Novel Noise Parameter Determination for On ... - Semantic Scholar
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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 57, NO. 11, NOVEMBER 2008
Novel Noise Parameter Determination for On-Wafer Microwave Noise Measurements Chih-Hung Chen, Member, IEEE, Ying-Lien Wang, Mohamed H. Bakr, Member, IEEE, and Zheng Zeng
Abstract—A novel method to determine the noise parameters of receivers or devices under test (DUTs) for on-wafer microwave noise measurements is presented. An iterative technique is utilized, and fast convergence is achieved by the proposed impedance selection principle. This proposed method reduces the parameter variations in the conventional methods. The impact of the impedance difference on noise parameter determination is experimentally evaluated using a DUT fabricated in a standard 90-nm CMOS technology. Index Terms—High-frequency noise, noise calibration, noise measurement, noise parameters.
I. I NTRODUCTION
T
HE NOISE performance of a noisy linear two-port network is characterized by its noise factor (or noise figure in decibels) and/or its three noise parameters: 1) minimum noise figure N Fmin ; 2) equivalent noise resistance Rn ; and 3) optimized source admittance (Yopt = Gopt + j · Bopt ). The noise factor (figure) concept was first introduced by Friis in 1944 as the ratio of the available signal-to-noise ratio at the input terminals of a two-port network to the available signal-tonoise ratio at its output terminals when the source admittance (or impedance) is at standard temperature To of 290 K [1]. In 1957, the Institute of Radio Engineers (IRE), in practice, defined the spot noise factor (figure) of a linear network at a specified frequency as the ratio of the total output noise power per unit bandwidth available at the output port to the portion of the aforementioned power that was produced by the input terminal at standard temperature To [2]. In 1960, the IRE defined standard methods to measure the noise factor of a noisy two-port network [3], which led to the so-called “Y-factor” method developed later [4]. In the same year, the IRE derived the relationship between the noise factor and its four noise parameters [5]. Since then, two approaches to obtain the noise factors and the noise parameters of a noisy twoport network have been developed. In the first approach, four (or more) noise factors at different source admittances are first Manuscript received June 3, 2007; revised September 30, 2007. First published May 30, 2008; current version published October 10, 2008. This work was supported in part by the National Sciences and Engineering Research Council of Canada, by United Microelectronics Corporation (UMC), by the Canada Foundation for Innovation, by Ontario Innovation Trust, by the Maury Microwave Corporation, CA, and by Giga-Tron Assoc. Ltd., ON, Canada. C.-H. Chen, Y.-L. Wang, and M. H. Bakr are with the Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON L8S 4K1, Canada (e-mail: [email protected]). Z. Zeng is with United Microelectronics Corporation, Sunnyvale, CA 940853903 USA. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIM.2008.925021
obtained using the Y-factor method. This approach requires the noise powers measured in both hot (the noise source is turned on) and cold (the noise source is turned off) states at each source admittance. The four noise parameters are then obtained by solving the linearized noise equations with different algorithms to take care of the experimental errors and the uncertainties in noise factors and source admittances [6]–[15]. The second approach, on the other hand, solves the noise parameters using the power relationship (the noise power is expressed as a function of source admittances with noise parameters as the coefficients). The noise factors are then calculated based on the noise parameters obtained from the power equation [16], [17]. This approach is the foundation of the so-called “cold-only” method, in which the noise power in the hot state is only measured in the system calibration but not in the DUT measurement [18], [19]. With the aggressive downscaling of MOSFET dimensions to sub-100-nm regimes, the unity-gain frequencies fT of sub100-nm MOSFETs have increased to beyond 100 GHz [20]. As predicted by the International Technology Roadmap for Semiconductors 2005, in 2013, transistors with a 22-nm gate length will have their peak fT at about 400 GHz and their N Fmin smaller than 0.2 dB at 5 GHz [21]. The most accurate algorithm calculating the noise parameters of a receiver achieves 0.2-dB accuracy on N Fmin [22]. This means that the maximum uncertainty for the N Fmin characterization of future transistors can be as high as 100% at 5 GHz. Therefore, the algorithm used to obtain the noise parameters plays an increasingly important role in the noise characterization of a DUT with such a small N Fmin . Traditional methods using the Y-factor approach or the power equation approach assume that the source admittances of a noise source in hot (Ysh ) and cold (Ysc ) states are the same. However, as pointed out by Kuhn [23], there is always a difference ΔYs between Ysh and Ysc . This difference results in a change in the DUT gain and consequently affects the noise figure calculation. In 1989, Davidson et al. proposed a method to take care of the impact of this nonzero ΔYs by introducing a k factor [24]. This k factor is defined as k = [Ph /go − Pc /go ]/EN R, where Ph and Pc are the measured noise powers in the hot and cold states, respectively; go is the relative gain; and EN R is the excess noise ratio. However, the relative transducer gain gs and the noise equation Fs = EN R/(Y − 1) used to derive the constant k factor are only valid when ΔYs is zero and cannot be applied to the case when ΔYs is not zero. It thus degrades the accuracy of the method. An improved Y-factor method proposed by Tiemeijer et al. aims at correcting the errors due to ΔYs by calculating the effective Y-factor and effective excess noise ratio [25]. This method needs to measure
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THRU line is connected between the input and output probes. The noise reference plane in Fig. 2 is located at plane B in Fig. 1. The impedance tuner in Fig. 2 includes all the components between the tuner reference plane and plane B. For the receiver, it includes the LNA, the microwave cable, and the NFA. On the other hand, in the device measurement, the THRU line is replaced by the DUT. The noise reference plane is moved to plane A in Fig. 1. The receiver block now includes all the components from the DUT to the NFA. In both calibration and measurement stages, we first measure the S-parameters of the impedance tuner ST and the receiver SR and the reflection coefficients of the source Γs and the receiver Γinr . Based on the noise reference plane defined in Fig. 2, the noise power Pn detected by the NFA is then given by Pn = Fig. 1.
System configuration for high-frequency noise measurements.
both hot and cold noise powers and is much more complicated in solving the noise parameters than conventional cold-only methods. Another method uses the noise power equation to avoid the impact of ΔYs by simultaneously optimizing the receiver gain and the noise parameters [26]. The simultaneous optimization of all parameters of interest, however, may result in a local minimum. This paper presents a novel and simple cold-only powerequation-based algorithm to obtain the power gain and the noise parameters of a receiver (or DUT). Measured Ysh and Ysc are used to avoid the impact of ΔYs when solving the parameters of interest in a noise-measurement system. An iterative approach is utilized to eliminate the impact of the noise parameters on the gain extraction. Finally, the effect of ΔYs and the accuracy of the proposed algorithm are evaluated by the noise parameters of the noise-measurement system and an n-type MOSFET fabricated in a standard 90-nm CMOS technology. As will be demonstrated later in this paper, if the source impedance at 50 Ω is used, the small ΔYs will not affect the calculated noise parameters of a low-gain receiver in practice. However, for the high-gain receiver, the ΔYs needs to be accounted for. II. N EW A LGORITHM FOR R ECEIVER C HARACTERIZATION Our noise measurement system consists of a noise source (Agilent 346C), a vector network analyzer, a noise figure analyzer (NFA), microwave tuners, a low-noise amplifier (LNA), and other peripheral components (e.g., a personal computer and controllers), as shown in Fig. 1. The source tuner provides different source impedances for the receiver, and the load tuner matches the output of the DUT for maximum power transfer. The LNA is used to boost the weak noise signal to increase the accuracy of the measured noise power. It also helps to reduce the noise figure of the receiver by increasing the noise figure accuracy of the DUT, particularly when Friis’ equation is applied in de-embedding the receiver’s noise contribution. In general, the noise system can be modeled as follows: 1) a noise source; 2) an impedance tuner; and 3) a receiver connected in a cascade configuration, as shown in Fig. 2. In the system calibration, a
Gtr · 4kTseff Δf Rs + |iun |2 |Zs |2 + |u|2 4Rs (1) · 1 + |Ycor |2 |Zs |2 + 2Gcor Rs − 2Bcor Xs
where k Δf Rs Xs Zs
Boltzmann’s constant; noise bandwidth; source resistance; source reactance; source impedance seen at the noise reference plane (= Rs + j · Xs ); u ¯ input referred noise voltage [27]; iun input referred noise current [27]; Gcor correlation conductance; Bcor correlation susceptance; complex correlation admittance (= Gcor + j · Ycor Bcor ) [27]; transducer power gain of the receiver; Gtr Tseff effective source temperature experienced at the noise reference plane. It can be shown (see Appendix) that (1) can be rearranged as
Pn Gs |1−Γinr Γs |2 · kTo Δf 1 − |Γs |2 = Tseffnor Gs +|Ys |2 ·A+B +2Gs ·C +2Bs ·D ·Go where To Tseffnor
(2)
standard temperature (= 290 K); normalized effective source temperature (= Tseff /To ); input reflection coefficient of the receiver; Γinr source reflection coefficient; Γs source conductance; Gs source susceptance; Bs source admittance (= Gs + j · Bs ); Ys receiver gain, which is not a function of Γs ; Go A noise parameter (= |u|2 /4kTo Δf ); B noise parameter (= |iun |2 /4kTo Δf + |Ycor |2 · |u|2 /4kTo Δf ); C noise parameter (= Gcor · |u|2 /4kTo Δf ); D noise parameter (= Bcor · |u|2 /4kTo Δf ). As suggested in [16] and [17], the receiver gain Go in (2) can be solved by having one “hot” noise power Ph (Pn measured
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Fig. 2. Schematic diagram for the measurement system shown in Fig. 1.
in the hot state) in addition to four “cold” noise power Pc (Pn measured in the cold state). Here, we assume that the source admittances Ys (or source reflection coefficients Γs ) in both the hot (Ysh = Gsh + j · Bsh or Γsh ) and cold (Ysc = Gsc + j · Bsc or Γsc ) states are not the same. To eliminate the impact of A, B, C, and D in (2) due to ΔYs , an iterative procedure is proposed for the Go extraction. Before applying the procedure, one set of Ph and Pc at one source impedance and N different Pc (N ≥ 4) at other N mutually independent source impedances [10] are first measured. Gain Go and noise parameters A, B, C, and D are extracted in four steps (there is no additional measurement performed between steps).
Once A, B, C, and D are obtained, parameters Ru , Giun , and Ycor are calculated by Ru = A Giun = B −
·
1 kTo Δf · (Tseffnorh Gsh − Tseffnorc Gsc )
Ph Gsh ·
|1 − Γinr Γsh |2 |1 − Γinr Γsc |2 −P G · c sc 1 − |Γsh |2 1 − |sc |2
(3)
(4)
and A, B, C, and D in (4) are solved using the N different Pc values. • Step 3) With the new parameter values of A, B, C, and D obtained in Step 2, calculate gain Go , again using the same set of Ph and Pc used in Step 1 using (5), shown at the bottom of the page. • Step 4) Repeat Steps 2 and 3 until the absolute changes in Go (ΔGo ) are less than a predefined termination value (i.e., ΔGo < ε · Go ). In our case, we use ε = 10−5 .
Go =
Gcor = C/A
(8)
Bcor = D/A.
(9)
N Fmin = 1 + 2Ru Gcor + 2 Ru Giun + (Ru Gcor )2
|Ys |2 · A + B + 2Gs · C + 2Bs · D Pn |1 − Γinr Γs |2 = Gs · · − Tseffnor kTo Δf Go 1 − |Γs |2
Ph Gsh ·
(7)
(10)
where subscripts h and c represent the parameter in the hot and cold states, respectively. • Step 2) With gain Go obtained in Step 1, (2) becomes
C +D A
2
Finally, the noise parameters of the receiver are given by [5]
• Step 1) By setting A = B = C = D = 0 and using the set of measured Ph and Pc values, calculate gain Go by Go =
(6) 2
Rn = Ru Giun + G2cor Gopt = Ru
(11)
Bopt = −Bcor .
(13)
(12)
After the noise parameters at planes A and B defined in Fig. 1 are obtained, the noise parameters of the DUT can be calculated using the noise correlation matrix [30]
dut A
B out † dut † CA = CA − [Adut ][Aout ] CA [A ] [A ]
out dut † [A ] . (14) − [Adut ] CA dut out Here, [CA ] and [CA ] are the correlation matrices of the DUT and the output stage, which starts from the output port of the A ] DUT to the input port of the LNA, respectively. Matrices [CA B and [CA ] are the noise correlation matrices at planes A and B, respectively. Matrices [Adut ] and [Aout ] are the chain matrices of the DUT and the output stage, respectively. Finally, the noise parameters of the DUT can be calculated from its correlation dut ] [31]. matrix [CA
|1−Γinr Γsh |2 1−|Γsh |2
− Pc Gsc ·
|1−Γinr Γsc |2 1−|Γsc |2
kTo Δf · [(Tseffnorh Gsh − Tseffnorc Gsc ) + (|Ysh |2 − |Ysc |2 ) · A + 2(Gsh − Gsc ) · C + 2(Bsh − Bsc ) · D]
(5)
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Fig. 3. Measured output impedances Zns of an Agilent 346C noise source in both (∗) hot and (◦) cold states.
Fig. 5. Source impedances Zs seen at the noise reference plane B in both hot (∗) and (◦) cold states.
Fig. 4. Normalized difference in Zns for a representative noise source between its hot and cold states.
III. M EASUREMENT AND D ISCUSSION The measurement system used in this study (see Fig. 1) operates from 4 to 26.5 GHz. Fig. 3 shows the measured output impedances Zns versus the frequency characteristics of a representative noise source in both hot and cold states from 0.5 to 26.5 GHz. At most of the frequencies studied, Zns is about 50 Ω in both states. However, there exist finite differences ΔZns in Zns between its hot (Znsh ) and cold (Znsc ) states, and Fig. 4 shows the normalized difference. This normalized difference between impedances decreases from 18.4% to 5% when the operation frequency increases from 0.5 to 26.5 GHz. Fig. 5 shows source impedances Zs (seen at the reference plane B) at different tuner positions in the system calibration. These impedance points are calculated based on the measured output impedances of the noise source in both hot and cold states, and the measured S-parameters of the source tuner, the THRU line, and the load tuner in a cascade configuration at 8 GHz. The ΔZns is manifested as the difference ΔZs in Zs between its hot (Zsh ) and cold (Zsc ) states. ΔZs (i.e., |Zsh − Zsc |) is large for the tuner position, resulting in the
Fig. 6. Measured noise powers Ph and Pc as a function of the source impedance at 8 GHz.
source impedance close to the center of the Smith chart. On the other hand, ΔZs is small for the tuner position corresponding to the source impedance away from the center of the chart. In addition, the source impedances close to the center of the Smith chart are more sensitive to the impedance uncertainty. For example, if Z1 = 50 Ω, Z2 = 1000 Ω, and ΔZs = 5%, then ΔΓ1 = 0.0244 and ΔΓ2 = 0.0043 in a 50-Ω system, i.e., ΔΓ1 is more than five times larger than ΔΓ2 . Therefore, according to the classical method requiring Zsh = Zsc (or Γsh = Γsc ) [17], it seems that these tuner positions, resulting in the source impedances close to the border of the Smith chart, are better choices. This is because their Zsh and Zsc (or Γsh and Γsc ) are about the same and less sensitive to the impedance error. Fig. 6, however, shows, that at these tuner positions, because of the high tuner attenuations, it results in low measured noise powers, particularly for Ph . Due to the reduced power
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Fig. 9.
Extracted receiver gain Go as a function of the number of iterations.
Fig. 7. Selection of tuner position index Mindex and its corresponding source impedance in cold state on the Smith chart.
Fig. 8. Calculated receiver gain Go as a function of Mindex using (−) the proposed method and (◦) the classical method in [17].
difference between Ph and Pc , the solution of the receiver gain Go obtained by (3) is more vulnerable to measurement errors (see Fig. 8). Next, we would like to compare the extracted receiver gain Go obtained using our proposed method and the classical method in [16] (or [17]). The classical method does not specifically indicate at which tuner position its Ph and Pc should be used to extract Go . Therefore, receiver gain Go is extracted, demonstrated, and compared using the measured Ph and Pc at each calibrated tuner position. To have a clear demonstration of these parameters versus the tuner position characteristics, we introduce a tuner position index Mindex . Fig. 7 shows how this Mindex is defined and its corresponding location (in the cold state) on the Smith chart. For example, the impedance points for Mindex = 1−50 have the largest |Γs | (∼0.75 at 8 GHz). On the other hand, the point with Mindex = 225 is the impedance closest to 50 Ω. Fig. 8 shows the extracted receiver gain Go as a function of Mindex in the calibration stage. The results are obtained
using the classical method [17] and our proposed method. As demonstrated in the derivation [see (16)], the receiver gain Go should be independent of the source impedance (or Mindex ). However, we observed in Fig. 8 that the extracted Go based on the classical method shows a strong impedance dependency and a large gain variation. This gain uncertainty complicates the determination of the single-valued receiver gain Go expected in theory. On the other hand, the extracted gain Go using our proposed method has a very weak Mindex dependency for Mindex , ranging from 50 to 225 (i.e., |Γs | < 0.7). The small gain variation in this range might result from the uncertainties in the measured Ph and Pc [32]. Therefore, the big gain uncertainty in the classical method for |Γs | < 0.7 is mainly due to not taking care of the difference ΔΓs between Γsh and Γsc . Our proposed method reduces the gain uncertainty (or fluctuation) from 8.98% to 2.45% in the extracted Go values. Another observation in Fig. 8 is that the gain variation in the classical method is reduced and converges when the Mindex used in the Go extraction moves toward the center of the Smith chart. This is because a higher Ph and a higher Tseffnorh are obtained when Mindex moves toward 50 Ω, and they become the dominant terms (i.e., Ph Pc and Tseffnorh Tseffnorc ) in (5). In this case, ΔΓs is not critical when solving receiver gain Go in the calibration stage. Therefore, in this paper, the noise powers at the source impedances closest to 50 Ω will be used to solve the receiver gains in both the calibration and measurement stages. The other observation seen in Fig. 8 is that for |Γs | > 0.7 (i.e., Mindex = 1−50), the extracted receiver gain using our proposed method also shows a large gain variation (or uncertainty), even if it is smaller than that using the classical method. Because the ΔΓs in this region is small (see Fig. 5), it should not be fully responsible for this large gain uncertainty. The exact physical mechanism is not clear to us at this moment. This might be due to the impedance uncertainties caused by the calibration accuracy of the network analyzer [15], and further investigations are needed. Fig. 9 shows the extracted receiver gain Go versus the number of iterations using our algorithm. We found that the solution usually converges after the third iteration, and this makes our
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TABLE I EXTRACTED NOISE PARAMETERS AND GAIN Go OF THE RECEIVER IN THE C ALIBRATION S TAGE U SING THE P ROPOSED M ETHOD AND THE C LASSICAL M ETHOD (V ALUES IN B RACKETS )
Fig. 10. Measured and simulated Pc of the whole noise measurement system in the calibration stage at 8 GHz.
Fig. 11. Measured and simulated Ph of the whole noise measurement system in the calibration stage at 8 GHz.
proposed method very practical in real applications. With the source impedance at (or close to) 50 Ω, it results in a very high Ph and a very high Tseffnorh and reduces the impact of A, B, C, and D in (5). Therefore, the number of iterations required for the parameters of interest to converge can always be minimized in practice. Figs. 10 and 11 show the measured and simulated noise powers (Ph and Pc ) of the whole measurement system in the calibration stage, respectively. The operation frequency is 8 GHz, and ambient temperature Tc is 26 ◦ C. The simulation results are obtained using N Fmin = 3.81 dB, Rn = 20.9 Ω, Γopt = 0.276 ∠ 117◦ , and Go = −6.18 dB, with the noise reference plane at plane B in Fig. 1. A very good agreement between the measured and simulated noise powers has been achieved. This demonstrates the accuracy of the noise model and the extracted parameter values for the measurement system at 8 GHz. Table I shows the extracted noise parameters and power gains of the receiver from 4 to 26 GHz, with a 2-GHz frequency step.
Fig. 12. Measured transducer gain of the NFA, the available gain of the cable, and the available gain of the LNA in the calibration stage.
All these results have similar accuracy as that at 8 GHz. The parameter values in brackets are obtained using the classical method. It can be seen that, using the Ph and the Pc at 50 Ω to extract Go , both methods predict similar results at all frequencies in the calibration stage. We noticed that the receiver gains of the measurement system in Table I are all less than 0 dB. To find the origin of the loss, the gains of the receiver’s components, i.e., the NFA, the cable, and the LNA, are measured. Fig. 12 shows that the transducer gain
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Fig. 13. Measured and calculated noise figures of the receiver in the calibration stage.
of the NFA is between −26 and −33 dB, the available gain of the cable is between −0.9 and −2.5 dB, and the available gain of the LNA is between 20 and 22 dB. Therefore, we conclude that the negative Go in decibels is because of the huge loss in the NFA. Fig. 13 shows the measured and calculated noise figures of the receiver in the calibration stage. The calculated noise figures are based on the noise parameters in Table I. They are within ±5% of the measured data. Because the uncertainty of the measured noise figures is about 10% [32], Fig. 13 shows that the ±5% difference between the measured and calculated noise figures is within the measurement uncertainty. It also confirms the accuracy of both the extracted noise parameters in Table I and the noise model for the noise measurement system at all calibrated frequencies. After the system calibration, the THRU line is replaced by the DUT, which includes probe pads, metal interconnections, and an n-type MOSFET with W/L = 128 × 1 μm/90 nm fabricated in a standard 90-nm CMOS technology. This DUT is biased at VGS = 1.0 V and VDS = 0.8 V with dc current IDS = 36.8 mA. The noise parameters of this “new” receiver with the DUT and the noise reference plane at plane A in Fig. 1 are extracted at each frequency. The noise parameters of the DUT are then calculated using (14). To avoid the potential error due to a small number of preselected impedance points, noise powers at all calibrated impedance points are measured and used in the noise parameter extraction. However, this implies a long measurement time at each frequency (e.g., it takes about 1.5 h to measure the noise powers for about 200 impedance points using mechanical tuners). To keep a good probe contact on the aluminum pads throughout the measurement, we measured the DUT from 4 to 22 GHz, with a 2-GHz step. This allows us to finish the noise measurement for one bias condition within 15 h, which is the longest time to maintain a reliable probe contact, based on our experience. Figs. 14–17 show the extracted noise parameters of the DUT (without de-embedding the parasitic effects of probe pads and
Fig. 14. Calculated N Fmin as a function of frequency for an n-type MOSFET with W/L = 128 × 1 μm/90 nm biased at VGS = 1.0 V and VDS = 0.8 V using the classical method, the method in [24], and the proposed method.
Fig. 15. Calculated Rn as a function of frequency for an n-type MOSFET with W/L = 128 × 1 μm/90 nm biased at VGS = 1.0 V and VDS = 0.8 V using the classical method, the method in [24], and the proposed method.
Fig. 16. Calculated |Γopt | as a function of frequency for an n-type MOSFET with W/L = 128 × 1 μm/90 nm biased at VGS = 1.0 V and VDS = 0.8 V using the classical method, the method in [24], and the proposed method.
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that the hot noise power and the cold noise power at 50-Ω source impedance should be used to solve the receiver gains. Our proposed method improves the parameter accuracy when the impedance point other than 50 Ω is used to solve the receiver gain. The small impedance difference between the hot and cold states needs to be taken care of, particularly for the high-gain receiver. A PPENDIX In (1), Gtr is the transducer power gain of the receiver, which is defined as [29] Gtr = Fig. 17. Calculated ∠Γopt as a function of frequency for an n-type MOSFET with W/L = 128 × 1 μm/90 nm biased at VGS = 1.0 V and VDS = 0.8 V using the classical method, the method in [24], and the proposed method.
interconnections) as a function of frequency using the classical method [16], the method in [24], and our proposed method. The symbols are obtained using the k factor and Go at 50-Ω source impedance. The upper and lower bounds of the error bars at each frequency represent the maximum and minimum parameter values obtained using the k factor and Go at other impedance points. In comparison with the results from the classical method, both the method in [24] and our proposed method improve the accuracy by reducing the data variation, particularly for N Fmin and |Γopt |. The poor accuracy in the classical method is because receiver gain Go increases as a result of the active device (e.g., Go increases from −5.16 to 6.05 dB at 6 GHz). When Go becomes high, from (20), the measured noise powers are much more sensitive to the mismatch between the output impedances of the noise source in the hot and cold states. Therefore, the impedance mismatch has to be taken care of when measuring high-gain devices using a noise source with high EN R values [33]. Based on the observations in Table I (for a low-gain receiver) and in Figs. 14–17 (for a high-gain receiver), we conclude that when the Ph and the Pc at 50-Ω source impedance are used to extract receiver gain Go , the impact of ΔYs needs to be considered only for the high-gain receiver but not for the low-gain receiver. Finally, when comparing the parameter values with the k factor and Go obtained at impedance points other than 50 Ω, the parameters from the method in [24] show a bigger parameter variation (i.e., longer error bars) compared to those obtained by our proposed method, particularly for N Fmin and Rn . This is because the k factor derived in [24] is based on Fs = EN R/(Y − 1), which is only valid when Γsh = Γsc . For Γsh = Γsc , the improved Y-factor equation in [25] should be used in the derivation of the k factor.
=
1 − |Γs |2 |s21r |2 1 − |Γl |2
|(1 − s11r Γs )(1 − s22r Γl ) − s12r s21r Γs Γl |2 1 − |Γs |2 · Go |1 − Γinr Γs |2
(15)
where Γinr is the input reflection coefficient of the receiver. Here, Go is a parameter that is not a function of source impedance and is given by Go =
|s21r |2 1 − |Γl |2 . |1 − s22r Γl |2
(16)
On the other hand, Tseff in (1) is the effective source temperature experienced at the noise reference plane, which is given by Tseff = (Ts − Tc ) · Gavt + Tc
(17)
where Ts is the source temperature, Tc is the ambient temperature, and
Gavt
1 − |Γns |2 |s21t |2 = 2 12t s21t Γns |1 − s11t Γns |2 1 − s22t + s1−s 11t Γns
(18)
which is the available power gain of the impedance tuner. For the source temperature Ts in (17), it is equal to Tc in the cold state and Th in the hot state, where Th is given by [4], [25] Th = (EN R + 1)To .
(19)
Now, if we define three new parameters Tseffnor , Ru , and Giun as Tseffnor = Tseff /To , Ru = |u|2 /4kTo Δf , and Giun = |iun |2 /4kTo Δf , (1) then becomes kTo Δf 1 − |Γs |2 · · Go [tseffnor Gs + Ru Gs |1 − Γinr Γs |2 · |Ys |2 + |Ycor |2 + 2Gcor Gs + 2Bcor Bs + Giun .
Pn = IV. C ONCLUSION A novel iterative method to improve the noise parameter determination without requiring the same source impedance value in the hot and cold states was presented. Our results show
(20)
If we define A = Ru , B = Giun +|Ycor |22 ·Ru , C = Gcor ·Ru , and D = Bcor · Ru , (20) can be rearranged to become (2).
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ACKNOWLEDGMENT The authors would like to thank G. Simpson, E. Kueckels, and R. Wallace of Maury Microwave, CA, for their assistance in operating their automated tuner system; Prof. M. J. Deen and Dr. O. Marinov of the Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON, Canada, for their assistance in microwave noise measurements; and B. Hung, V. Liang, J. S. Jan, K. C. Wang, and C. S. Yeh of United Microelectronics Corporation for their assistance in device fabrication. R EFERENCES [1] H. T. Friis, “Noise figures of radio receivers,” Proc. IRE, vol. 32, no. 7, pp. 419–422, Jul. 1944. [2] “IRE standards on electron tubes: Definitions of terms, 1957,” Proc. IRE, vol. 45, no. 7, pp. 983–1010, Jul. 1957. [3] “IRE standards on methods of measuring noise in linear two ports, 1959,” Proc. IRE, vol. 48, no. 1, pp. 60–68, Jan. 1960. [4] Fundamentals of RF and Microwave Noise Figure Measurements. Agilent Application Note 57-1. [5] “Representation of noise in linear two ports,” Proc. IRE, vol. 48, no. 1, pp. 69–74, Jan. 1960. [6] R. Q. Lane, “The determination of device noise parameters,” Proc. IEEE, vol. 57, no. 8, pp. 1461–1462, Aug. 1969. [7] M. S. Gupta, “Determination of the noise parameters of a linear 2-port,” Electron. Lett., vol. 6, no. 17, pp. 543–544, Aug. 20, 1970. [8] G. Caruso and M. Sannino, “Computer-aided determination of microwave two-port noise parameters,” IEEE Trans. Microw. Theory Tech., vol. MTT26, no. 9, pp. 639–642, Sep. 1978. [9] M. Mitama and H. Katoh, “An improved computational method for noise parameter measurement,” IEEE Trans. Microw. Theory Tech., vol. MTT27, no. 6, pp. 612–615, Jun. 1979. [10] M. Sannino, “On the determination of device noise and gain parameters,” Proc. IEEE, vol. 67, no. 9, pp. 1364–1366, Sep. 1979. [11] G. I. Vasilescu, G. Alquie, and M. Krim, “Exact computation of twoport noise parameters,” Electron. Lett., vol. 25, no. 4, pp. 292–293, Feb. 16, 1988. [12] J. M. O’Callaghan and J. P. Mondal, “A vector approach for noise parameter fitting and selection of source admittances,” IEEE Trans. Microw. Theory Tech., vol. 39, no. 8, pp. 1376–1382, Aug. 1991. [13] J. W. Archer and R. A. Batchelor, “Fully automated on-wafer noise characterization of GaAs MESFET’s and HEMT’s,” IEEE Trans. Microw. Theory Tech., vol. 40, no. 2, pp. 209–216, Feb. 1992. [14] A. Boudiaf and M. Laporte, “An accurate and repeatable technique for noise parameter measurements,” IEEE Trans. Instrum. Meas., vol. 42, no. 2, pp. 532–537, Apr. 1993. [15] W. Wiatr and D. K. Walker, “Systematic errors of noise parameter determination caused by imperfect source impedance measurement,” IEEE Trans. Instrum. Meas., vol. 54, no. 2, pp. 696–700, Apr. 2005. [16] V. Adamian and A. Uhlir, “A novel procedure for receiver noise characterization,” IEEE Trans. Instrum. Meas., vol. IM-22, no. 2, pp. 181–182, Jun. 1973. [17] M. N. Tutt, “Low and high frequency noise properties of heterojunction transistors,” Ph.D. dissertation, Dept. Elect. Eng., Comput. Sci., Univ. Michigan, Ann Harbor, MI, 1994. [18] R. Meierer and C. Tsironis, “An on-wafer noise parameter measurement technique with automatic receiver calibration,” Microw. J., vol. 38, no. 3, pp. 22–37, Mar. 1995. [19] M. Kantanen, M. Lahdes, T. Vähä-Heikkilä, and J. Tuovinen, “A wideband on-wafer noise parameter measurement system at 50–75 GHz,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 5, pp. 1489–1495, May 2003. [20] J.-C. Guo and Y.-M. Lin, “A new lossy substrate de-embedding method for sub-100 nm RF CMOS noise extraction and modeling,” IEEE Trans. Electron Devices, vol. 53, no. 2, pp. 339–347, Feb. 2006. [21] International Technology Roadmap for Semiconductors (ITRS), 2005. [Online]. Available: http://www.itrs.net/reports.html [22] L. Escottee, R. Plana, and J. Graffeuil, “Evaluation of noise parameter extraction methods,” IEEE Trans. Microw. Theory Tech., vol. 41, no. 3, pp. 382–387, Mar. 1993. [23] N. J. Kuhn, “Curing a subtle but significant cause of noise figure error,” Microw. J., vol. 27, no. 6, pp. 85–98, Jun. 1984.
[24] A. C. Davidson, B. W. Leake, and E. Strid, “Accuracy improvements in microwave noise parameter measurements,” IEEE Trans. Microw. Theory Tech., vol. 37, no. 12, pp. 1973–1978, Dec. 1989. [25] L. F. Tiemeijer, R. Havens, R. Kort, and A. J. Scholten, “Improved Y-factor method for wide-band on-wafer noise parameter measurements,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 9, pp. 2917–2925, Sep. 2005. [26] Theory of Noise Measurement, Jul. 6, 1999, Maury Microwave. Application Note: 5C-042. [27] H. Rothe and W. Dahlke, “Theory of noisy fourpoles,” Proc. IRE, vol. 44, no. 6, pp. 811–818, Jun. 1956. [28] V. Adamian and A. Uhlir, “Simplified noise evaluation of microwave receivers,” IEEE Trans. Instrum. Meas., vol. IM-33, no. 2, pp. 136–140, Jun. 1984. [29] M. W. Medley, Microwave and RF Circuits: Analysis, Synthesis and Design. Norwood, MA: Artech House, 1993. [30] H. Hillbrand and P. H. Russer, “An efficient method for computer-aided noise analysis of linear amplifier networks,” IEEE Trans. Circuits Syst., vol. CAS-23, no. 4, pp. 235–238, Apr. 1976. [31] C. H. Chen, M. J. Deen, Y. Cheng, and M. Matloubian, “Extraction of the induced gate noise, channel thermal noise and their correlation in submicron MOSFETs from RF noise measurements,” IEEE Trans. Electron Devices, vol. 48, no. 12, pp. 2884–2892, Dec. 2001. [32] Agilent Noise Figure Analyzers NFA Series Calibration and Performance Verification Guide, Agilent Technol., Santa Clara, CA, 2001, p. 95. [33] 10 Hints for Making Successful Noise Figure Measurements, p. 4. Agilent Application Note 57-3.
Chih-Hung Chen (S’95–M’03) received the B.S. degree in electrical engineering from National Central University, Chungli, Taiwan, R.O.C., in 1991, the M.S. degree in engineering science from Simon Fraser University, Burnaby, BC, Canada, in 1997, and the Ph.D. degree from McMaster University, Hamilton, ON, Canada, in 2002. During the summers of 1998–2000, he was with Conexant Systems Inc., Newport Beach, CA, where he was involved in the high-frequency noise characterization and modeling of MOSFETs and BJTs. During the summer of 2001, he was with Transilica Inc. (now Microtune Inc.), San Diego, CA, where he was engaged in the design of differential LNAs and VCOs for Bluetooth. In 2002, he joined the faculty of the Department of Electrical and Computer Engineering, McMaster University, as an Assistant Professor of electrical and computer engineering. His research interests are high-frequency noise characterization techniques, modeling of sub-100-nm MOSFETs, and designs of low-noise RF CMOS integrated circuits for wireless applications. Dr. Chen was the recipient of the New Opportunities Fund Award 2004 from the Canada Foundation for Innovation and the Best Invited Paper Award at the 2002 IEEE Custom Integrated Circuits Conference.
Ying-Lien Wang received the B.A.Sc. degree in electrical engineering from the University of Waterloo, Waterloo, ON, Canada, in 2005. He is currently working toward the M.A.Sc. degree with the Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON. His current research interest is accuracy improvement of high-frequency noise measurements for sub100-nm MOSFETs.
CHEN et al.: NOVEL NOISE PARAMETER DETERMINATION FOR ON-WAFER MICROWAVE NOISE MEASUREMENTS
Mohamed H. Bakr (S’98–M’00) received the B.Sc. degree [with distinction (honors)] in electronics and communications engineering and the M.Sc. degree in engineering mathematics from Cairo University, Giza, Egypt, in 1992 and 1996, respectively, and the Ph.D. degree from McMaster University, Hamilton, ON, Canada, in 2000. In 1997, he was a Student Intern with Optimization Systems Associates, Inc., Dundas, ON. From 1998 to 2000, he was a Research Assistant with the Simulation Optimization Systems Research Laboratory, McMaster University. In November 2000, he joined the Computational Electromagnetics Research Laboratory, University of Victoria, Victoria, BC, Canada, as an NSERC Postdoctoral Fellow. He is currently an Associate Professor with the Department of Electrical and Computer Engineering, McMaster University. His research interests include optimization methods, computeraided design and modeling of microwave and photonic circuits, neural network applications, smart analysis of microwave circuits, efficient optimization using time/frequency-domain methods, and bioelectromagnetism. Dr. Bakr was a recipient of a Premier’s Research Excellence Award from the province of Ontario in 2003.
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Zheng Zeng received the Ph.D. degree from the Department of Electronic Engineering, Xi’an Jiaotong University, Xi’an, China, in 1993. In December 1993, he joined Xi’an Jiaotong University as an Associate Professor of electronic engineering. From 1997 to 2001, he was a Principal Engineer with Chartered Semiconductor MFG, Singapore, where he worked on process integration and device modeling for BiCMOS and RFCMOS processes. In 2002, he joined United Microelectronics Corporation, Sunnyvale, CA, as a Senior Engineering Manager for device modeling, where he works on device characterization and modeling for advanced RFCMOS process.
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 57, NO. 11, NOVEMBER 2008
Novel Noise Parameter Determination for On-Wafer Microwave Noise Measurements Chih-Hung Chen, Member, IEEE, Ying-Lien Wang, Mohamed H. Bakr, Member, IEEE, and Zheng Zeng
Abstract—A novel method to determine the noise parameters of receivers or devices under test (DUTs) for on-wafer microwave noise measurements is presented. An iterative technique is utilized, and fast convergence is achieved by the proposed impedance selection principle. This proposed method reduces the parameter variations in the conventional methods. The impact of the impedance difference on noise parameter determination is experimentally evaluated using a DUT fabricated in a standard 90-nm CMOS technology. Index Terms—High-frequency noise, noise calibration, noise measurement, noise parameters.
I. I NTRODUCTION
T
HE NOISE performance of a noisy linear two-port network is characterized by its noise factor (or noise figure in decibels) and/or its three noise parameters: 1) minimum noise figure N Fmin ; 2) equivalent noise resistance Rn ; and 3) optimized source admittance (Yopt = Gopt + j · Bopt ). The noise factor (figure) concept was first introduced by Friis in 1944 as the ratio of the available signal-to-noise ratio at the input terminals of a two-port network to the available signal-tonoise ratio at its output terminals when the source admittance (or impedance) is at standard temperature To of 290 K [1]. In 1957, the Institute of Radio Engineers (IRE), in practice, defined the spot noise factor (figure) of a linear network at a specified frequency as the ratio of the total output noise power per unit bandwidth available at the output port to the portion of the aforementioned power that was produced by the input terminal at standard temperature To [2]. In 1960, the IRE defined standard methods to measure the noise factor of a noisy two-port network [3], which led to the so-called “Y-factor” method developed later [4]. In the same year, the IRE derived the relationship between the noise factor and its four noise parameters [5]. Since then, two approaches to obtain the noise factors and the noise parameters of a noisy twoport network have been developed. In the first approach, four (or more) noise factors at different source admittances are first Manuscript received June 3, 2007; revised September 30, 2007. First published May 30, 2008; current version published October 10, 2008. This work was supported in part by the National Sciences and Engineering Research Council of Canada, by United Microelectronics Corporation (UMC), by the Canada Foundation for Innovation, by Ontario Innovation Trust, by the Maury Microwave Corporation, CA, and by Giga-Tron Assoc. Ltd., ON, Canada. C.-H. Chen, Y.-L. Wang, and M. H. Bakr are with the Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON L8S 4K1, Canada (e-mail: [email protected]). Z. Zeng is with United Microelectronics Corporation, Sunnyvale, CA 940853903 USA. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIM.2008.925021
obtained using the Y-factor method. This approach requires the noise powers measured in both hot (the noise source is turned on) and cold (the noise source is turned off) states at each source admittance. The four noise parameters are then obtained by solving the linearized noise equations with different algorithms to take care of the experimental errors and the uncertainties in noise factors and source admittances [6]–[15]. The second approach, on the other hand, solves the noise parameters using the power relationship (the noise power is expressed as a function of source admittances with noise parameters as the coefficients). The noise factors are then calculated based on the noise parameters obtained from the power equation [16], [17]. This approach is the foundation of the so-called “cold-only” method, in which the noise power in the hot state is only measured in the system calibration but not in the DUT measurement [18], [19]. With the aggressive downscaling of MOSFET dimensions to sub-100-nm regimes, the unity-gain frequencies fT of sub100-nm MOSFETs have increased to beyond 100 GHz [20]. As predicted by the International Technology Roadmap for Semiconductors 2005, in 2013, transistors with a 22-nm gate length will have their peak fT at about 400 GHz and their N Fmin smaller than 0.2 dB at 5 GHz [21]. The most accurate algorithm calculating the noise parameters of a receiver achieves 0.2-dB accuracy on N Fmin [22]. This means that the maximum uncertainty for the N Fmin characterization of future transistors can be as high as 100% at 5 GHz. Therefore, the algorithm used to obtain the noise parameters plays an increasingly important role in the noise characterization of a DUT with such a small N Fmin . Traditional methods using the Y-factor approach or the power equation approach assume that the source admittances of a noise source in hot (Ysh ) and cold (Ysc ) states are the same. However, as pointed out by Kuhn [23], there is always a difference ΔYs between Ysh and Ysc . This difference results in a change in the DUT gain and consequently affects the noise figure calculation. In 1989, Davidson et al. proposed a method to take care of the impact of this nonzero ΔYs by introducing a k factor [24]. This k factor is defined as k = [Ph /go − Pc /go ]/EN R, where Ph and Pc are the measured noise powers in the hot and cold states, respectively; go is the relative gain; and EN R is the excess noise ratio. However, the relative transducer gain gs and the noise equation Fs = EN R/(Y − 1) used to derive the constant k factor are only valid when ΔYs is zero and cannot be applied to the case when ΔYs is not zero. It thus degrades the accuracy of the method. An improved Y-factor method proposed by Tiemeijer et al. aims at correcting the errors due to ΔYs by calculating the effective Y-factor and effective excess noise ratio [25]. This method needs to measure
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THRU line is connected between the input and output probes. The noise reference plane in Fig. 2 is located at plane B in Fig. 1. The impedance tuner in Fig. 2 includes all the components between the tuner reference plane and plane B. For the receiver, it includes the LNA, the microwave cable, and the NFA. On the other hand, in the device measurement, the THRU line is replaced by the DUT. The noise reference plane is moved to plane A in Fig. 1. The receiver block now includes all the components from the DUT to the NFA. In both calibration and measurement stages, we first measure the S-parameters of the impedance tuner ST and the receiver SR and the reflection coefficients of the source Γs and the receiver Γinr . Based on the noise reference plane defined in Fig. 2, the noise power Pn detected by the NFA is then given by Pn = Fig. 1.
System configuration for high-frequency noise measurements.
both hot and cold noise powers and is much more complicated in solving the noise parameters than conventional cold-only methods. Another method uses the noise power equation to avoid the impact of ΔYs by simultaneously optimizing the receiver gain and the noise parameters [26]. The simultaneous optimization of all parameters of interest, however, may result in a local minimum. This paper presents a novel and simple cold-only powerequation-based algorithm to obtain the power gain and the noise parameters of a receiver (or DUT). Measured Ysh and Ysc are used to avoid the impact of ΔYs when solving the parameters of interest in a noise-measurement system. An iterative approach is utilized to eliminate the impact of the noise parameters on the gain extraction. Finally, the effect of ΔYs and the accuracy of the proposed algorithm are evaluated by the noise parameters of the noise-measurement system and an n-type MOSFET fabricated in a standard 90-nm CMOS technology. As will be demonstrated later in this paper, if the source impedance at 50 Ω is used, the small ΔYs will not affect the calculated noise parameters of a low-gain receiver in practice. However, for the high-gain receiver, the ΔYs needs to be accounted for. II. N EW A LGORITHM FOR R ECEIVER C HARACTERIZATION Our noise measurement system consists of a noise source (Agilent 346C), a vector network analyzer, a noise figure analyzer (NFA), microwave tuners, a low-noise amplifier (LNA), and other peripheral components (e.g., a personal computer and controllers), as shown in Fig. 1. The source tuner provides different source impedances for the receiver, and the load tuner matches the output of the DUT for maximum power transfer. The LNA is used to boost the weak noise signal to increase the accuracy of the measured noise power. It also helps to reduce the noise figure of the receiver by increasing the noise figure accuracy of the DUT, particularly when Friis’ equation is applied in de-embedding the receiver’s noise contribution. In general, the noise system can be modeled as follows: 1) a noise source; 2) an impedance tuner; and 3) a receiver connected in a cascade configuration, as shown in Fig. 2. In the system calibration, a
Gtr · 4kTseff Δf Rs + |iun |2 |Zs |2 + |u|2 4Rs (1) · 1 + |Ycor |2 |Zs |2 + 2Gcor Rs − 2Bcor Xs
where k Δf Rs Xs Zs
Boltzmann’s constant; noise bandwidth; source resistance; source reactance; source impedance seen at the noise reference plane (= Rs + j · Xs ); u ¯ input referred noise voltage [27]; iun input referred noise current [27]; Gcor correlation conductance; Bcor correlation susceptance; complex correlation admittance (= Gcor + j · Ycor Bcor ) [27]; transducer power gain of the receiver; Gtr Tseff effective source temperature experienced at the noise reference plane. It can be shown (see Appendix) that (1) can be rearranged as
Pn Gs |1−Γinr Γs |2 · kTo Δf 1 − |Γs |2 = Tseffnor Gs +|Ys |2 ·A+B +2Gs ·C +2Bs ·D ·Go where To Tseffnor
(2)
standard temperature (= 290 K); normalized effective source temperature (= Tseff /To ); input reflection coefficient of the receiver; Γinr source reflection coefficient; Γs source conductance; Gs source susceptance; Bs source admittance (= Gs + j · Bs ); Ys receiver gain, which is not a function of Γs ; Go A noise parameter (= |u|2 /4kTo Δf ); B noise parameter (= |iun |2 /4kTo Δf + |Ycor |2 · |u|2 /4kTo Δf ); C noise parameter (= Gcor · |u|2 /4kTo Δf ); D noise parameter (= Bcor · |u|2 /4kTo Δf ). As suggested in [16] and [17], the receiver gain Go in (2) can be solved by having one “hot” noise power Ph (Pn measured
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Fig. 2. Schematic diagram for the measurement system shown in Fig. 1.
in the hot state) in addition to four “cold” noise power Pc (Pn measured in the cold state). Here, we assume that the source admittances Ys (or source reflection coefficients Γs ) in both the hot (Ysh = Gsh + j · Bsh or Γsh ) and cold (Ysc = Gsc + j · Bsc or Γsc ) states are not the same. To eliminate the impact of A, B, C, and D in (2) due to ΔYs , an iterative procedure is proposed for the Go extraction. Before applying the procedure, one set of Ph and Pc at one source impedance and N different Pc (N ≥ 4) at other N mutually independent source impedances [10] are first measured. Gain Go and noise parameters A, B, C, and D are extracted in four steps (there is no additional measurement performed between steps).
Once A, B, C, and D are obtained, parameters Ru , Giun , and Ycor are calculated by Ru = A Giun = B −
·
1 kTo Δf · (Tseffnorh Gsh − Tseffnorc Gsc )
Ph Gsh ·
|1 − Γinr Γsh |2 |1 − Γinr Γsc |2 −P G · c sc 1 − |Γsh |2 1 − |sc |2
(3)
(4)
and A, B, C, and D in (4) are solved using the N different Pc values. • Step 3) With the new parameter values of A, B, C, and D obtained in Step 2, calculate gain Go , again using the same set of Ph and Pc used in Step 1 using (5), shown at the bottom of the page. • Step 4) Repeat Steps 2 and 3 until the absolute changes in Go (ΔGo ) are less than a predefined termination value (i.e., ΔGo < ε · Go ). In our case, we use ε = 10−5 .
Go =
Gcor = C/A
(8)
Bcor = D/A.
(9)
N Fmin = 1 + 2Ru Gcor + 2 Ru Giun + (Ru Gcor )2
|Ys |2 · A + B + 2Gs · C + 2Bs · D Pn |1 − Γinr Γs |2 = Gs · · − Tseffnor kTo Δf Go 1 − |Γs |2
Ph Gsh ·
(7)
(10)
where subscripts h and c represent the parameter in the hot and cold states, respectively. • Step 2) With gain Go obtained in Step 1, (2) becomes
C +D A
2
Finally, the noise parameters of the receiver are given by [5]
• Step 1) By setting A = B = C = D = 0 and using the set of measured Ph and Pc values, calculate gain Go by Go =
(6) 2
Rn = Ru Giun + G2cor Gopt = Ru
(11)
Bopt = −Bcor .
(13)
(12)
After the noise parameters at planes A and B defined in Fig. 1 are obtained, the noise parameters of the DUT can be calculated using the noise correlation matrix [30]
dut A
B out † dut † CA = CA − [Adut ][Aout ] CA [A ] [A ]
out dut † [A ] . (14) − [Adut ] CA dut out Here, [CA ] and [CA ] are the correlation matrices of the DUT and the output stage, which starts from the output port of the A ] DUT to the input port of the LNA, respectively. Matrices [CA B and [CA ] are the noise correlation matrices at planes A and B, respectively. Matrices [Adut ] and [Aout ] are the chain matrices of the DUT and the output stage, respectively. Finally, the noise parameters of the DUT can be calculated from its correlation dut ] [31]. matrix [CA
|1−Γinr Γsh |2 1−|Γsh |2
− Pc Gsc ·
|1−Γinr Γsc |2 1−|Γsc |2
kTo Δf · [(Tseffnorh Gsh − Tseffnorc Gsc ) + (|Ysh |2 − |Ysc |2 ) · A + 2(Gsh − Gsc ) · C + 2(Bsh − Bsc ) · D]
(5)
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Fig. 3. Measured output impedances Zns of an Agilent 346C noise source in both (∗) hot and (◦) cold states.
Fig. 5. Source impedances Zs seen at the noise reference plane B in both hot (∗) and (◦) cold states.
Fig. 4. Normalized difference in Zns for a representative noise source between its hot and cold states.
III. M EASUREMENT AND D ISCUSSION The measurement system used in this study (see Fig. 1) operates from 4 to 26.5 GHz. Fig. 3 shows the measured output impedances Zns versus the frequency characteristics of a representative noise source in both hot and cold states from 0.5 to 26.5 GHz. At most of the frequencies studied, Zns is about 50 Ω in both states. However, there exist finite differences ΔZns in Zns between its hot (Znsh ) and cold (Znsc ) states, and Fig. 4 shows the normalized difference. This normalized difference between impedances decreases from 18.4% to 5% when the operation frequency increases from 0.5 to 26.5 GHz. Fig. 5 shows source impedances Zs (seen at the reference plane B) at different tuner positions in the system calibration. These impedance points are calculated based on the measured output impedances of the noise source in both hot and cold states, and the measured S-parameters of the source tuner, the THRU line, and the load tuner in a cascade configuration at 8 GHz. The ΔZns is manifested as the difference ΔZs in Zs between its hot (Zsh ) and cold (Zsc ) states. ΔZs (i.e., |Zsh − Zsc |) is large for the tuner position, resulting in the
Fig. 6. Measured noise powers Ph and Pc as a function of the source impedance at 8 GHz.
source impedance close to the center of the Smith chart. On the other hand, ΔZs is small for the tuner position corresponding to the source impedance away from the center of the chart. In addition, the source impedances close to the center of the Smith chart are more sensitive to the impedance uncertainty. For example, if Z1 = 50 Ω, Z2 = 1000 Ω, and ΔZs = 5%, then ΔΓ1 = 0.0244 and ΔΓ2 = 0.0043 in a 50-Ω system, i.e., ΔΓ1 is more than five times larger than ΔΓ2 . Therefore, according to the classical method requiring Zsh = Zsc (or Γsh = Γsc ) [17], it seems that these tuner positions, resulting in the source impedances close to the border of the Smith chart, are better choices. This is because their Zsh and Zsc (or Γsh and Γsc ) are about the same and less sensitive to the impedance error. Fig. 6, however, shows, that at these tuner positions, because of the high tuner attenuations, it results in low measured noise powers, particularly for Ph . Due to the reduced power
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Fig. 9.
Extracted receiver gain Go as a function of the number of iterations.
Fig. 7. Selection of tuner position index Mindex and its corresponding source impedance in cold state on the Smith chart.
Fig. 8. Calculated receiver gain Go as a function of Mindex using (−) the proposed method and (◦) the classical method in [17].
difference between Ph and Pc , the solution of the receiver gain Go obtained by (3) is more vulnerable to measurement errors (see Fig. 8). Next, we would like to compare the extracted receiver gain Go obtained using our proposed method and the classical method in [16] (or [17]). The classical method does not specifically indicate at which tuner position its Ph and Pc should be used to extract Go . Therefore, receiver gain Go is extracted, demonstrated, and compared using the measured Ph and Pc at each calibrated tuner position. To have a clear demonstration of these parameters versus the tuner position characteristics, we introduce a tuner position index Mindex . Fig. 7 shows how this Mindex is defined and its corresponding location (in the cold state) on the Smith chart. For example, the impedance points for Mindex = 1−50 have the largest |Γs | (∼0.75 at 8 GHz). On the other hand, the point with Mindex = 225 is the impedance closest to 50 Ω. Fig. 8 shows the extracted receiver gain Go as a function of Mindex in the calibration stage. The results are obtained
using the classical method [17] and our proposed method. As demonstrated in the derivation [see (16)], the receiver gain Go should be independent of the source impedance (or Mindex ). However, we observed in Fig. 8 that the extracted Go based on the classical method shows a strong impedance dependency and a large gain variation. This gain uncertainty complicates the determination of the single-valued receiver gain Go expected in theory. On the other hand, the extracted gain Go using our proposed method has a very weak Mindex dependency for Mindex , ranging from 50 to 225 (i.e., |Γs | < 0.7). The small gain variation in this range might result from the uncertainties in the measured Ph and Pc [32]. Therefore, the big gain uncertainty in the classical method for |Γs | < 0.7 is mainly due to not taking care of the difference ΔΓs between Γsh and Γsc . Our proposed method reduces the gain uncertainty (or fluctuation) from 8.98% to 2.45% in the extracted Go values. Another observation in Fig. 8 is that the gain variation in the classical method is reduced and converges when the Mindex used in the Go extraction moves toward the center of the Smith chart. This is because a higher Ph and a higher Tseffnorh are obtained when Mindex moves toward 50 Ω, and they become the dominant terms (i.e., Ph Pc and Tseffnorh Tseffnorc ) in (5). In this case, ΔΓs is not critical when solving receiver gain Go in the calibration stage. Therefore, in this paper, the noise powers at the source impedances closest to 50 Ω will be used to solve the receiver gains in both the calibration and measurement stages. The other observation seen in Fig. 8 is that for |Γs | > 0.7 (i.e., Mindex = 1−50), the extracted receiver gain using our proposed method also shows a large gain variation (or uncertainty), even if it is smaller than that using the classical method. Because the ΔΓs in this region is small (see Fig. 5), it should not be fully responsible for this large gain uncertainty. The exact physical mechanism is not clear to us at this moment. This might be due to the impedance uncertainties caused by the calibration accuracy of the network analyzer [15], and further investigations are needed. Fig. 9 shows the extracted receiver gain Go versus the number of iterations using our algorithm. We found that the solution usually converges after the third iteration, and this makes our
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TABLE I EXTRACTED NOISE PARAMETERS AND GAIN Go OF THE RECEIVER IN THE C ALIBRATION S TAGE U SING THE P ROPOSED M ETHOD AND THE C LASSICAL M ETHOD (V ALUES IN B RACKETS )
Fig. 10. Measured and simulated Pc of the whole noise measurement system in the calibration stage at 8 GHz.
Fig. 11. Measured and simulated Ph of the whole noise measurement system in the calibration stage at 8 GHz.
proposed method very practical in real applications. With the source impedance at (or close to) 50 Ω, it results in a very high Ph and a very high Tseffnorh and reduces the impact of A, B, C, and D in (5). Therefore, the number of iterations required for the parameters of interest to converge can always be minimized in practice. Figs. 10 and 11 show the measured and simulated noise powers (Ph and Pc ) of the whole measurement system in the calibration stage, respectively. The operation frequency is 8 GHz, and ambient temperature Tc is 26 ◦ C. The simulation results are obtained using N Fmin = 3.81 dB, Rn = 20.9 Ω, Γopt = 0.276 ∠ 117◦ , and Go = −6.18 dB, with the noise reference plane at plane B in Fig. 1. A very good agreement between the measured and simulated noise powers has been achieved. This demonstrates the accuracy of the noise model and the extracted parameter values for the measurement system at 8 GHz. Table I shows the extracted noise parameters and power gains of the receiver from 4 to 26 GHz, with a 2-GHz frequency step.
Fig. 12. Measured transducer gain of the NFA, the available gain of the cable, and the available gain of the LNA in the calibration stage.
All these results have similar accuracy as that at 8 GHz. The parameter values in brackets are obtained using the classical method. It can be seen that, using the Ph and the Pc at 50 Ω to extract Go , both methods predict similar results at all frequencies in the calibration stage. We noticed that the receiver gains of the measurement system in Table I are all less than 0 dB. To find the origin of the loss, the gains of the receiver’s components, i.e., the NFA, the cable, and the LNA, are measured. Fig. 12 shows that the transducer gain
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Fig. 13. Measured and calculated noise figures of the receiver in the calibration stage.
of the NFA is between −26 and −33 dB, the available gain of the cable is between −0.9 and −2.5 dB, and the available gain of the LNA is between 20 and 22 dB. Therefore, we conclude that the negative Go in decibels is because of the huge loss in the NFA. Fig. 13 shows the measured and calculated noise figures of the receiver in the calibration stage. The calculated noise figures are based on the noise parameters in Table I. They are within ±5% of the measured data. Because the uncertainty of the measured noise figures is about 10% [32], Fig. 13 shows that the ±5% difference between the measured and calculated noise figures is within the measurement uncertainty. It also confirms the accuracy of both the extracted noise parameters in Table I and the noise model for the noise measurement system at all calibrated frequencies. After the system calibration, the THRU line is replaced by the DUT, which includes probe pads, metal interconnections, and an n-type MOSFET with W/L = 128 × 1 μm/90 nm fabricated in a standard 90-nm CMOS technology. This DUT is biased at VGS = 1.0 V and VDS = 0.8 V with dc current IDS = 36.8 mA. The noise parameters of this “new” receiver with the DUT and the noise reference plane at plane A in Fig. 1 are extracted at each frequency. The noise parameters of the DUT are then calculated using (14). To avoid the potential error due to a small number of preselected impedance points, noise powers at all calibrated impedance points are measured and used in the noise parameter extraction. However, this implies a long measurement time at each frequency (e.g., it takes about 1.5 h to measure the noise powers for about 200 impedance points using mechanical tuners). To keep a good probe contact on the aluminum pads throughout the measurement, we measured the DUT from 4 to 22 GHz, with a 2-GHz step. This allows us to finish the noise measurement for one bias condition within 15 h, which is the longest time to maintain a reliable probe contact, based on our experience. Figs. 14–17 show the extracted noise parameters of the DUT (without de-embedding the parasitic effects of probe pads and
Fig. 14. Calculated N Fmin as a function of frequency for an n-type MOSFET with W/L = 128 × 1 μm/90 nm biased at VGS = 1.0 V and VDS = 0.8 V using the classical method, the method in [24], and the proposed method.
Fig. 15. Calculated Rn as a function of frequency for an n-type MOSFET with W/L = 128 × 1 μm/90 nm biased at VGS = 1.0 V and VDS = 0.8 V using the classical method, the method in [24], and the proposed method.
Fig. 16. Calculated |Γopt | as a function of frequency for an n-type MOSFET with W/L = 128 × 1 μm/90 nm biased at VGS = 1.0 V and VDS = 0.8 V using the classical method, the method in [24], and the proposed method.
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that the hot noise power and the cold noise power at 50-Ω source impedance should be used to solve the receiver gains. Our proposed method improves the parameter accuracy when the impedance point other than 50 Ω is used to solve the receiver gain. The small impedance difference between the hot and cold states needs to be taken care of, particularly for the high-gain receiver. A PPENDIX In (1), Gtr is the transducer power gain of the receiver, which is defined as [29] Gtr = Fig. 17. Calculated ∠Γopt as a function of frequency for an n-type MOSFET with W/L = 128 × 1 μm/90 nm biased at VGS = 1.0 V and VDS = 0.8 V using the classical method, the method in [24], and the proposed method.
interconnections) as a function of frequency using the classical method [16], the method in [24], and our proposed method. The symbols are obtained using the k factor and Go at 50-Ω source impedance. The upper and lower bounds of the error bars at each frequency represent the maximum and minimum parameter values obtained using the k factor and Go at other impedance points. In comparison with the results from the classical method, both the method in [24] and our proposed method improve the accuracy by reducing the data variation, particularly for N Fmin and |Γopt |. The poor accuracy in the classical method is because receiver gain Go increases as a result of the active device (e.g., Go increases from −5.16 to 6.05 dB at 6 GHz). When Go becomes high, from (20), the measured noise powers are much more sensitive to the mismatch between the output impedances of the noise source in the hot and cold states. Therefore, the impedance mismatch has to be taken care of when measuring high-gain devices using a noise source with high EN R values [33]. Based on the observations in Table I (for a low-gain receiver) and in Figs. 14–17 (for a high-gain receiver), we conclude that when the Ph and the Pc at 50-Ω source impedance are used to extract receiver gain Go , the impact of ΔYs needs to be considered only for the high-gain receiver but not for the low-gain receiver. Finally, when comparing the parameter values with the k factor and Go obtained at impedance points other than 50 Ω, the parameters from the method in [24] show a bigger parameter variation (i.e., longer error bars) compared to those obtained by our proposed method, particularly for N Fmin and Rn . This is because the k factor derived in [24] is based on Fs = EN R/(Y − 1), which is only valid when Γsh = Γsc . For Γsh = Γsc , the improved Y-factor equation in [25] should be used in the derivation of the k factor.
=
1 − |Γs |2 |s21r |2 1 − |Γl |2
|(1 − s11r Γs )(1 − s22r Γl ) − s12r s21r Γs Γl |2 1 − |Γs |2 · Go |1 − Γinr Γs |2
(15)
where Γinr is the input reflection coefficient of the receiver. Here, Go is a parameter that is not a function of source impedance and is given by Go =
|s21r |2 1 − |Γl |2 . |1 − s22r Γl |2
(16)
On the other hand, Tseff in (1) is the effective source temperature experienced at the noise reference plane, which is given by Tseff = (Ts − Tc ) · Gavt + Tc
(17)
where Ts is the source temperature, Tc is the ambient temperature, and
Gavt
1 − |Γns |2 |s21t |2 = 2 12t s21t Γns |1 − s11t Γns |2 1 − s22t + s1−s 11t Γns
(18)
which is the available power gain of the impedance tuner. For the source temperature Ts in (17), it is equal to Tc in the cold state and Th in the hot state, where Th is given by [4], [25] Th = (EN R + 1)To .
(19)
Now, if we define three new parameters Tseffnor , Ru , and Giun as Tseffnor = Tseff /To , Ru = |u|2 /4kTo Δf , and Giun = |iun |2 /4kTo Δf , (1) then becomes kTo Δf 1 − |Γs |2 · · Go [tseffnor Gs + Ru Gs |1 − Γinr Γs |2 · |Ys |2 + |Ycor |2 + 2Gcor Gs + 2Bcor Bs + Giun .
Pn = IV. C ONCLUSION A novel iterative method to improve the noise parameter determination without requiring the same source impedance value in the hot and cold states was presented. Our results show
(20)
If we define A = Ru , B = Giun +|Ycor |22 ·Ru , C = Gcor ·Ru , and D = Bcor · Ru , (20) can be rearranged to become (2).
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ACKNOWLEDGMENT The authors would like to thank G. Simpson, E. Kueckels, and R. Wallace of Maury Microwave, CA, for their assistance in operating their automated tuner system; Prof. M. J. Deen and Dr. O. Marinov of the Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON, Canada, for their assistance in microwave noise measurements; and B. Hung, V. Liang, J. S. Jan, K. C. Wang, and C. S. Yeh of United Microelectronics Corporation for their assistance in device fabrication. R EFERENCES [1] H. T. Friis, “Noise figures of radio receivers,” Proc. IRE, vol. 32, no. 7, pp. 419–422, Jul. 1944. [2] “IRE standards on electron tubes: Definitions of terms, 1957,” Proc. IRE, vol. 45, no. 7, pp. 983–1010, Jul. 1957. [3] “IRE standards on methods of measuring noise in linear two ports, 1959,” Proc. IRE, vol. 48, no. 1, pp. 60–68, Jan. 1960. [4] Fundamentals of RF and Microwave Noise Figure Measurements. Agilent Application Note 57-1. [5] “Representation of noise in linear two ports,” Proc. IRE, vol. 48, no. 1, pp. 69–74, Jan. 1960. [6] R. Q. Lane, “The determination of device noise parameters,” Proc. IEEE, vol. 57, no. 8, pp. 1461–1462, Aug. 1969. [7] M. S. Gupta, “Determination of the noise parameters of a linear 2-port,” Electron. Lett., vol. 6, no. 17, pp. 543–544, Aug. 20, 1970. [8] G. Caruso and M. Sannino, “Computer-aided determination of microwave two-port noise parameters,” IEEE Trans. Microw. Theory Tech., vol. MTT26, no. 9, pp. 639–642, Sep. 1978. [9] M. Mitama and H. Katoh, “An improved computational method for noise parameter measurement,” IEEE Trans. Microw. Theory Tech., vol. MTT27, no. 6, pp. 612–615, Jun. 1979. [10] M. Sannino, “On the determination of device noise and gain parameters,” Proc. IEEE, vol. 67, no. 9, pp. 1364–1366, Sep. 1979. [11] G. I. Vasilescu, G. Alquie, and M. Krim, “Exact computation of twoport noise parameters,” Electron. Lett., vol. 25, no. 4, pp. 292–293, Feb. 16, 1988. [12] J. M. O’Callaghan and J. P. Mondal, “A vector approach for noise parameter fitting and selection of source admittances,” IEEE Trans. Microw. Theory Tech., vol. 39, no. 8, pp. 1376–1382, Aug. 1991. [13] J. W. Archer and R. A. Batchelor, “Fully automated on-wafer noise characterization of GaAs MESFET’s and HEMT’s,” IEEE Trans. Microw. Theory Tech., vol. 40, no. 2, pp. 209–216, Feb. 1992. [14] A. Boudiaf and M. Laporte, “An accurate and repeatable technique for noise parameter measurements,” IEEE Trans. Instrum. Meas., vol. 42, no. 2, pp. 532–537, Apr. 1993. [15] W. Wiatr and D. K. Walker, “Systematic errors of noise parameter determination caused by imperfect source impedance measurement,” IEEE Trans. Instrum. Meas., vol. 54, no. 2, pp. 696–700, Apr. 2005. [16] V. Adamian and A. Uhlir, “A novel procedure for receiver noise characterization,” IEEE Trans. Instrum. Meas., vol. IM-22, no. 2, pp. 181–182, Jun. 1973. [17] M. N. Tutt, “Low and high frequency noise properties of heterojunction transistors,” Ph.D. dissertation, Dept. Elect. Eng., Comput. Sci., Univ. Michigan, Ann Harbor, MI, 1994. [18] R. Meierer and C. Tsironis, “An on-wafer noise parameter measurement technique with automatic receiver calibration,” Microw. J., vol. 38, no. 3, pp. 22–37, Mar. 1995. [19] M. Kantanen, M. Lahdes, T. Vähä-Heikkilä, and J. Tuovinen, “A wideband on-wafer noise parameter measurement system at 50–75 GHz,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 5, pp. 1489–1495, May 2003. [20] J.-C. Guo and Y.-M. Lin, “A new lossy substrate de-embedding method for sub-100 nm RF CMOS noise extraction and modeling,” IEEE Trans. Electron Devices, vol. 53, no. 2, pp. 339–347, Feb. 2006. [21] International Technology Roadmap for Semiconductors (ITRS), 2005. [Online]. Available: http://www.itrs.net/reports.html [22] L. Escottee, R. Plana, and J. Graffeuil, “Evaluation of noise parameter extraction methods,” IEEE Trans. Microw. Theory Tech., vol. 41, no. 3, pp. 382–387, Mar. 1993. [23] N. J. Kuhn, “Curing a subtle but significant cause of noise figure error,” Microw. J., vol. 27, no. 6, pp. 85–98, Jun. 1984.
[24] A. C. Davidson, B. W. Leake, and E. Strid, “Accuracy improvements in microwave noise parameter measurements,” IEEE Trans. Microw. Theory Tech., vol. 37, no. 12, pp. 1973–1978, Dec. 1989. [25] L. F. Tiemeijer, R. Havens, R. Kort, and A. J. Scholten, “Improved Y-factor method for wide-band on-wafer noise parameter measurements,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 9, pp. 2917–2925, Sep. 2005. [26] Theory of Noise Measurement, Jul. 6, 1999, Maury Microwave. Application Note: 5C-042. [27] H. Rothe and W. Dahlke, “Theory of noisy fourpoles,” Proc. IRE, vol. 44, no. 6, pp. 811–818, Jun. 1956. [28] V. Adamian and A. Uhlir, “Simplified noise evaluation of microwave receivers,” IEEE Trans. Instrum. Meas., vol. IM-33, no. 2, pp. 136–140, Jun. 1984. [29] M. W. Medley, Microwave and RF Circuits: Analysis, Synthesis and Design. Norwood, MA: Artech House, 1993. [30] H. Hillbrand and P. H. Russer, “An efficient method for computer-aided noise analysis of linear amplifier networks,” IEEE Trans. Circuits Syst., vol. CAS-23, no. 4, pp. 235–238, Apr. 1976. [31] C. H. Chen, M. J. Deen, Y. Cheng, and M. Matloubian, “Extraction of the induced gate noise, channel thermal noise and their correlation in submicron MOSFETs from RF noise measurements,” IEEE Trans. Electron Devices, vol. 48, no. 12, pp. 2884–2892, Dec. 2001. [32] Agilent Noise Figure Analyzers NFA Series Calibration and Performance Verification Guide, Agilent Technol., Santa Clara, CA, 2001, p. 95. [33] 10 Hints for Making Successful Noise Figure Measurements, p. 4. Agilent Application Note 57-3.
Chih-Hung Chen (S’95–M’03) received the B.S. degree in electrical engineering from National Central University, Chungli, Taiwan, R.O.C., in 1991, the M.S. degree in engineering science from Simon Fraser University, Burnaby, BC, Canada, in 1997, and the Ph.D. degree from McMaster University, Hamilton, ON, Canada, in 2002. During the summers of 1998–2000, he was with Conexant Systems Inc., Newport Beach, CA, where he was involved in the high-frequency noise characterization and modeling of MOSFETs and BJTs. During the summer of 2001, he was with Transilica Inc. (now Microtune Inc.), San Diego, CA, where he was engaged in the design of differential LNAs and VCOs for Bluetooth. In 2002, he joined the faculty of the Department of Electrical and Computer Engineering, McMaster University, as an Assistant Professor of electrical and computer engineering. His research interests are high-frequency noise characterization techniques, modeling of sub-100-nm MOSFETs, and designs of low-noise RF CMOS integrated circuits for wireless applications. Dr. Chen was the recipient of the New Opportunities Fund Award 2004 from the Canada Foundation for Innovation and the Best Invited Paper Award at the 2002 IEEE Custom Integrated Circuits Conference.
Ying-Lien Wang received the B.A.Sc. degree in electrical engineering from the University of Waterloo, Waterloo, ON, Canada, in 2005. He is currently working toward the M.A.Sc. degree with the Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON. His current research interest is accuracy improvement of high-frequency noise measurements for sub100-nm MOSFETs.
CHEN et al.: NOVEL NOISE PARAMETER DETERMINATION FOR ON-WAFER MICROWAVE NOISE MEASUREMENTS
Mohamed H. Bakr (S’98–M’00) received the B.Sc. degree [with distinction (honors)] in electronics and communications engineering and the M.Sc. degree in engineering mathematics from Cairo University, Giza, Egypt, in 1992 and 1996, respectively, and the Ph.D. degree from McMaster University, Hamilton, ON, Canada, in 2000. In 1997, he was a Student Intern with Optimization Systems Associates, Inc., Dundas, ON. From 1998 to 2000, he was a Research Assistant with the Simulation Optimization Systems Research Laboratory, McMaster University. In November 2000, he joined the Computational Electromagnetics Research Laboratory, University of Victoria, Victoria, BC, Canada, as an NSERC Postdoctoral Fellow. He is currently an Associate Professor with the Department of Electrical and Computer Engineering, McMaster University. His research interests include optimization methods, computeraided design and modeling of microwave and photonic circuits, neural network applications, smart analysis of microwave circuits, efficient optimization using time/frequency-domain methods, and bioelectromagnetism. Dr. Bakr was a recipient of a Premier’s Research Excellence Award from the province of Ontario in 2003.
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Zheng Zeng received the Ph.D. degree from the Department of Electronic Engineering, Xi’an Jiaotong University, Xi’an, China, in 1993. In December 1993, he joined Xi’an Jiaotong University as an Associate Professor of electronic engineering. From 1997 to 2001, he was a Principal Engineer with Chartered Semiconductor MFG, Singapore, where he worked on process integration and device modeling for BiCMOS and RFCMOS processes. In 2002, he joined United Microelectronics Corporation, Sunnyvale, CA, as a Senior Engineering Manager for device modeling, where he works on device characterization and modeling for advanced RFCMOS process.
