Noise figure is a parameter well-known to receiver designers, and a key measure of determining a receiver’s ultimate signal sensitivity. Measurements of noise figure have often been reserved for specialized test systems. But this needn’t be the case, thanks to the new noise-figure measurement capability (option MS-4640A-041) that can be built into the VectorStar MS4640A and ME7838A series vector network analyzers (VNAs) from Anritsu Co. (www.anritsu.com). These workhorses can now make noise-figure measurements from 70 kHz to 70 GHz. And by adding the optional broadband receiver (model SM6609) the frequency range can be extended to 125 GHz *(Fig. 1)*.

*1. The VectorStar MS4640A series and ME7838A series (not shown) VNAs are eligible for two new options that add noise-figure measurement capability and extend the coaxial frequency coverage to 125 GHz. *

The SM6609 broadband receiver equips an ME7838A VNA for continuous broadband frequency coverage from 70 kHz to 125 GHz via a small-dimensioned coaxial connector. Back in 1983, Anritsu (then Wiltron Co.) introduced the K-connector with 2.92-mm dimensions for frequency coverage to 40 GHz, in support of its line of scalar network analyzers. Over the years, the firm’s Bill Oldfield has been instrumental in developing smaller coaxial connector configurations for higher-frequency use. The 1-mm connector, for example, is specified to 110 GHz, but can operate up to 125 GHz. Anritsu plans to support the new architecture with coaxial as well as waveguide adapters for those making noise-figure measurements on waveguide DUTs.

The new millimeter-wave noise-figure measurement systems are suitable for both research and production tasks, with S-parameter measurement speed of 55 ms for 201 data points using an intermediate-frequency (IF) bandwidth of 10 kHz. They offer noise-figure measurement resolution of < 0.1 dB, backed by calibration and measurement stability of 0.1 dB over 24 h. The system dynamic range for S-parameter measurements is 108 dB at 65 GHz and 107 dB at 110 GHz.

The SM6609 receiver uses the same nonlinear-transmission-line (NLTL) technology employed in the firm’s model 3743A VectorStar frequency extension modules. The compact size of those frequency-extension units, which are a fraction of the size and weight of conventional frequency-converter modules, enabled ease of positioning on wafer probe stations when making on-wafer measurements. The firm will offer additional optional frequency-conversion modules for waveguide-based millimeter-wave coverage through 750 GHz and beyond for higher-millimeter-wave and quasi-optical measurements.

Noise-figure measurements on the VectorStar MS4640A and ME7838A series VNAs equipped with the optional SM6609 receiver are supported by optional measurement software. The analyzers run under simple graphical user interfaces (GUI) that offer various other active-device measurements related to noise figure—including gain and compression point—as either standard or optional capabilities.

Accurate noise-figure measurements, of course, are aided by some understanding of how these measurements are made and why. Noise figure essentially describes the degradation of a system or component’s signal-to-noise ratio (SNR) due to the output noise power (N_{o}) added by a device under test (DUT), usually an active device such as an amplifier. Measuring the noise figure of the DUT can help determine the impact it will have on a system’s SNR.

Noise figure (NF) in decibels can be calculated as a function of noise factor, F:

NF = 10logF

where:

F = (S_{i}/ N_{i})/( S_{o}/ N_{o})

and:

S_{i} = the input signal power;

N_{i} = the input noise power;

S_{o} = the output signal power; and

N_{o} = the output noise power.

Over the years, noise-figure measurements have improved due to better understanding of how to make the measurements,^{1-6} more sensitive receivers, and more accurate noise-power measurements. Option MS-4640A-041 (which equips a VectorStar MS4640A or ME7838A VNA) and a model SM6609 receiver (with noise-figure capability through 70 to 125 GHz) incorporates many of these noise-figure advances, including the use of the cold-source measurement method rather than the hot-cold or Y-factor measurement approach.

*2. This block diagram shows a simple representation of the VNA-based noise figure measurement system.*

The Y-factor (hot-cold) measurement technique uses a noise source capable of producing a low-temperature (cold) noise power (N_{c}) and a hot noise power (N_{h}). Such a noise source is the Input Noise Signal in *Fig. 2*. The Y factor is simply the ratio of hot to cold noise powers, Y = N_{h}/N_{c}.^{2} The Y factor was useful for a quick calculation of noise figure using Eq. 1:

F = [(T_{h}/T_{c}) – 1]/(Y – 1) (1)

where:

T_{h} = the equivalent hot temperature of the noise source; and

T_{c} = the equivalent cold temperature of the noise source, which is often assumed to be equal to 290 K per IEEE definition.

By making noise-figure measurements of the receiver alone, and then the receiver with the device under test (DUT), it is possible to deconvolve the noise figure of the DUT using the Friis equation^{1}:

F_{DUT} = F_{SYS} – (F_{rcvr} – 1)/G (2)

where:

F_{DUT} = the noise factor of the DUT;

F_{SYS} = the noise factor of the whole system (receiver + DUT);

F_{rcvr} = the noise factor of the receiver alone; and

G = the gain of the DUT.

The DUT gain, G, can be measured separately, such as by means of scattering (S) parameters; it can also be determined from the change in measured noise powers during calibration and measurement. The hot-cold noise-figure measurement approach is based totally on ratios and therefore does not require absolute power calibrations. This was important when the available measurement dynamic range over broad bandwidths was limited.

Calibration of the equivalent hot temperature, T_{h}, for a noise source is difficult and usually left to a handful or qualified laboratories. Another problem with the hot/cold noise-figure measurement approach is related to minimizing impedance match changes when the noise source changes between its hot and cold states.^{4} Match changes result in large measurement errors, which can be partially overcome by source correction methods.^{3}

The cold-source noise-figure measurement method was developed to eliminate the need for the hot/cold noise source. In the cold-source method, the noise factor can be found from Eq. 3:

F = (kT_{0}B + N)/( kT_{0}BG) (3)

where:

k = Boltzmann’s constant (~1.3807 × 10^{−23} J/°K);

N = the noise power added by the DUT;

G = the gain of the DUT; and

B = the measurement bandwidth.

This method requires an accurate measurement of absolute noise power, implying the need for an effective measurement receiver calibration. It also calls for an accurate measurement of bandwidth which, in the case of using a VNA with a digital IF system, can be readily determined. The bandwidth can also be found when measuring absolute power, provided a noise source is used. Isolating the noise factor of the DUT using this method, the noise contributions of the receiver must be known, which can be performed with only a cold source attached to the receiver’s input port. Once receiver noise is known, Eq. 3 can be rewritten as Eq. 4:

F = (1/G) + (N_{DUT} + rcvr – N_{rcvr})/kT_{0}BG (4)

This method places great import on gain measurements, with errors in measuring gain or noise power transferred almost on a dB-for-dB basis to the noise-figure results. Again, impedance matching is also important for maintaining good measurement accuracy, and the receiver noise power may be affected by the source impedance. By considering that the response of a DUT can be represented by its minimum noise factor (F_{min}), its resistive noise (R_{n}, and its optimum impedance (Γ_{opt}),^{7} the net noise figure of the DUT can be found from Eq. 5:

F = F_{min} + (4R_{n} | Γ_{S} − Γ_{opt} | ^{2})/[Z_{0}(1 − | Γ_{S} | ^{2})

| 1 + Γ_{opt} | ^{2} ] (5)

where:

Z_{0} = the system characteristic impedance.

If R_{n} is small relative to Z_{0}, the net noise figure will be relatively insensitive to changes in source reflection coefficient, Γ_{S}. Typically, measurement receiver effective R_{n} is small. When examining typical noise circles for a measurement receiver at 50 GHz (not shown), even if the DUT’s output port is poorly matched, the effective receiver noise figure only changes by about 0.65 dB from F_{min}. For a DUT with 10-dB gain and 2-dB noise figure, this would only add 0.1-dB uncertainty, and only 0.01-dB uncertainty for a DUT with 20-dB gain and 2-dB noise figure.

A number of factors affect noise-factor measurement uncertainty, ~F, arising from deviations (Δ) that can occur during measurements or calibrations:

~F = 1 + (G + ΔG) + (N_{DUT + rcvr} – N_{rcvr}) +

(ΔN_{DUT + rcvr} – ΔN_{rcvr})](1 + ΔR)/[kT_{0}B(G + ΔG)] (6)

Equation 6 does not list all possible uncertainty sources—just the dominant ones. Gain variation (ΔG) is usually associated with S-parameter measurements. Other variations are related to measurements of noise power, including ΔR terms related to a user’s power calibration and receiver calibration, and ΔN terms related to impedance match interactions.

To help understand different uncertainty scenarios, the VectorStar Noise Figure Uncertainty Calculator, based on Monte Carlo methods,^{8} was created as a companion to the new 125-GHz noise-figure measurement capability. The program runs on an external personal computer (PC) or on the desktop of a VectorStar VNA and is helpful in determining the optimum measurement setup for achieving a desired measurement uncertainty target. The program takes into account receiver parameters, DUT parameter, power measurement parameters, source parameters, and the cold source temperature. It can provide plots of noise figure uncertainty versus frequency and versus gain as well as the receiver gain required to achieve a desired noise-figure uncertainty.

Option MS4640A-041, which adds noise-figure-measurement capability to Anritsu’s VectorStar MS4640A and ME7838A series VNAs, is priced at $15,000 (plus the cost of the analyzer). VectorStar MS4640A series VNAs are available in standard frequency ranges from 10 MHz to 20, 40, 50, or 70 GHz (with frequency extension option to 70 kHz), while the ME7838A series VNAs offer single-sweep capability from 70 kHz to 110 GHz through a 1-mm connector.

The SM6609 receiver option extends the overall frequency range of the VNAs to 125 GHz through the same type of 1.0-mm coaxial connector. P&A: $15,000 (noise-figure capability); 8 wks, and $30,250 (SM6609 receiver for 125-GHz coverage); 16 wks. MWRF

**Anritsu Co., 490 Jarvis Dr., Morgan Hill, CA 95037-2809; (408) 778-2000, FAX: (408) 776-1744, www.anritsu.com.**

*References*

1. H.T. Friis, “Noise figure of radio receivers,” Proceedings of the IRE, Vol. 32, July 1944, pp. 419-422.

2. “Noise Figure,” Anritsu Co. (www.anritsu.com), Application Note 11410-00210, August 2000.

3. David Vondran, “Noise figure measurement: corrections related to match and gain,” Microwave Journal, March 1999, pp. 22-38.

4. N. Otegi, J.M. Collantes, and M. Sayed, “Cold-source measurements for noise figure calculation in spectrum analyzers,” 67th ARFTG Conference Digest, June 2006, pp. 223-228.

5. N. Otegi, J.M. Collantes, and M. Sayed, “Receiver noise calibration for vector network analyzer,” 76th ARFTG Conference Digest, December 2010,

pp. 1-5.

6. J.M. Collantes, R.D. Pollard, and M. Sayed, “Effects of DUT mismatch on the noise figure characterization: A comparative analysis of two Y-factor techniques,” IEEE Transactions on Instrumentation & Measurements, Vol. 51, December 2002, pp. 1150-1156.

7. L. Escotte, R. Plana, and J. Graffeuil, “Evaluation of noise parameter extraction methods,” IEEE Transactions on Microwave Theory & Techniques, Vol. 41, March 1993, pp. 382-387.

8. “Supplement 1 to the “Guide to the expression of uncertainty in measurement,” Propagation of distributions using a Monte Carlo method,” Joint Committee for Guides in Metrology, 2008.