuit, or system under test (in Hz).

At room temperature (290 K), the available power is:
Pa = kTB = (1.38 1023 J/K)(290
K)(1 Hz) = 4 1021 W

Converting this to dBm yields:
dBm = 10log(4 1021 W 1000 mW/W) = 174 dBm

Both passive and active components contribute to the overall signal-to-noise ratio of a system. Noise factor (F) is a figure of merit that describes how much a network degrades the incoming signal-to-noise ratio, and it is defined as the input signal-to-noise ratio (SNR) divided by the output SNR, or:

where:
Si = the input signal power (W),
Ni = the input noise power (W),
So = the output signal power (W), and
No = the output noise power (W).

Since only an ideal network is noiseless, the output SNR for practical networks will also be lower than the input SNR, and F will always be greater than 1. The parameter noise figure (NF) expresses F in terms of decibels, with NF = 10log(F). Yet another parameter used to describe degradation in SNR is the effective input temperature (Te), which is the equivalent temperature (in degrees K) of an input termination connected to an ideal network or component. It is related to noise factor by Te = 290(F 1). This parameter is most commonly used for low-noise amplifiers (LNAs) with noise figures below 1 dB, typically in satellite-communications systems.

Noise-figure measurements can be made with a number of different instruments. These include dedicated instruments, such as noise-figure analyzers, and more general-purpose instruments, such as spectrum analyzers and VNAs. Two main methods are used to measure noise figure: the Y-factor (or hot/cold source) technique, and the cold-source (or direct noise) technique. In the Y-factor approach, as commonly employed with spectrum analyzers and noise-figure analyzers, a calibrated noise source is placed at the input of a DUT. The noise source can be turned on and off to create "hot" and "cold" (or "high" noise and "low" noise) states. The noise source's on state represents the excess noise it generates compared to a room-temperature termination (at 290 K). Its off state represents a passive termination at room temperature. By measuring the resulting noise powers at the output of the DUT, a noise-figure analyzer or properly equipped spectrum analyzer can calculate the noise figure and gain of the DUT.

In its simplest form, the cold-source or direct noise technique makes only one noise power measurement at the output of the DUT, with the DUT's input terminated in a source impedance at room temperature. This approach requires an independent measurement of the DUT's gain, but is ideally suited to a VNA, which can make extremely accurate gain and loss measurements through its use of vector error correction. By using a VNA for the cold-source technique, noise-figure measurements as well as S-parameter measurements can be made with a single connection to a DUT, provided that the VNA's receivers can measure both sinusoidal and noise power. The added benefits of the PNAX VNA, with its internal second signal generator and internal signal-combining capabilities, enable a complete suite of measurements to be made with a single connection, including tests of harmonics, compression, and intermodulation distortion (IMD).

Achieving Accuracy
No matter which test technique is used, noise-figure measurement accuracy is influenced by a variety of factors. For example, the noise figure of a DUT is a function of source impedance. From the noise-parameter equation:

it is known that a device's minimum noise figure (Fmin) occurs at some optimum source impedance ( opt) and that the device's noise figure will increase at any other source impedance. This optimum source impedance is typically found by varying the source impedance with an input impedance tuner while making a series of noise-figure measurements. Although test systems are designed for nominal 50-ohm operation, the actual source impedance seen by a DUT is not exactly 50 ohms, and it varies as a function of frequency. These variations result in noise-figure measurement errors. Source match imperfections are often one of the biggest contributors to overall noise-figure measurement uncertainty.

Noise-figure measurements based on the Y-factor approach can deliver good accuracy in cases when the noise source is connected directly to the input of a DUT. Unfortunately, it is not always possible to make this direct connection, as when making on-wafer measurements or testing LNAs that are part of other assemblies, such as transmit/receive (T/R) modules. By adding cables, adapters, switches, or probes to make the connection to the DUT, the effective system source match is significantly degraded.

It can be difficult to surpass the accuracy of a Y-factor-based noise-figure test system with a VNA-based cold-noise system, since the raw source match of the VNA is often worse than the match of a noise source. The PNA-X VNA (Fig. 1)with the cold-source approach minimizes uncertainties due to imperfect source match by essentially using an Agilent ECal solid-state calibration module as an impedance tuner to measure the noise parameters of the DUT. The ECal module is placed in series with the DUT's input path and a series of swept-frequency noise power measurements are made while switching calibration states within the ECal module to provide a set of known impedances to the DUT. A set of impedances and noise-power measurements are used at each frequency point in the sweep to solve the noise parameter equation. The noise parameters are then used to accurately calculate the 50-ohm noise figure as a function of frequency for the DUT. This process greatly reduces the measurement error due to noise-parameter-induced interaction between the DUT and the test system.

The noise parameters are solved with the DUT connected rather than during system calibration. The VNA is calibrated by measuring the normal S-parameter terms, and by an additional calibration of gain and noise figure of the PNAX's built-in noise receiver (with the noise source connected). Once the PNA-X is calibrated, the noise source is not needed for noise-figure or S-parameter measurements on the DUT, making single-connection measurements of noise figure and S-parameters possible through 26.5 GHz.

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The improved accuracy possible with the PNA-X and cold-source measurement technique with source correction can be significant, especially for DUTs with low noise figures (Figures 2 and 3). For those who must characterize other parameters, including its gain and linearity characteristics, the PNA-X VNA offers the speed and simplicity of single-connection measurements. The PNA-X's capabilities of performing S-parameter, noise-figure, and other measurements with a single connection (Figure 4) eliminates the need for a switch matrix, and reduces the number of instruments needed in a test rack. This reduces test-system development, calibration, and maintenance costs. The single-connection approach also results in reduced wear on test connectors and probes, minimized risk of wafer damage (for on-wafer noise-figure measurements), and increased throughput for manufacturing test lines.

Two- and four-port versions of the Agilent PNA-X VNA are available. As a VNA, the instrument can make both single-ended and mixed-mode (differential) S-parameter measurements. It can be equipped with an (optional) second test source that can be used as a local oscillator (LO) in mixer measurements or as a second test signal when performing amplifier intermodulation distortion (IMD), hot S22, or true-differential measurements. The analyzer supports a wide range of mixer measurements, including conversion loss, phase, third-order intercept point, and absolute group delay. The analyzer boasts an internal signal-combining network to simplify the setup of two-tone measurements, and features built-in pulse modulators and pulse generators for pulsed S-parameter and pulse-profile measurements of radar and electronic-warfare (EW) components.

Admittedly, the PNA-X VNA noise-figure measurement solution is not for everyone. For those not needing the ultimate in source-corrected accuracy, or the additional cost of built-in S-parameter measurement capability to 26.5 GHz, a noise-figure analyzer such as the Agilent NFA Series using the Y-factor technique can provide accurate, simple, and cost-effective noise-figure measurements. But when accuracy is paramount, and full DUT characterization is required, the PNA-X VNA with source-corrected noise-figure capability offers high accuracy as well as the speed and convenience of single-connection measurements.

For more information about the PNA-X's noise-figure capability, go to www.agilent.com/find/pnax-noise.

For further reading
"Applying Error Correction to Network Analyzer Measurements," Agilent Application Note AN 1287-3, Agilent Technologies (www.agilent.com).

"Fundamentals of RF and Microwave Noise Figure Measurements," Agilent Application Note AN 57-1, Agilent Technologies (www.agilent.com).

"Noise Figure Measurement AccuracyThe Y-Factor Method," Agilent Application Note 57-2, Agilent Technologies (www.agilent.com).

"Understanding the Fundamental Principles of Vector Network Analysis," Agilent Application Note AN 1287-1, Agilent Technologies (www.agilent.com).

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