Theory of Noise Measurement

Model MAURY MICROWAVE MT993A

CORPORATION 06 Jul 1999 THEORY OF NOISE MEASUREMENT

Introduction Maury Microwave's noise characterization software (MT993A) is designed to find the complete set of Noise is a natural phenomenon that affects most Γ noise parameters consisting of Fmin, opt, and Rn. Since microwave and RF systems. Because noise masks Γ opt is complex, this makes a total of four scalar desired signals, it is important to understand and Γ parameters. opt is the source reflection coefficient minimize its effects on the performance of micro- which corresponds to Fmin. Rn is a scale factor which wave and RF devices. Although there are several Γ shows how fast F changes with s. (The software types of noise, thermal noise is an important actually displays rn, which is Rn normalized to consideration for microwave designers because it 50 ohms.) greatly affects the linear microwave and RF systems they work with. Thermal noise is the focus of this Γ To find Fmin, opt, and Rn, the simple noise figure application note. must be measured at a variety of source impedances. In principle, since four scalar variables are Noise figure (a measure of the noise generated to be found, only four measurements are required. by two-port devices) can easily be determined by In practice, however, it is much more effective using commercial noise figure meters, but the to measure more points, and use a "least means measurements they provide are limited to SIMPLE square’s" mathematical technique to extract the NOISE FIGURE. Simple noise figure is the noise parameters. The MT993A software requires a mini- figure of a device terminated with a particular value mum of six positions, but more may be used. of source impedance. The problem with this is that the noise figure of a given device usually varies as the source reflection varies. Noise Characterization To minimize the effects of device noise figure, the Noise characterization also requires the parameters relationship between noise figure and source of the Device-Under-Test (DUT) to be separated impedance (or source reflection coefficient) must from the parameters of the measuring system to be known. The noise figure depends on the which the DUT is connected. To do this, the system COMPLETE NOISE PARAMETERS as shown below. must be calibrated to learn the system parameters. Equation 1: The noise contribution of the system (often called Γ Γ 2 4 Rn | s – opt| the second stage since it follows the DUT) will vary F = Fmin + with its source impedance according to equation 1. Γ 2 Γ 2 Zo |1+ opt| (1–| s| ) Therefore, the complete noise and gain parameters where of the system must be known to determine the F = Noise figure (linear ratio) system noise contribution when a particular DUT is connected. Fmin= Minimum noise figure (linear ratio) After the system is calibrated, noise characterization Γ = Optimum complex reflection coefficient opt of a DUT can be done. This consists of measuring the total noise figure, F , with several different Rn = Noise resistance total source impedances. The noise figure of the DUT Γ s = Complex source reflection coefficient for each position, Fdut, is then given from the Friis

2900 Inland Empire Blvd. • Ontario, California 91764-4804 application note 5C-042 Tel: 909-987-4715 • Fax: 909-987-1112 • http://www.maurymw.com Copyright  1999 Maury Microwave Inc., all rights reserved. SPECIFICATIONS SUBJECT TO CHANGE WITHOUT NOTICE Page 1 of 3 06 Jul 1999

cascade equation as shown in equation 2 Another practical consideration is that the reflection

(below). Gdut is the available gain of the DUT coefficient of the noise source usually changes when as resolved from the DUT S-parameters and switched between the hot and cold states. This soft- the source reflection coefficient. ware takes this rigorously into account by using the noise power function given in Equation 3. The noise Equation 2: power equations allow the source impedance to be Fsys – 1 independent for each power measurement, and there- F = F – dut total fore eliminate this traditional source of error. Gdut One practical consideration shown by Equation 3: Equation 2 is that if F is high and G sys dut P = kB{[tns + t0(F1-1)]Gal + t0(F2-1)}Gt2 is low, then Fdut will be a small difference between large numbers. This would make it where very sensitive to errors. Therefore, if DUTs P = The total measured noise power. with low noise figure values are to be k = Boltzmann’s constant. measured, it is important to keep Fsys as low as practical. That is why a load tuner is B = The system bandwidth. important when the DUT has a high output t = 290 kelvins. reflection coefficient. The effect of losses in o the tuners, bias tees, and the fixture is tns = Temperature of the noise source in kelvins. eliminated in the MT993A software. Since the losses are resistive in nature, they add F1 = The DUT noise figure (function of noise in proportion to the ambient tempera- source impedance). ture in kelvins (absolute temperature scale). F2 = The system noise figure (a function of During the setup, the ambient temperature the DUT output impedance). is entered in degrees Celsius and is later Ga1= The DUT's available gain (a function of read by the program during a calibration. source impedance). Conversion to kelvins is done automatically. Gt2 = System transducer gain (function of DUT output impedance). Figure 1: Noise Characterization

¥ Determines the Four Noise Parameters Ð Minimum Noise Figure Ð Real Part (Magnitude of Optimum Z, Y, or Γ Ð Imaginary Part (Angle) of Optimum Z, Y, or Γ

5C-042 application note 2900 Inland Empire Blvd. • Ontario, California 91764-4804 Tel: 909-987-4715 • Fax: 909-987-1112 • http://www.maurymw.com SPECIFICATIONS SUBJECT TO CHANGE WITHOUT NOTICE Page 2 of 3 MAURY MICROWAVE 06 Jul 1999

CORPORATION Figure 2: Noise Characterization Block Diagram

Noise Gain Analyzer

MT986B02 Tuner Controller

MT868C Amp. MT98* Tuners Converter RF Out Bias T Bias T

LO In MT950B Test Fixture

MT960A Bias Supply Signal Generator