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Measurement of Onwafer Transistor Noise Parameters Without a Tuner Using Unrestricted Noise Sources
This article presents a method for calibrating the four noise parameters of a noise receiver which does not require a tuner. The method permits using general (mismatched) noise sources, which may present very different source reflection coefficients between their hot and cold states. The method is applied to the calibration of a noise setup using onwafer noise sources (a reversebiased coldFET and an avalanche noise diode). Experimental validation of the receiver calibration and its application to the determination of onwafer FET noise parameters to 40 GHz is presented.
A. Lázaro, M.C. Maya and L. Pradell
Universitat Politècnica de Catalunya (UPC)
Barcelona, Spain
An accurate knowledge of transistor noise parameters (NP) is essential to the design of low noise amplifiers (LNA). Before the NPs of the deviceundertest can be measured, the noise receiver must be calibrated. Calibration consists of the determination of the four receiver NPs. Conventional calibration techniques require measurements of noise powers presented at the receiver input for a number of reflection coefficients produced by a broadband tuner.^{1} However, this technique is costly and timeconsuming. An alternate method^{2} permits determining the receiver NPs from 50 W noisefigure measurements, by using a commercial, wellmatched coaxial noise source. This method has demonstrated an accuracy comparable to that obtained by using tunerbased methods.
While a matched source is the noise reference most commonly used, it has been shown^{3} that an onwafer diode noise source is a convenient noise reference to calibrate the receiver for measuring NPs of onwafer transistors directly. However, onwafer diode noise sources are highly mismatched devices and their reflection coefficient varies significantly between the hot and cold states. Therefore, the previously proposed method^{2} to calibrate the receiver cannot be applied, because it assumes that the receiver noisefigure does not change noticeably between both noise source states. An onwafer attenuator pad to achieve a broadband matching condition is normally introduced after the noise diode,^{3} but this lossy pad has the drawback of reducing the effective level of excess noise ratio (ENR) at the onwafer referenceplane.
Alternatively, this work presents a novel method to calibrate the noise receiver with a general (mismatched) noise source and does not require a tuner, which adds flexibility to the design of new types of noise sources, specifically onwafer noise sources. There is no restriction on the variation of the source reflection coefficient between the hot and cold states, and the receiver noisefigure need not be constant for both noise source states. To verify the method, calibration results are compared to those obtained with a tunerbased method,^{1} and the NPs of a passive semiconductor device (commongate, onwafer, cold transistor) are measured and the results are compared to those derived from its Sparameters. The proposed method is used to calibrate the noise receiver with mismatched onwafer noise sources and applied to the determination of the NPs of FETs. The experimental results are presented in two bands, 2 to 22 GHz and 26 to 40 GHz.
Fig. 1 Noise figure and nosie parameter measurement system.
Experimental Setup
Figure 1 shows the experimental setup. It is a typical configuration for the determination of onwafer transistor noise parameters, but without the inclusion of a tuner. It consists of the following components: A VNA (HP8510C) for calibration and measurement of the setup reflection coefficients and the deviceundertest (DUT) Sparameters; a test fixture for inserting the DUT  a waferprobe station (SUMMIT9000 from CascadeMicrotech) is used; three remotely controlled coaxial switches (SW) to select between the lower and the upper noise measurement bands (2 to 22 GHz and 26 to 40 GHz, respectively), and between VNA and noise measurements; two biastees; noise sources  in this work, two onwafer noise sources (OWNS) and one coaxial (HP346C) noise source are used; a noise receiver composed of a spectrum analyzer (SA) (HP70000 series), a low noise amplifier (LNA) for the lower frequency band (2 to 22 GHz) to reduce the SA noisefigure, a low noise block downconverter (LNB264250 from MITEQ), which includes an input LNA to convert the upper frequency band (26 to 40 GHz) into an IF range (5 to 19 GHz) within the SA range, and an external detector connected to the SA 21.4 MHz IF output. All measurements are automated and controlled with an external PC via GPIB.
Fig. 2 Receiver equivalent wave noise sources b_{n1} and b_{n2} .
Method for Receiver Calibration With Unrestricted Noise Sources
Since the LNAs in the receiver frontends are basically unilateral devices, their scattering noisematrix representation^{4} can be simplified by assuming that their equivalent wave noise sources b_{N1} , b_{N2} (see Figure 2 ) are uncorrelated
Under this hypothesis, the receiver noisefigure FREC can be approximated by^{5}
where
G_{S} = source reflection coefficient
Since the LNAs are basically unilateral, it has been also assumed in Equations 1 and 2 that S_{11} » G_{R} , where G_{R} is the receiver input reflection coefficient and S_{11} , S_{21} are the receiver S parameters. The impact of such hypothesis on the determination of the receiver noise parameters (in particular F_{min} and R_{n} ) is discussed later. Note that a(G_{R} , G_{S} ) is a quantity that only depends on the reflection coefficients measured with the VNA. To determine the normalized noise power wave
the noise powers delivered to the receiver for two states (hot and cold) of the noise source, P_{HOT} and P_{COLD} respectively, are measured. Then the following ratio R of noise powers available at the plane 22' can be computed
where
m(G_{R} ,G_{S} ) = mismatch coefficient that only depends on reflection coefficients
G_{S_COLD} = cold source reflection coefficients
G_{S_HOT} = hot source reflection coefficients
Then, the power ratio R is written in terms of the receiver noise temperature T_{REC} = (F_{REC} 1) T0, where F_{REC} is given by Equation 1 and T_{0} is the standard temperature (T_{0} = 290K), as
where
T_{HOT} = noise source hot temperature
T_{COLD} = cold temperature (room temperature)
From Equation 5, the quantity
is computed as
Using Equation 6, the receiver NPs are readily computed assuming the same approximation made previously for the receiver
where
Z_{0} = normalizing impedance
It is assumed in Equation 9 that the LNA has been designed for minimum noise.
Note that, in contrast with previous methods^{2} , significant variations in the receiver noisefigure due to different hot and cold noise source reflection coefficients are allowed and taken into account in Equation 6 through the quantity a(G_{R} , G_{S} ) defined in Equation 2. Furthermore, the noise device which provides the hot state temperature (T_{HOT} ) may be physically different from the device at cold temperature (T_{COLD} ). In this work, examples of calibration using onwafer noise sources for the hot state and a coplanar 50 W load for the cold state are given.
Finally, the receiver gainbandwidth constant kGB (where G is the receiver transducer gain for G_{S} = 0, and B is the noise measurement bandwidth) must be determined using
After calibration, the noisefigure of an arbitrary DUT can be obtained as follows. The total noisefigure (DUT plus receiver) for a measured reflection coefficient at plane 11' (G_{s} ') computed from the measured noise power P(G_{S} ') is
where
G_{OUT} = DUT ouput reflection coefficient
T_{f} = physical temperature of the source termination (typically, room temperature)
G_{DUT} = DUT available gain
The DUT noisefigure is obtained using Friis' formula
Finally, assuming that the DUT is an onwafer FET, its measured noisefigure (Equation 13) is applied to determine the FET noise parameters using the method proposed in reference.^{6} This method (socalled F_{50} ) is based on the determination of the FET intrinsic noisematrix elements by frequencyfitting the measured device noisefigure for a known source reflection coefficient (usually a matched load at room temperature). It does not require a tuner, and has demonstrated a good accuracy up to 26 GHz.^{6}
Fig. 3 Measured receiver noise parameters to 26 GHz.
Receiver Calibration Results
The receiver calibration method described in the previous section is based on approximations in Equations 1, 2 and 9, whose impact on the calculation of the receiver noise parameters must be assessed. To this end, the receiver noise parameters are measured up to 26 GHz using the method proposed here (Equations 3 to 9) and by a tunerbased method.1 In both tests, a noisefigure measurement system (HP 8970S) is used as the noise receiver and a wellmatched noise source (HP346C) as the noise reference. The tuner used in the second case is a broadband device (NPTS26, 2 to 26 GHz) from CascadeMicrotech. The results, obtained in 15 measurement sessions, are compared graphically on the next page. The values displayed are mean values at every frequency (24 frequency points) over the 15 sessions and their standard deviations (s) are also shown as error bars. The numerical values displayed in Appendix A are listed in frequency steps of 4 GHz. It is observed that the differences in F_{min} between the two methods are small (the average deviation over the 24 frequency points is 0.075 dB), and are of the same order of magnitude than the deviations for each method between measurement sessions. The main impact of the approximations made in Equations 1, 2 and 9 is observed in R_{n} (the average deviation over the 24 frequency points is 9.75 W), mainly in the lower frequency region, where the approximation of Equation 9 does not hold in phase. Also, the differences in G_{opt} indicate that this approximation depends on the frequency point and LNA. In contrast, deviations in R_{n} and G_{opt} for each method between measurement sessions are much smaller. In conclusion, the differences in R_{n} and G_{opt} between both methods are systematic, and cannot be attributed to measurement errors, but to the method. Figure 3 shows the measured receiver noise parameters.
Fig. 4 Total noise figure (typical HEMT and receiver) to 22 GHz.
The differences between methods translate into errors in the determination of the noisefigure of DUTs (transistors). The error introduced is (from Equation 13) DF_{DUT} = DF_{REC} / G_{DUT} . Therefore, for moderately high gain DUTs (transistors), the impact on the F_{DUT} calculation from errors in the receiver noise parameters is small. To illustrate this point, Figure 4 shows the total noisefigure F_{TOT} (DUT + receiver), where the DUT is a typical HEMT, computed using the receiver noise parameters extracted with a tunerbased method^{1} and the method proposed here. The source reflection coefficient D'_{S} corresponds to real data from a wellmatched noise source (HP346CK01). Since only differences between the two methods are considered, DF_{TOT} = DF_{DUT} . Typical differences are 0.2 dB. The worst case at 2 GHz (0.7 dB) is due to the significant difference between G_{OPT} using both methods.
Fig. 5 Noise parameters of a typical HEMT to 22 GHz computed using the F50 method.^{6}
The differences in the extraction of the noise parameters of the HEMT due to the differences between receiver calibration methods (tunerbased method and Equations 3 to 9) are evaluated in Figure 5 and Appendix B , where the F_{50} method proposed^{6} is used to determine the FET noise parameters. It is observed that the differences are very small for F_{min} and G_{OPT} (less than 0.12 dB in F_{min} at 22 GHz and 0.5 percent in G_{OPT} ). The difference in R_{n} is higher (but less than 8.5 percent at 22 GHz) because this parameter is somewhat more sensitive to the optimization performed to extract the intrinsic correlation matrix.^{6} The small sensitivity shown by the F_{50} method to the receiver calibration method is due to the redundancy in frequency and the use of matched source states.
To verify the receiver calibration, the noisefigure of a passive commongate FET is measured (as previously suggested^{7} ). This is a nonfavorable case since, according to Friis, Equation 13, small errors in the measurement of the receiver noisefigure (F_{REC} ) are translated into large errors in the measured DUT noisefigure (F_{DUT} ) when the DUT is a mismatched low noise device without gain.^{8} The noisefigure of a passive FET is measured using the calibration method proposed here and compared to the noisefigure computed from the available gain calculated from its measured Sparameters. The coaxial noise source is used as a noise reference. The measured results are shown in Figure 6 and tabulated in Table 1 . The values displayed are mean values at every frequency (21 frequency points) over six sessions and their standard deviations (s) are also shown as error bars. The differences range from very small (0.01 dB) to moderate (0.41 dB), except in two particular points (18 and 21 GHz) where it is large (1.13 dB). In these two points, the 2 to 22 GHz LNA does not fulfill G_{OPT} = G_{R} *, in particular with respect to the phase.
Fig. 6 Noise figure of a passive commongate FET measured by the proposed method and calculated from its available gain.
As a conclusion to this section, the receiver calibration method proposed, using Equations 3 to 9, is suited for the extraction of transistor noise parameters, in particular when the noise parameter extraction method^{6} (F_{50} ) is applied, saving time (fewer power measurements are required  only from ON/OFF noise source states) and cost compared to tunerbased methods.
Table 1  
f  NF  s_{NF}  Gain  s_{Gain}  NFGain 
2  3.25  0.07  3.23  0.03  0.02 
6  3.69  0.11  3.68  0.12  0.01 
10  3.38  0.14  3.72  0.05  0.35 
14  4.10  0.15  3.95  0.06  0.16 
18  2.15  0.23  3.28  0.06  1.13 
22  6.09  0.29  5.68  0.09  0.41 
Using Onwafer Noise Sources for Receiver Calibration and FET Noise Parameter Determination
When using coaxial and waveguide noisesources for measuring noiseparameters of microwave and millimeterwave onwafer FETs, the noisesource ENR, known from manufacturers' data, must be translated to the waferprobe referenceplane through an input twoport adapter in order to calibrate the receiver. This step requires the determination of the adapter insertion loss (G_{adapter} ) from two calibrations performed with a network analyzer: twoport onwafer (planes 11' and 22'); oneport (OSL) at the noisesource (coaxial or waveguide) port (plane 00'). The excess noise ratio (ENR') at the probe plane (plane 11') is determined from the known noise source ENR at plane 00' and the measured insertion loss of the input twoport adapter
At millimeterwave frequencies, the OSL calibration uncertainty increases; therefore, the accuracy with which insertion loss and translated ENR are computed degrades. Furthermore, since the adapter insertion loss increases with frequency, the effective ENR at the waferprobe plane is reduced to unpractical values. A solution to these problems is an onwafer diode noisesource placed at the waferprobe plane. Since there is no input adapter, the determination of diode ENR at the probetip does not require an OSL calibration, but only measured noisepowers and reflection coefficients G_{S} , G_{R} , determined from the onwafer calibration.
Fig. 7 Noise diode wirebonded to a Jmicro transition.
Two types of onwafer noise sources have been considered and used here. First, a coldFET (V_{DS} = 0) with the gate reversebiased. The device is a 0.5 mm gatelength, 2 x 50 mm gatewidth DPDSQW HEMT from the Foundry of Fraunhofer Institut, Freiburg, Germany (FhGIAF). The gate bias point is fixed with a current source, close to the transistor breakdown point. This FET is used in a commonsource configuration and its gatesource port is connected to the onwafer referenceplane 22' as an inexpensive onwafer diode. A commercial avalanche noise diode chip (NoiseCom NC406) wirebonded to the microstrip end (see Figure 7 ) of a coplanartomicrostrip transition, Probe Point™ 1003 Adapter Substrate from Jmicro, is used as a hot source. To determine the equivalent noisetemperature T_{d} of every noise device for a selected bias point, its noise power delivered to the receiver P_{d} and its reflection coefficient (G_{S HOT} ) are measured. Combined with the measured noise power (P_{REF} ) and the reflection coefficient (G_{REF} ) of an onwafer passive wellmatched referenceload, the following expression is obtained for T_{d} :
In Equation 15, T_{REC} is the receiver noisetemperature evaluated for G_{REF} and G_{S HOT} , respectively, m is the mismatch coefficient defined in Equation 4 and G_{R} is the receiver input reflection coefficient. To compute TREC, the receiver NPs previously determined from calibration with the coaxial noise source (Equations 7 to 9) are used. From T_{d} computed in Equation 15, the diode ENR is readily obtained. To reduce the uncertainty in this measured onwafer noise source ENR, equivalent circuit models for a coldFET and an avalanche diode (including their intrinsic noise sources) are determined from the measured ENR and Sparameters (in the case of coldFET) or reflection coefficient (in the case of avalanche diode), and their intrinsic noise current sources are fitted with frequency using their smooth frequency characteristic.^{9,10} Then, a final estimate of the ENR is computed from the model. Figure 8 shows the final estimate of the ENR and compares it to the measured ENR. Note that the ENR values obtained are high at the onwafer plane 22', ranging from 8 to 20 dB with the coldFET and from 20 to 34 dB with the avalanche diode, depending on frequency and bias point.
Fig. 8 Onwafer noise source ENR; (a) a coldFET and (b) an avalanche noise diode.
Figure 9 compares the receiver NPs measured with a standard coaxial noisesource, to those measured with the onwafer noisesources whose ENR has been determined, using the receiver calibration method (Equations 3 to 9). The highly mismatched onwafer noisesources are used as the hot state, whereas a wellmatched coplanar load at room temperature is used as cold state. A good agreement is obtained (agreement in the receiver F_{min} measured with the avalanche diode is within the coaxialsource ENR uncertainty, ±0.34 dB at 40 GHz), demonstrating the applicability of the proposed calibration method to onwafer noise sources.
Fig. 9 Measured receiver noise parameter to 40 GHz.
Figure 10 shows an example of measured noise parameters of a PHEMT up to 40 GHz using the F_{50} technique^{6} and the receiver noise parameters, previously calibrated with both the coldFET and avalanche diode noise sources. The FET noisefigure (F_{50} ) is obtained by using the above procedure (Equations 11 to 13). The results show very small differences by using either of the onwafer noise sources.
Fig. 10 Measured noise parameters of a PHEMT biased at V_{ds} = 1.5 V, I_{ds} = 17.9 mA.
Conclusion
A general method for calibrating the four receiver noise parameters using unrestricted noise sources, which does not require a tuner, has been presented. Specifically, this method allows very different hot/cold state impedances, simplifying the design of onwafer noise sources (no lossy pad after the noise diode is required). The method makes some assumptions in the receiver. The influence of such assumptions in the receiver calibration and the determination of FET noise parameters (using the F_{50} method) are studied through a comparison with tunerbased methods. The receiver calibration is verified by measuring a mismatched passive device (commongate FET). A reversebiased coldFET and an avalanche noise diode are used as mismatched onwafer noise sources up to 40 GHz. The four receiver noise parameters are calibrated with the onwafer noise sources and the receiver calibration method presented here, and applied to the measurement of an onwafer HEMT noise parameter, using F_{50} .
Acknowledgment
This work has been supported by Spanish government grants 2FD970960C0505 and 2FD971769C0403 (CICYTFEDER).
References
1. A. Lázaro, L. Pradell and J.M. O'Callaghan, "Method for Measuring Noise Parameters of Microwave Twoport," IEE Electronics Letters , Vol. 34, No. 12, 1998, pp. 13321333.
2. A. Lázaro and L. Pradell, "Extraction of Noise Parameters of Transistor Using a Spectrum Analyzer and 50 W Noisefigure Measurements Only," IEE Electronics Letters, Vol. 34, No. 24, 1998, pp. 23532354.
3. L.P. Dunleavy, J. Randa, D.K. Walker, R. Billinger and J. Rice, "Characterization and Applications of Onwafer Diode Noise," IEEE Transactions on Microwave Theory and Techniques , Vol. 46, No. 12, December 1998, pp. 26202627.
4. R.P. Hecken, "Analysis of Linear Noisy Twoports Using Scattering Waves," IEEE Transactions on Microwave Theory and Techniques , Vol. 29, No. 12, October 1981, pp. 9971004.
5. T. Werling, E. Bourdel, D. Pasquet and A. Boudiaf, "Determination of Wave Noise Sources Using Spectral Parametric Modeling," IEEE MTTS International Microwave Symposium Digest , June 1997.
6. A. Lázaro, L. Pradell and J.M. O'Callaghan, "FET Noise Parameter Determination Using a Novel Technique Based on 50 W Noisefigure Measurements," IEEE Transactions on Microwave Theory and Techniques , Vol. 47, No. 3, March 1999, pp.315324.
7. L. Escotte, R. Plana and J. Graffeuil, "Evaluation of Noise Parameters Extraction Methods," IEEE Transactions on Microwave Theory and Techniques , Vol. 41, No. 3, March 1993, pp. 382387.
8. "Noisefigure Measurement Accuracy," Hewlett Packard Application Note572, November 1988.
9. M.C. Maya, A. Lázaro and L. Pradell, "Calibración del ENR de Fuentes de Ruido en Oblea," XV Symposium Nacional URSI , Zaragoza, Spain, September 2000, pp. 13.
10. R.H. Haitz and F.W. Voltmer, "Noise of a Selfsustaining Avalanche Discharge in Silicon: Studies at Microwave Frequencies," Journal of Applied Physics , Vol. 39, No. 6, 1968, pp. 33793384.
A. Lázaro received his MS and PhD degrees in telecommunication engineering from the Universitat Politècnica de Catalunya (UPC), Barcelona, Spain, in 1994 and 1998, respectively. He then joined the faculty at UPC, where he has been teaching a course on microwave circuits and antennas. His research interests are in microwave device modeling, onwafer noise measurements, MMICs, low noise oscillators and MEMS.
M.C. Maya received her MSc degree in electronics and telecommunications from the CICESE Research Center, Ensenada, BC, Mexico, in 1998, and is currently working toward her PhD degree at the Universitat Politècnica de Catalunya (UPC), Barcelona, Spain. Her research interests are in MESFET, HEMT and HBT device modeling, and onwafer noise measurements techniques.
L. Pradell received his telecommunication engineering degree from the Universitat Politècnica de Catalunya (UPC), Barcelona, Spain, in 1981. From 1981 to 1985, he worked at Mier Allende, S.A. (Barcelona) as an RF and microwave system design engineer. In 1985, he joined the faculty at UPC, where he received his PhD degree in 1989. Since 1985, he has been teaching courses on microwave circuits and antennas, and performing research on microwave and millimeterwave devices and systems.
APPENDIX A
APPENDIX B

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