A NEW QUALITY INDICATOR FOR WIDEBAND UN- TERMINATION BY USING REFLECTIVE STANDARDS
|
|
- Gilbert Wiggins
- 5 years ago
- Views:
Transcription
1 Prgress In Electrmagnetics Research Letters, Vl. 39, 81 95, 213 A NEW QUALITY INDICATOR FOR WIDEBAND UN- TERMINATION BY USING REFLECTIVE STANDARDS Jsé Fays-Fernández *, Antni Lzan-Guerrer, and Juan Mnzó-Cabrera Departament de Tecnlgías de la Infrmación y las Cmunicacines, Universidad Plitécnica de Cartagena, Plaza del Hspital 1, Cartagena 322, Spain Abstract In this paper a new quality indicatr fr tw-tier calibratin prcedures that use nly reflectin standards is presented and applied t caxial-t-waveguide transitins. The quality indicatr is based n the algebraic cnditining f the system f equatins slved fr btaining transitin characteristics. The study has been carried ut in a wide bandwidth as a difference with previus wrks. The btained results indicate that a threshld value fr this indicatr arund 1% can be established. Fr values belw this limit the errr grws t unacceptable values. Additinally, it has been shwn that an expnential relatinship between quality indicatr and the errr can be predicted. 1. INTRODUCTION Caxial-t-waveguide transitins are emplyed in waveguide measurements such as permittivity estimatin, characterizatin f waveguide devices, etcetera, since vectr netwrk analyzers (VNA) emply caxial interfaces. Therefre, it is necessary t have a gd characterizatin f these structures in rder t perfrm precise measurements in waveguide technlgy. Hwever, the measurement f transitin scattering parameters is nt straightfrward and these must be characterized frm measurements made at the VNA reference plane when knwn standards are embedded in the waveguide prt f the transitin. This prcess is referred t as unterminating [1]. Received 8 March 213, Accepted 8 April 213, Scheduled 14 April 213 * Crrespnding authr: Jsé Fays-Fernández (jse.fays@upct.es).
2 82 Fays-Fernández, Lzan-Guerrer, and Mnzó-Cabrera There are several prcedures fr unterminating depending n the standards types and errr minimizatin prcedures. Fr instance penshrt-lad (OSL) r thru-reflect-line (TRL) standards may be used [1 3] fr unterminating. Hwever, several studies based n iterative appraches [1, 4] shw that it is pssible t use redundant standards in rder t increase accuracy versus cnventinal calibratin prcedures. Freeware sftware packages such as MultiCal and StatistiCAL develped at the Natinal Institute f Standards and Technlgy (NIST) implement calibratin algrithms based n different studies such as [1, 2, 4 7] that perfrm bth ne and tw-tier deembedding. The tw-tier calibratin prcedure can be used t electrically characterize prbe heads r ther cmpnents such as caxial-twaveguide transitins and can handle up t 4 different standard types. In [8] is presented a calibratin prcedure specifically applied t caxial-t-waveguide transitins knwn as the three-cavity technique. It makes use f three cavities and their input reflectin cefficients fr btaining three linear equatins with which the tw-prt scattering matrix f the transitin can be calculated, by impressing the incident wave in the caxial line nly. The main drawback f this methd is a restrictin regarding the phases f the reflectin cefficient f the shrtcircuited waveguide sectins, which must nt have 36 differences at a given frequency. The authrs suggest using phase differences f 12 and 24. In [9], a tw-tier inverse technique fr characterizing caxial t waveguide transitins based n the use f genetic algrithms and the gradient descent methd is described and cmpared t different well-knwn calibratin techniques prviding gd results. In [1] this prcedure is extended and bth the transitins and the device under test are simultaneusly characterized. Nne f previus wrks, hwever, prvide estimatins r indicatins f hw gd the calibratin prcedure is and n clue is prvided abut the selectin criteria fr the different standards. In fact, this is a key issue that has nt been studied in depth althugh sme attempts have been made. Bauer and Penfield [2], fr instance, shw in a DC study that the calibratin precisin is better as the number f standards grws. Her [11] studies the best length fr a precisin transmissin line fr calibrating netwrk analyzers and cncludes that lines with phases near 18 r multiples shuld be avided in rder t achieve a well-cnditined equatin system. Williams [12] uses the nrmalized variance f the unterminating prcedure as indicatr fr the calibratin quality as a functin f the number f thrus and shrts and cncludes that the best calibratin prcess is achieved when the maximum number f available shrts is used. Maury et al. [13] recmmend that fr line-reflect-line (LRL) calibratin prcedures lines
3 Prgress In Electrmagnetics Research Letters, Vl. 39, shuld shw phase differences between 3 and 15. All these studies are carried ut at single frequencies r narrw bandwidths. Hwever, the selectin f standard number r phases is nt clear. Fr instance, Adalev et al. [14] shw that using a greater number f standards des nt guarantee that accuracy is increased. On the cntrary, Marks [4] shws that the additinal infrmatin prvided by redundant standards minimizes the effects f randm errrs, such as thse caused by imperfect cnnectr repeatability. The resulting methd exhibits imprvements in bth accuracy and bandwidth ver cnventinal methds. Cmmercial calibratin kits, which cnsist f 3 reflectin standards typically, might be used fr unterminating caxial-twaveguide transitins. Nevertheless, adding sme extra standards fr the unterminatin prcess might increase the calibratin quality [4]. In this paper, we present a simple indicatr fr standard selectin and we relate this indicatr t calibratin errrs and final accuracy. We exclusively use reflectin standards in rder t calibrate caxialt-waveguide transitins and we assess the calibratin quality in terms f the algebraic cnditining f the system f equatins slved fr btaining transitin characteristics. As a difference frm previus wrks, we carry ut this study in a 1 GHz bandwidth in rder t evaluate the utility f the prpsed calibratin quality indicatr as a functin f frequency. In additin, in the result sectin a cmparisn f the system f equatins quality when using a cmmercial calibratin kit standalne and when using it supplemented with extra standards is presented. 2. CALIBRATION PROCEDURE AND QUALITY ESTIMATION The bjective f the calibratin prcedure is t accurately estimate the scattering parameters f the caxial-t-waveguide transitin. This kind f devices can be mdeled as a 2-prt micrwave netwrk. In this study, it is assumed that the prt 1 is linked t its caxial interface, whereas prt 2 is t its waveguide interface. Let us represent the transitin thrugh its scattering parameter matrix: [ ] S11 S [S] = 12 (1) S 21 S 22 This investigatin used a cllectin f waveguide shrt standards with different lengths that were cnnected t the prt tw f the transitin. This means that measurements were nly available at the caxial prt. Let us call Γ i t the ith reflectin cefficient measured at prt ne
4 84 Fays-Fernández, Lzan-Guerrer, and Mnzó-Cabrera when the ith shrt standard is applied t the waveguide prt f the transitin and Γ Li as the theretical reflectin cefficient f the ith shrt standard with i [1, N]. N is the number f standards used during the calibratin prcess. The reflectin cefficients f the shrted guides can be cmputed as Γ Li = e j2βl i, where β is the waveguide prpagatin cnstant and L i are the lengths f the shrted guides. Figure 1 summarizes this explanatin. VECTORIAL NETWORK ANALYZER Γ i L i [, ] cm TRANSITION COAXIAL-TO-WAVEGUIDE SHORTED WAVEGUIDES (STANDARDS) Γ L i Figure 1. Scheme shwing the different magnitudes emplyed during calibratin prcedure. By expanding the methdlgy emplyed in [8], ne can express the equatins relating Γ i, Γ Li and [S] as expressed in Equatin (2) when N shrts are emplyed as standards: 1 Γ 1 Γ L1 Γ L1 1 Γ 2 Γ L2 Γ L2 [ 1 Γ 3 Γ L3 Γ L Γ N Γ LN Γ LN S 11 S 22 S 12 S 21 S 11 S 22 ] = Γ 1 Γ 2 Γ 3. Γ N Suppsing that each shrt prvides an independent equatin in (2), the system can be easily slved by algebraic prcedures when its matrix has a full rank and N = 3. Nevertheless, when N > 3 the system f equatins is verdetermined, and it must be slved by applying Least Square Methd (LSM) as implemented in Matlab TM sftware. In rder t assess the quality f the calibratin prcess, it was used the 2-nrm cnditin number f the first matrix in Equatin (2) (2)
5 Prgress In Electrmagnetics Research Letters, Vl. 39, as: 1 Γ 1 Γ L1 Γ L1 1 Γ 2 Γ L2 Γ L2 C = cnd 1 Γ 3 Γ L3 Γ L Γ N Γ LN Γ LN 1 Γ 1 Γ L1 Γ L1 1 Γ 1 Γ L1 Γ L1 1 Γ 2 Γ L2 Γ L2 1 Γ 2 Γ L2 Γ L2 = 1 Γ 3 Γ L3 Γ L3 inv 1 Γ 3 Γ L3 Γ L Γ N Γ LN Γ LN 1 Γ N Γ LN Γ LN In Equatin (3) the peratr indicates the 2-nrm f the matrix, and inv is the inverse matrix peratr. C yields a value f 1 fr well-cnditined systems r it will tend t infinity as the cnditin system gets wrse tward an undetermined system. Therefre, it seems mre cnvenient t express the quality f the system f equatins as a percentage frm % t 1%. The fllwing relatinship was chsen in rder t estimate the quality f the slved system f equatins at each frequency pint: (3) Q i (f i ) = 1/C(f i ) (%) (4) where f i is the ith frequency pint where the quality indicatr is cmputed. The prcedure f slving the system f Equatin (2) and btaining the quality indicatr was simultaneusly applied t all the frequency pints f the measurement by using vectr peratins and n iterative prcedures were emplyed. The Equatin (5) was used fr averaging values f the quality indicatr within the cnsidered bandwidth [2, 3] GHz with k sampled frequencies. Q i (f i ) i=f 1 Q average = (5) k Fr ill-cnditined systems the quality indicatr will tend t %, and fr well-cnditined systems it will apprach t 1%. This indicatr system must be carried ut fr each frequency pint within the cnsidered bandwidth. It is difficult t estimate a threshld value fr Q i in rder t decide whether the calibratin is precise enugh r nt. Hwever, a limit value f 1% was set due t multiple bservatins carried ut with the experimental data. Cnsequently, the calibratin prcess is cnsidered having a lw quality fr Q < 1%. f k
6 86 Fays-Fernández, Lzan-Guerrer, and Mnzó-Cabrera Fr validatin purpses, the errr was cmputed at each frequency pint as shwn in Equatin (6): Errr(f i ) = Γ VNA n (f i ) Γ CAL n (f i ) (6) where Errr(f i ) is the errr cmputed fr the ith frequency pint, Γ VNA n (f i ) the reflectin cefficient f the nth standard chsen fr the validatin measured at the caxial prt f the transitin, and Γ CAL n (f i ) the cmputed reflectin cefficient calculated as the scattering parameters f the unterminated transitin cascaded t the chsen standard. The average errr within the cnsidered bandwidth with k sampled frequencies has been cmputed as: f k Errr(f i ) i=f i Errr average = k (7) Scattering parameters (mdulus) Unterminated Caxial-t-Waveguide transitin using standards: S 11 S 12 S 21 Quality System equatin quality (percentage) Scattering parameters (phase) Figure 2. Extracted S-parameters fr the caxial-t-waveguide transitin using a bad cmbinatin f standards fr its unterminatin. S 11 S 12S 21
7 Prgress In Electrmagnetics Research Letters, Vl. 39, EXPERIMENTAL SETUP A Rhde&Schwarz ZVA 67 VNA has been used in rder t measure the scattering matrix frequency behavir f the caxial-t-waveguide transitins when using different standards. The reflectin standards were built as a cmbinatin f a shrtplate r any f tw ffset shrt-circuited waveguides (lengths f 1.82 and 5.46 cm) with fur different waveguide sectins available fr building up the transmissin standards. As a result, up t 48 different reflectin standards with physical lengths ranging frm cm up t cm were available fr shrt-circuiting the waveguide prt f each transitin as shwn in Figure 1. The cmplete list f the shrt-circuited waveguide sectins used in the calibratin prcess and their physical lengths are prvided in Appendix A. In each measurement, 11 pints were sampled hmgeneusly distributed within the [2, 3] GHz frequency range, which yields a 1 khz frequency reslutin. Therefre, it was ensured that waveguide cmpnents wrked nly with the TE 1 main mde. A Rhde & Schwarz ZV-Z32 PC 3.5 fixed matched calibratin kit Verificatin with shrtlad #48 Unterminatin standards used: #21 #22 #39 S VNA 11 Std.#48 S EST 11 Std.#48 Verificatin with shrtlad #48 Unterminatin standards used: #21 #22 #39 S VNA 11 Std.#48 S EST 11 Std.#48 Figure 3. Verificatin f the untermined transitin using a bad cmbinatin f standards using standard #48 as lad.
8 88 Fays-Fernández, Lzan-Guerrer, and Mnzó-Cabrera was emplyed in rder t calibrate the VNA at prt 1 f the transitin. The caxial-t-waveguide transitin that was used t carry ut the study belngs t a Cntinental Micrwave WCK34-HP waveguide calibratin kit [15]. All the waveguide sectins used t build the ffset shrt standards accmplished the WR-34 standard. 4. RESULTS Figure 2 shws a calibratin prcedure using shrts {#21, #22, #39}. The btained quality indicatr f the system f equatins Q i is near zer fr all frequencies, and bth the phase and magnitude values shw a nisy and errneus behavir. In this case, the phase values and phase slpes fr shrts #21 and #22 were very similar and therefre the equatin system had nt enugh infrmatin t prperly carry ut the characterizatin f the transitin. Figure 3 shws the cmparisn f the measured reflectin cefficient f a validatin standard that was nt used during the calibratin prcedure and the reflectin cefficient f that standard cmputed by using the btained values f the scattering parameters f the transitin. The standard #48 was chsen fr the prcedure Scattering parameters (mdulus) Unterminated Caxial-t-Waveguide transitin using standards: S 11 S 12 S 21 Quality System equatin quality (percentage) Scattering parameters (phase) Figure 4. Extracted S-parameters fr the caxial-t-waveguide transitin using a gd cmbinatin f standards fr its unterminatin. S 11 S 12S 21
9 Prgress In Electrmagnetics Research Letters, Vl. 39, validatin. It can be bserved that the transitin characterizatin is cmpletely errneus: magnitude and phase values were nt crrectly cmputed due t an imprecise calibratin prcedure. Figure 4 shws a calibratin prcedure using shrts {#1, #2, #5}. In this case, the calibratin quality indicatr stays abve the 1% threshld alng the bandwidth, s the calibratin prcess can be cnsidered precise. In fact, nisy values fr the [S] matrix f the transitin are n lnger bserved. This is cnfirmed in Figure 5, where the magnitude f the measured reflectin cefficient fr validatin standard #48 is cmpared t the cncatenatin f the scattering matrix f the transitin btained with the calibratin prcess and the theretical value f the reflectin cefficient f the validatin standard Γ L48. The agreement is cmplete bth in magnitude and phase fr the cnsidered bandwidth. Therefre, it can be bserved that there is a strng crrelatin between the quality indicatr prpsed in this paper and the precisin f the calibratin prcedure. Fr values f Q greater than 1% the calibratin prcess culd be cnsidered f acceptable, whereas errneus calibratins are expected t ccur fr values lwer than this threshld VNA S 11 Std.#48 EST S 11 Std.#48 Verificatin with shrtlad #48 Unterminatin standards used: #1 #2 #5 Verificatin with shrtlad #48 Unterminatin standards used: #1 #2 #5 VNA S 11 Std.#48 EST S 11 Std.#48-18 Figure 5. Verificatin f the untermined transitin using a gd cmbinatin f standards using standard #48 as lad.
10 9 Fays-Fernández, Lzan-Guerrer, and Mnzó-Cabrera Verificatin errr with shrtlad 48. Unterminatin stds.: Verificatin errr with shrtlad 48. Unterminatin stds.: S S Scattering parameters (mdulus) Unterminated Caxial-t-Waveguide transitin using standards: (a) S 11 S 12 S 21 Quality (c) 5 System equatin quality (percentage) Scattering parameters (mdulus) Unterminated Caxial-t-Waveguide transitin using standards: (b) S 11 S 12 S 21 Quality Figure 6. Cmparisn f (a), (b) validatins and (c), (d) system qualities f tw different calibratin prcesses by using (a), (c) 1 and (b), (d) 2 standards. (d) System equatin quality (percentage) Figure 6 shws a cmparisn fr tw calibratin prcedures where 1 and 2 shrts are emplyed. In the first case, shwn in the left side f the figure, 1 shrts with minimum phase cincidences within the cnsidered bandwidth were chsen, which are {#1 #4 #5 #6 #16 #2 #24 #27 #46 #47}. That case is cmpared t a calibratin prcedure where shrts {#2 #3 #6 #7 #14 #15 #17 #18 #21 #22 #25 #26 #29 #3 #31 #32 #38 #39 #43 #44} were emplyed, shwn at the right side f the Figure 6. It can be bserved that bth calibratin prcedures have very similar values fr the quality indicatr. In fact, the errr fr bth prcedures when cmparing t the validatin standard number #48 is very similar fr bth cases. Mrever, it can be stated that using a greater number f standards des nt necessarily guarantee that accuracy is increased. Figure 7 shws the frequency-averaged quality indicatr Q average and the average errr Errr average as a functin f the number f standards by fllwing different shrt selectin strategies. In the first selectin strategy, the standards were sequentially cllected in
11 Prgress In Electrmagnetics Research Letters, Vl. 39, % 9% 8% 7% 6% 5% 4% 3% 2% 1% % Unterminatin sequence strategy N.1 System Eq. Quality Verificatin errr Amunt f standards used 1% 9% 8% 7% 6% 5% 4% 3% 2% 1% % Unterminatin sequence strategy N.2 System Eq. Quality Verificatin errr Amunt f standards used 1% 9% 8% 7% 6% 5% 4% 3% 2% 1% Unterminatin sequence strategy N.3 System Eq. Quality Verificatin errr % Amunt f standards used 1% 9% 8% 7% 6% 5% 4% 3% 2% 1% Unterminatin sequence strategy N.4 System Eq. Quality Verificatin errr % Amunt f standards used Figure 7. Frequency-averaged quality indicatr Q average and average errr Errr average as a functin f the number f standards fr different standard selectin strategies. Sequence strategy number 1: { }, sequence strategy number 2: { }, sequence strategy number 3: { }, sequence strategy number 4: { }. grups f 3, 4,... up t the 47 available standards in ascending length rder. In sequence strategy number 2, the standards were cllected frm a randmly rdered sequence. Fr the unterminatin sequence strategy number 3, thse shrts with less phase cincidences within the cnsidered bandwidth were cllected first and thse with mre phase cincidences last. Fr sequence strategy number 4, the selectin strategy f shrts was the reverse versin f strategy number 3. The calibratin prcedure was cmpared t standard #48 in all cases. Several cmmn behavirs are bserved in all cases. Fr instance,
12 92 Fays-Fernández, Lzan-Guerrer, and Mnzó-Cabrera Q average increases as the number f standards used fr the calibratin rises as a general trend. Hwever, it cannt be stated that this is a mntnic behavir frm the results bserved when using the unterminatin strategy number 1. In this figure it is nticeable that using 12 standards gives a better cnditining fr the system f equatins rather than using greater amunts starting frm 13 t 3 shrts. Additinally, it can als be bserved that the mre standards used during the calibratin prcess the lwer the average errr Errr average is. Hwever, it is bserved that the reductin f errr with the number f standards is nt linear but fllws an expnential behavir. Furthermre, fr quality indicatr values near r belw 1% the errr grws substantially. Fr higher values f Q average the errr reduces at a much lwer rate when the number f standards used grws. An interesting cnclusin that can be derived frm Figure 7 is that the selectin criterin f the shrts, when the number f standards is lw, is mre critical than in the case f using mre standards. In fact, selectin strategy number 3, where the phase cincidences are minimized, prvides higher Q average values and lwer Errr average values than the ther selectin strategies fr lw numbers f standards. Therefre, it seems that a gd selectin criterin wuld be t minimize phase cincidences amng shrts within the cnsidered bandwidth. Fr higher number f standards phase cincidences grw and the errr and quality indicatr imprve very slwly. 1 9 Errr in verificatin using cntrl standard #48 Vs. Quality f unterminating system equatins Verificatin Errr Vs. Quality Fitting curve 8 7 Errr in predictin (%) System Equatin Quality (%) Figure 8. Expnential relatinship between Errr average and Q average.
13 Prgress In Electrmagnetics Research Letters, Vl. 39, Finally, Figure 8 shws Errr average as a functin f Q average fr all the data btained in the previus selectin sequences. An expnential functin f the type f(x) = a e bx + c e dx has been fitted t experimental data in rder t mdel the relatinship between Errr average and Q average. The cefficients btained fr the fitting are a = 91.7, b =.4252, c = and d = Cmmercial waveguide calibratin kits are designed fr a specific peratin bandwidth. Nevertheless, such a wideband culd be expanded cnveniently by adding mre calibratin standards. Figure 9 shws a practical use f this research fr demnstrating that supplementing the Cntinental Micrwave WCK-34 Waveguide Calibratin Kit (identified in this paper as standards #1, #2 and #6) with tw extra standards (standards #11 and #13) imprves the unterminatin quality, while it bradens its peratinal bandwidth cvering the full mnmde waveguide frequency range [1.74, 3.47] GHz. 1 9 Unterminatin quality imprvement fr the cmmercial WCK-34 Calibratin Kit WCK-34 WCK-34 supplemented Quality (%) Figure 9. Example f a desterminatin quality imprvement f a cmmercial waveguide calibratin kit by supplementing it with tw additinal standards. 5. CONCLUSIONS The relatinship between the cnditining f the systems f equatins and the calibratin errr when using shrt standards in rder t calculate the scattering parameters f caxial-t-waveguide transitins
14 94 Fays-Fernández, Lzan-Guerrer, and Mnzó-Cabrera has been studied. Frm the btained results, an expnential relatinship between the calibratin quality indicatr and the calibratin errr has been established. A threshld value fr this quality indicatr has been set t 1%, belw this limit the calibratin errr grws expnentially. The usage f redundant standards has increased the quality indicatr and reduced the errr when cmparing with a validating standard as a general trend. Fr lwer number f standards, nevertheless, the selectin criterin is f utmst imprtance. In this last case, it has als been shwn that chsing thse shrts with less number f phase cincidences within the cnsidered bandwidth prvides better quality indicatrs and lwer errr values. APPENDIX A. 48 Chart f standards fr reflexin Standard N Std.# Std.# Std.# Length (cm) Length (cm) Length (cm) Length (cm) Figure A1. Number and physical length f the shrt standards used in the calibratin prcess. REFERENCES 1. Williams, D., De-embedding and unterminating micrwave fixtures with nnlinear least squares, IEEE Trans. Micrw. Thery Tech., Vl. 38, , Bauer, R. F. and P. Penfield, De-embedding and unterminating, IEEE Trans. Micrw. Thery Tech., Vl. 22, , 1974.
15 Prgress In Electrmagnetics Research Letters, Vl. 39, Challa, R. K., D. Kajfez, V. Demir, J. R. Gladden, and A. Z. Elsherbeni, Permittivity measurement with a nn-standard waveguide by using TRL calibratin and fractinal linear data, Prgress In Electrmagnetics Research B, Vl. 2, 1 13, Marks, R. B., A multiline methd f analyzer calibratin, IEEE Trans. Micrw. Thery Tech., Vl. 39, N. 7, , Marks, R. B. and D. F. Williams, Characteristic impedance determinatin using prpagatin cnstant measurement, IEEE Micrw. Guided Wave Lett., Vl. 1, N. 6, , Marks, R. B. and D. F. Williams, Accurate transmissin line characterizatin, IEEE Micrw. Guided Wave Lett., Vl. 3, N. 8, , Marks, R. B. and D. F. Williams, Accurate experimental characterizatin f intercnnects, IEEE Trans. Cmpn., Hybrids, Manuf. Technl., Vl. 15, N. 4, 61 62, Liang, J. F., H. Chang, and K. A. Zaki, Caxial prbe mdeling in waveguides and cavities, IEEE Trans. Micrw. Thery Tech., Vl. 4, N. 12, , Lzan-Guerrer, A. J., et al., Precise evaluatin f caxial t waveguide transitins by means f inverse techniques, IEEE Trans. Micrw. Thery Tech., Vl. 5, N. 1, , Lzan-Guerrer, A. J., et al., Caxial t waveguide transitins and device under test characterizatin by means f inverse techniques, Micrwave and Optical Technlgy Letters, Vl. 52, N. 6, , Her, C. A., Chsing line lengths fr calibrating netwrk analyzers, IEEE Trans. Micrw. Thery Tech., Vl. 31, N. 1, 76 78, Williams, D., De-embedding and unterminating micrwave fixtures with nnlinear least squares, IEEE Trans. Micrw. Thery Tech., Vl. 38, N. 6, , Maury, M. A., S. March, and G. Simpsn, LRL calibratin f vectr autmatic netwrk analyzers, Micrwave Jurnal, Vl. 3, N. 5, , Adalev, A. S., N. V. Krvkin, M. Hayakawa, and J. B. Nitsch, Deembedding and unterminating micrwave fixtures with the genetic algrithm, IEEE Trans. Micrw. Thery Tech., Vl. 54, N. 7, , Waveguide Cmpnent Specificatins and Design Handbk, 7th editin, Cntinental Micrw., Cbham, Drset, UK, 29.
Determining the Accuracy of Modal Parameter Estimation Methods
Determining the Accuracy f Mdal Parameter Estimatin Methds by Michael Lee Ph.D., P.E. & Mar Richardsn Ph.D. Structural Measurement Systems Milpitas, CA Abstract The mst cmmn type f mdal testing system
More informationBootstrap Method > # Purpose: understand how bootstrap method works > obs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(obs) >
Btstrap Methd > # Purpse: understand hw btstrap methd wrks > bs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(bs) > mean(bs) [1] 21.64625 > # estimate f lambda > lambda = 1/mean(bs);
More informationProgress In Electromagnetics Research M, Vol. 9, 9 20, 2009
Prgress In Electrmagnetics Research M, Vl. 9, 9 20, 2009 WIDE-ANGLE REFLECTION WAVE POLARIZERS USING INHOMOGENEOUS PLANAR LAYERS M. Khalaj-Amirhsseini and S. M. J. Razavi Cllege f Electrical Engineering
More informationSUPPLEMENTARY MATERIAL GaGa: a simple and flexible hierarchical model for microarray data analysis
SUPPLEMENTARY MATERIAL GaGa: a simple and flexible hierarchical mdel fr micrarray data analysis David Rssell Department f Bistatistics M.D. Andersn Cancer Center, Hustn, TX 77030, USA rsselldavid@gmail.cm
More informationPerfrmance f Sensitizing Rules n Shewhart Cntrl Charts with Autcrrelated Data Key Wrds: Autregressive, Mving Average, Runs Tests, Shewhart Cntrl Chart
Perfrmance f Sensitizing Rules n Shewhart Cntrl Charts with Autcrrelated Data Sandy D. Balkin Dennis K. J. Lin y Pennsylvania State University, University Park, PA 16802 Sandy Balkin is a graduate student
More informationLeast Squares Optimal Filtering with Multirate Observations
Prc. 36th Asilmar Cnf. n Signals, Systems, and Cmputers, Pacific Grve, CA, Nvember 2002 Least Squares Optimal Filtering with Multirate Observatins Charles W. herrien and Anthny H. Hawes Department f Electrical
More informationA New Evaluation Measure. J. Joiner and L. Werner. The problems of evaluation and the needed criteria of evaluation
III-l III. A New Evaluatin Measure J. Jiner and L. Werner Abstract The prblems f evaluatin and the needed criteria f evaluatin measures in the SMART system f infrmatin retrieval are reviewed and discussed.
More informationDepartment of Electrical Engineering, University of Waterloo. Introduction
Sectin 4: Sequential Circuits Majr Tpics Types f sequential circuits Flip-flps Analysis f clcked sequential circuits Mre and Mealy machines Design f clcked sequential circuits State transitin design methd
More informationLinearization of the Output of a Wheatstone Bridge for Single Active Sensor. Madhu Mohan N., Geetha T., Sankaran P. and Jagadeesh Kumar V.
Linearizatin f the Output f a Wheatstne Bridge fr Single Active Sensr Madhu Mhan N., Geetha T., Sankaran P. and Jagadeesh Kumar V. Dept. f Electrical Engineering, Indian Institute f Technlgy Madras, Chennai
More informationDesign and Simulation of Dc-Dc Voltage Converters Using Matlab/Simulink
American Jurnal f Engineering Research (AJER) 016 American Jurnal f Engineering Research (AJER) e-issn: 30-0847 p-issn : 30-0936 Vlume-5, Issue-, pp-9-36 www.ajer.rg Research Paper Open Access Design and
More informationMethods for Determination of Mean Speckle Size in Simulated Speckle Pattern
0.478/msr-04-004 MEASUREMENT SCENCE REVEW, Vlume 4, N. 3, 04 Methds fr Determinatin f Mean Speckle Size in Simulated Speckle Pattern. Hamarvá, P. Šmíd, P. Hrváth, M. Hrabvský nstitute f Physics f the Academy
More informationNUROP CONGRESS PAPER CHINESE PINYIN TO CHINESE CHARACTER CONVERSION
NUROP Chinese Pinyin T Chinese Character Cnversin NUROP CONGRESS PAPER CHINESE PINYIN TO CHINESE CHARACTER CONVERSION CHIA LI SHI 1 AND LUA KIM TENG 2 Schl f Cmputing, Natinal University f Singapre 3 Science
More informationA Study on Pullout Strength of Cast-in-place Anchor bolt in Concrete under High Temperature
Transactins f the 7 th Internatinal Cnference n Structural Mechanics in Reactr Technlgy (SMiRT 7) Prague, Czech Republic, August 7 22, 23 Paper #H-2 A Study n Pullut Strength f Cast-in-place Anchr blt
More informationRevision: August 19, E Main Suite D Pullman, WA (509) Voice and Fax
.7.4: Direct frequency dmain circuit analysis Revisin: August 9, 00 5 E Main Suite D Pullman, WA 9963 (509) 334 6306 ice and Fax Overview n chapter.7., we determined the steadystate respnse f electrical
More informationBiplots in Practice MICHAEL GREENACRE. Professor of Statistics at the Pompeu Fabra University. Chapter 13 Offprint
Biplts in Practice MICHAEL GREENACRE Prfessr f Statistics at the Pmpeu Fabra University Chapter 13 Offprint CASE STUDY BIOMEDICINE Cmparing Cancer Types Accrding t Gene Epressin Arrays First published:
More informationCS 477/677 Analysis of Algorithms Fall 2007 Dr. George Bebis Course Project Due Date: 11/29/2007
CS 477/677 Analysis f Algrithms Fall 2007 Dr. Gerge Bebis Curse Prject Due Date: 11/29/2007 Part1: Cmparisn f Srting Algrithms (70% f the prject grade) The bjective f the first part f the assignment is
More information^YawataR&D Laboratory, Nippon Steel Corporation, Tobata, Kitakyushu, Japan
Detectin f fatigue crack initiatin frm a ntch under a randm lad C. Makabe," S. Nishida^C. Urashima,' H. Kaneshir* "Department f Mechanical Systems Engineering, University f the Ryukyus, Nishihara, kinawa,
More informationA Matrix Representation of Panel Data
web Extensin 6 Appendix 6.A A Matrix Representatin f Panel Data Panel data mdels cme in tw brad varieties, distinct intercept DGPs and errr cmpnent DGPs. his appendix presents matrix algebra representatins
More informationA mathematical model for complete stress-strain curve prediction of permeable concrete
A mathematical mdel fr cmplete stress-strain curve predictin f permeable cncrete M. K. Hussin Y. Zhuge F. Bullen W. P. Lkuge Faculty f Engineering and Surveying, University f Suthern Queensland, Twmba,
More informationthe results to larger systems due to prop'erties of the projection algorithm. First, the number of hidden nodes must
M.E. Aggune, M.J. Dambrg, M.A. El-Sharkawi, R.J. Marks II and L.E. Atlas, "Dynamic and static security assessment f pwer systems using artificial neural netwrks", Prceedings f the NSF Wrkshp n Applicatins
More information4th Indian Institute of Astrophysics - PennState Astrostatistics School July, 2013 Vainu Bappu Observatory, Kavalur. Correlation and Regression
4th Indian Institute f Astrphysics - PennState Astrstatistics Schl July, 2013 Vainu Bappu Observatry, Kavalur Crrelatin and Regressin Rahul Ry Indian Statistical Institute, Delhi. Crrelatin Cnsider a tw
More informationModeling the Nonlinear Rheological Behavior of Materials with a Hyper-Exponential Type Function
www.ccsenet.rg/mer Mechanical Engineering Research Vl. 1, N. 1; December 011 Mdeling the Nnlinear Rhelgical Behavir f Materials with a Hyper-Expnential Type Functin Marc Delphin Mnsia Département de Physique,
More informationECEN 4872/5827 Lecture Notes
ECEN 4872/5827 Lecture Ntes Lecture #5 Objectives fr lecture #5: 1. Analysis f precisin current reference 2. Appraches fr evaluating tlerances 3. Temperature Cefficients evaluatin technique 4. Fundamentals
More informationOptimization Programming Problems For Control And Management Of Bacterial Disease With Two Stage Growth/Spread Among Plants
Internatinal Jurnal f Engineering Science Inventin ISSN (Online): 9 67, ISSN (Print): 9 676 www.ijesi.rg Vlume 5 Issue 8 ugust 06 PP.0-07 Optimizatin Prgramming Prblems Fr Cntrl nd Management Of Bacterial
More informationBASD HIGH SCHOOL FORMAL LAB REPORT
BASD HIGH SCHOOL FORMAL LAB REPORT *WARNING: After an explanatin f what t include in each sectin, there is an example f hw the sectin might lk using a sample experiment Keep in mind, the sample lab used
More informationCHAPTER 3 INEQUALITIES. Copyright -The Institute of Chartered Accountants of India
CHAPTER 3 INEQUALITIES Cpyright -The Institute f Chartered Accuntants f India INEQUALITIES LEARNING OBJECTIVES One f the widely used decisin making prblems, nwadays, is t decide n the ptimal mix f scarce
More informationEnhancing Performance of MLP/RBF Neural Classifiers via an Multivariate Data Distribution Scheme
Enhancing Perfrmance f / Neural Classifiers via an Multivariate Data Distributin Scheme Halis Altun, Gökhan Gelen Nigde University, Electrical and Electrnics Engineering Department Nigde, Turkey haltun@nigde.edu.tr
More informationFebruary 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA
February 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA Mental Experiment regarding 1D randm walk Cnsider a cntainer f gas in thermal
More informationo o IMPORTANT REMINDERS Reports will be graded largely on their ability to clearly communicate results and important conclusions.
BASD High Schl Frmal Lab Reprt GENERAL INFORMATION 12 pt Times New Rman fnt Duble-spaced, if required by yur teacher 1 inch margins n all sides (tp, bttm, left, and right) Always write in third persn (avid
More informationInterference is when two (or more) sets of waves meet and combine to produce a new pattern.
Interference Interference is when tw (r mre) sets f waves meet and cmbine t prduce a new pattern. This pattern can vary depending n the riginal wave directin, wavelength, amplitude, etc. The tw mst extreme
More informationIntroduction to Smith Charts
Intrductin t Smith Charts Dr. Russell P. Jedlicka Klipsch Schl f Electrical and Cmputer Engineering New Mexic State University as Cruces, NM 88003 September 2002 EE521 ecture 3 08/22/02 Smith Chart Summary
More informationEric Klein and Ning Sa
Week 12. Statistical Appraches t Netwrks: p1 and p* Wasserman and Faust Chapter 15: Statistical Analysis f Single Relatinal Netwrks There are fur tasks in psitinal analysis: 1) Define Equivalence 2) Measure
More informationMODULE FOUR. This module addresses functions. SC Academic Elementary Algebra Standards:
MODULE FOUR This mdule addresses functins SC Academic Standards: EA-3.1 Classify a relatinship as being either a functin r nt a functin when given data as a table, set f rdered pairs, r graph. EA-3.2 Use
More informationSections 15.1 to 15.12, 16.1 and 16.2 of the textbook (Robbins-Miller) cover the materials required for this topic.
Tpic : AC Fundamentals, Sinusidal Wavefrm, and Phasrs Sectins 5. t 5., 6. and 6. f the textbk (Rbbins-Miller) cver the materials required fr this tpic.. Wavefrms in electrical systems are current r vltage
More informationLyapunov Stability Stability of Equilibrium Points
Lyapunv Stability Stability f Equilibrium Pints 1. Stability f Equilibrium Pints - Definitins In this sectin we cnsider n-th rder nnlinear time varying cntinuus time (C) systems f the frm x = f ( t, x),
More informationROUNDING ERRORS IN BEAM-TRACKING CALCULATIONS
Particle Acceleratrs, 1986, Vl. 19, pp. 99-105 0031-2460/86/1904-0099/$15.00/0 1986 Grdn and Breach, Science Publishers, S.A. Printed in the United States f America ROUNDING ERRORS IN BEAM-TRACKING CALCULATIONS
More informationAnalysis on the Stability of Reservoir Soil Slope Based on Fuzzy Artificial Neural Network
Research Jurnal f Applied Sciences, Engineering and Technlgy 5(2): 465-469, 2013 ISSN: 2040-7459; E-ISSN: 2040-7467 Maxwell Scientific Organizatin, 2013 Submitted: May 08, 2012 Accepted: May 29, 2012 Published:
More informationinitially lcated away frm the data set never win the cmpetitin, resulting in a nnptimal nal cdebk, [2] [3] [4] and [5]. Khnen's Self Organizing Featur
Cdewrd Distributin fr Frequency Sensitive Cmpetitive Learning with One Dimensinal Input Data Aristides S. Galanpuls and Stanley C. Ahalt Department f Electrical Engineering The Ohi State University Abstract
More informationSupporting information
Electrnic Supplementary Material (ESI) fr Physical Chemistry Chemical Physics This jurnal is The wner Scieties 01 ydrgen perxide electrchemistry n platinum: twards understanding the xygen reductin reactin
More informationKinetic Model Completeness
5.68J/10.652J Spring 2003 Lecture Ntes Tuesday April 15, 2003 Kinetic Mdel Cmpleteness We say a chemical kinetic mdel is cmplete fr a particular reactin cnditin when it cntains all the species and reactins
More informationCalculating the optimum pressure and temperature for vacancy minimization from theory; Niobium is an example. Jozsef Garai
Calculating the ptimum pressure and temperature fr vacancy minimizatin frm thery; Nibium is an example Jzsef Garai Department f Mechanical and Materials Engineering, Flrida Internatinal University, Miami,
More informationModule 4: General Formulation of Electric Circuit Theory
Mdule 4: General Frmulatin f Electric Circuit Thery 4. General Frmulatin f Electric Circuit Thery All electrmagnetic phenmena are described at a fundamental level by Maxwell's equatins and the assciated
More informationA Novel Electro-thermal Simulation Approach to Power IGBT Modules for Automotive Traction Applications
Special Issue Recent R&D Activities f Pwer Devices fr Hybrid Electric Vehicles 27 Research Reprt A Nvel Electr-thermal Simulatin Apprach t Pwer IGBT Mdules fr Autmtive Tractin Applicatins Takashi Kjima,
More informationPerformance Bounds for Detect and Avoid Signal Sensing
Perfrmance unds fr Detect and Avid Signal Sensing Sam Reisenfeld Real-ime Infrmatin etwrks, University f echnlgy, Sydney, radway, SW 007, Australia samr@uts.edu.au Abstract Detect and Avid (DAA) is a Cgnitive
More informationComputational modeling techniques
Cmputatinal mdeling techniques Lecture 4: Mdel checing fr ODE mdels In Petre Department f IT, Åb Aademi http://www.users.ab.fi/ipetre/cmpmd/ Cntent Stichimetric matrix Calculating the mass cnservatin relatins
More informationBuilding to Transformations on Coordinate Axis Grade 5: Geometry Graph points on the coordinate plane to solve real-world and mathematical problems.
Building t Transfrmatins n Crdinate Axis Grade 5: Gemetry Graph pints n the crdinate plane t slve real-wrld and mathematical prblems. 5.G.1. Use a pair f perpendicular number lines, called axes, t define
More informationCOMP 551 Applied Machine Learning Lecture 11: Support Vector Machines
COMP 551 Applied Machine Learning Lecture 11: Supprt Vectr Machines Instructr: (jpineau@cs.mcgill.ca) Class web page: www.cs.mcgill.ca/~jpineau/cmp551 Unless therwise nted, all material psted fr this curse
More informationIN a recent article, Geary [1972] discussed the merit of taking first differences
The Efficiency f Taking First Differences in Regressin Analysis: A Nte J. A. TILLMAN IN a recent article, Geary [1972] discussed the merit f taking first differences t deal with the prblems that trends
More informationTutorial 4: Parameter optimization
SRM Curse 2013 Tutrial 4 Parameters Tutrial 4: Parameter ptimizatin The aim f this tutrial is t prvide yu with a feeling f hw a few f the parameters that can be set n a QQQ instrument affect SRM results.
More information, which yields. where z1. and z2
The Gaussian r Nrmal PDF, Page 1 The Gaussian r Nrmal Prbability Density Functin Authr: Jhn M Cimbala, Penn State University Latest revisin: 11 September 13 The Gaussian r Nrmal Prbability Density Functin
More informationFunctional Form and Nonlinearities
Sectin 6 Functinal Frm and Nnlinearities This is a gd place t remind urselves f Assumptin #0: That all bservatins fllw the same mdel. Levels f measurement and kinds f variables There are (at least) three
More informationTechnical Bulletin. Generation Interconnection Procedures. Revisions to Cluster 4, Phase 1 Study Methodology
Technical Bulletin Generatin Intercnnectin Prcedures Revisins t Cluster 4, Phase 1 Study Methdlgy Release Date: Octber 20, 2011 (Finalizatin f the Draft Technical Bulletin released n September 19, 2011)
More informationENSC Discrete Time Systems. Project Outline. Semester
ENSC 49 - iscrete Time Systems Prject Outline Semester 006-1. Objectives The gal f the prject is t design a channel fading simulatr. Upn successful cmpletin f the prject, yu will reinfrce yur understanding
More informationSnow avalanche runout from two Canadian mountain ranges
Annals f Glacilgy 18 1993 Internati n al Glaciigicai Sciety Snw avalanche runut frm tw Canadian muntain ranges D.J. NIXON AND D. M. MCCLUNG Department f Civil Engineering, University f British Clumbia,
More informationmaking triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y=
Intrductin t Vectrs I 21 Intrductin t Vectrs I 22 I. Determine the hrizntal and vertical cmpnents f the resultant vectr by cunting n the grid. X= y= J. Draw a mangle with hrizntal and vertical cmpnents
More informationTHERMAL TEST LEVELS & DURATIONS
PREFERRED RELIABILITY PAGE 1 OF 7 PRACTICES PRACTICE NO. PT-TE-144 Practice: 1 Perfrm thermal dwell test n prtflight hardware ver the temperature range f +75 C/-2 C (applied at the thermal cntrl/munting
More informationEXPERIMENTAL STUDY ON DISCHARGE COEFFICIENT OF OUTFLOW OPENING FOR PREDICTING CROSS-VENTILATION FLOW RATE
EXPERIMENTAL STUD ON DISCHARGE COEFFICIENT OF OUTFLOW OPENING FOR PREDICTING CROSS-VENTILATION FLOW RATE Tmnbu Gt, Masaaki Ohba, Takashi Kurabuchi 2, Tmyuki End 3, shihik Akamine 4, and Tshihir Nnaka 2
More informationMultiple Source Multiple. using Network Coding
Multiple Surce Multiple Destinatin Tplgy Inference using Netwrk Cding Pegah Sattari EECS, UC Irvine Jint wrk with Athina Markpulu, at UCI, Christina Fraguli, at EPFL, Lausanne Outline Netwrk Tmgraphy Gal,
More informationStructural mechanics of wood composite materials h Ultrasonic evaluation of internal bond strength during an accelerated aging test
J Wd Sci (1998) 44:348-353 The Japan Wd Research Sciety 1998 Yu-Gu Sun Takanri Arima Structural mechanics f wd cmpsite materials h Ultrasnic evaluatin f internal bnd strength during an accelerated aging
More informationSequential Allocation with Minimal Switching
In Cmputing Science and Statistics 28 (1996), pp. 567 572 Sequential Allcatin with Minimal Switching Quentin F. Stut 1 Janis Hardwick 1 EECS Dept., University f Michigan Statistics Dept., Purdue University
More informationDead-beat controller design
J. Hetthéssy, A. Barta, R. Bars: Dead beat cntrller design Nvember, 4 Dead-beat cntrller design In sampled data cntrl systems the cntrller is realised by an intelligent device, typically by a PLC (Prgrammable
More informationStudy Group Report: Plate-fin Heat Exchangers: AEA Technology
Study Grup Reprt: Plate-fin Heat Exchangers: AEA Technlgy The prblem under study cncerned the apparent discrepancy between a series f experiments using a plate fin heat exchanger and the classical thery
More informationWRITING THE REPORT. Organizing the report. Title Page. Table of Contents
WRITING THE REPORT Organizing the reprt Mst reprts shuld be rganized in the fllwing manner. Smetime there is a valid reasn t include extra chapters in within the bdy f the reprt. 1. Title page 2. Executive
More informationACOUSTIC LOGGING GUIDED WAVES IN TRANSVERSELY ISOTROPIC FORMATIONS
ACOUSTIC LOGGING GUIDED WAVES IN TRANSVERSELY ISOTROPIC FORMATIONS by K. J. Ellefsen, C. H. Cheng, and D.P. Schmitt" Earth Resurces Labratry Department f Earth, Atmspheric, and Planetary Sciences Massachusetts
More informationCAUSAL INFERENCE. Technical Track Session I. Phillippe Leite. The World Bank
CAUSAL INFERENCE Technical Track Sessin I Phillippe Leite The Wrld Bank These slides were develped by Christel Vermeersch and mdified by Phillippe Leite fr the purpse f this wrkshp Plicy questins are causal
More informationEngineering Approach to Modelling Metal THz Structures
Terahertz Science and Technlgy, ISSN 1941-7411 Vl.4, N.1, March 11 Invited Paper ngineering Apprach t Mdelling Metal THz Structures Stepan Lucyszyn * and Yun Zhu Department f, Imperial Cllege Lndn, xhibitin
More informationOn the Quantification of the Constraint Effect Along a Three-Dimensional Crack Front
Internatinal Jurnal f Mechanical Engineering and Applicatins 206; 4(6): 226-23 http://www.sciencepublishinggrup.cm/j/ijmea di: 0.648/j.ijmea.2060406.3 ISSN: 2330-023X (Print); ISSN: 2330-0248 (Online)
More informationMath Foundations 10 Work Plan
Math Fundatins 10 Wrk Plan Units / Tpics 10.1 Demnstrate understanding f factrs f whle numbers by: Prime factrs Greatest Cmmn Factrs (GCF) Least Cmmn Multiple (LCM) Principal square rt Cube rt Time Frame
More informationhttps://goo.gl/eaqvfo SUMMER REV: Half-Life DUE DATE: JULY 2 nd
NAME: DUE DATE: JULY 2 nd AP Chemistry SUMMER REV: Half-Life Why? Every radiistpe has a characteristic rate f decay measured by its half-life. Half-lives can be as shrt as a fractin f a secnd r as lng
More information(2) Even if such a value of k was possible, the neutrons multiply
CHANGE OF REACTOR Nuclear Thery - Curse 227 POWER WTH REACTVTY CHANGE n this lessn, we will cnsider hw neutrn density, neutrn flux and reactr pwer change when the multiplicatin factr, k, r the reactivity,
More informationHypothesis Tests for One Population Mean
Hypthesis Tests fr One Ppulatin Mean Chapter 9 Ala Abdelbaki Objective Objective: T estimate the value f ne ppulatin mean Inferential statistics using statistics in rder t estimate parameters We will be
More informationA Correlation of. to the. South Carolina Academic Standards for Mathematics Precalculus
A Crrelatin f Suth Carlina Academic Standards fr Mathematics Precalculus INTRODUCTION This dcument demnstrates hw Precalculus (Blitzer), 4 th Editin 010, meets the indicatrs f the. Crrelatin page references
More informationModelling of NOLM Demultiplexers Employing Optical Soliton Control Pulse
Micwave and Optical Technlgy Letters, Vl. 1, N. 3, 1999. pp. 05-08 Mdelling f NOLM Demultiplexers Emplying Optical Slitn Cntrl Pulse Z. Ghassemly, C. Y. Cheung & A. K. Ray Electrnics Research Grup, Schl
More informationWhat is Statistical Learning?
What is Statistical Learning? Sales 5 10 15 20 25 Sales 5 10 15 20 25 Sales 5 10 15 20 25 0 50 100 200 300 TV 0 10 20 30 40 50 Radi 0 20 40 60 80 100 Newspaper Shwn are Sales vs TV, Radi and Newspaper,
More informationOn Huntsberger Type Shrinkage Estimator for the Mean of Normal Distribution ABSTRACT INTRODUCTION
Malaysian Jurnal f Mathematical Sciences 4(): 7-4 () On Huntsberger Type Shrinkage Estimatr fr the Mean f Nrmal Distributin Department f Mathematical and Physical Sciences, University f Nizwa, Sultanate
More informationResampling Methods. Chapter 5. Chapter 5 1 / 52
Resampling Methds Chapter 5 Chapter 5 1 / 52 1 51 Validatin set apprach 2 52 Crss validatin 3 53 Btstrap Chapter 5 2 / 52 Abut Resampling An imprtant statistical tl Pretending the data as ppulatin and
More informationWe can see from the graph above that the intersection is, i.e., [ ).
MTH 111 Cllege Algebra Lecture Ntes July 2, 2014 Functin Arithmetic: With nt t much difficulty, we ntice that inputs f functins are numbers, and utputs f functins are numbers. S whatever we can d with
More informationarxiv:hep-ph/ v1 2 Jun 1995
WIS-95//May-PH The rati F n /F p frm the analysis f data using a new scaling variable S. A. Gurvitz arxiv:hep-ph/95063v1 Jun 1995 Department f Particle Physics, Weizmann Institute f Science, Rehvt 76100,
More informationCHAPTER 24: INFERENCE IN REGRESSION. Chapter 24: Make inferences about the population from which the sample data came.
MATH 1342 Ch. 24 April 25 and 27, 2013 Page 1 f 5 CHAPTER 24: INFERENCE IN REGRESSION Chapters 4 and 5: Relatinships between tw quantitative variables. Be able t Make a graph (scatterplt) Summarize the
More informationHow do scientists measure trees? What is DBH?
Hw d scientists measure trees? What is DBH? Purpse Students develp an understanding f tree size and hw scientists measure trees. Students bserve and measure tree ckies and explre the relatinship between
More informationPhysical Layer: Outline
18-: Intrductin t Telecmmunicatin Netwrks Lectures : Physical Layer Peter Steenkiste Spring 01 www.cs.cmu.edu/~prs/nets-ece Physical Layer: Outline Digital Representatin f Infrmatin Characterizatin f Cmmunicatin
More informationA Novel Stochastic-Based Algorithm for Terrain Splitting Optimization Problem
A Nvel Stchastic-Based Algrithm fr Terrain Splitting Optimizatin Prblem Le Hang Sn Nguyen inh Ha Abstract This paper deals with the prblem f displaying large igital Elevatin Mdel data in 3 GIS urrent appraches
More informationSynchronous Motor V-Curves
Synchrnus Mtr V-Curves 1 Synchrnus Mtr V-Curves Intrductin Synchrnus mtrs are used in applicatins such as textile mills where cnstant speed peratin is critical. Mst small synchrnus mtrs cntain squirrel
More informationDrought damaged area
ESTIMATE OF THE AMOUNT OF GRAVEL CO~TENT IN THE SOIL BY A I R B O'RN EMS S D A T A Y. GOMI, H. YAMAMOTO, AND S. SATO ASIA AIR SURVEY CO., l d. KANAGAWA,JAPAN S.ISHIGURO HOKKAIDO TOKACHI UBPREFECTRAl OffICE
More informationA Regression Solution to the Problem of Criterion Score Comparability
A Regressin Slutin t the Prblem f Criterin Scre Cmparability William M. Pugh Naval Health Research Center When the criterin measure in a study is the accumulatin f respnses r behavirs fr an individual
More informationand the Doppler frequency rate f R , can be related to the coefficients of this polynomial. The relationships are:
Algrithm fr Estimating R and R - (David Sandwell, SIO, August 4, 2006) Azimith cmpressin invlves the alignment f successive eches t be fcused n a pint target Let s be the slw time alng the satellite track
More informationSPH3U1 Lesson 06 Kinematics
PROJECTILE MOTION LEARNING GOALS Students will: Describe the mtin f an bject thrwn at arbitrary angles thrugh the air. Describe the hrizntal and vertical mtins f a prjectile. Slve prjectile mtin prblems.
More informationANALYTICAL MODEL FOR PREDICTING STRESS-STRAIN BEHAVIOUR OF BACTERIAL CONCRETE
Internatinal Jurnal f Civil Engineering and Technlgy (IJCIET) Vlume 9, Issue 11, Nvember 018, pp. 383 393, Article ID: IJCIET_09_11_38 Available nline at http://www.iaeme.cm/ijciet/issues.asp?jtype=ijciet&vtype=9&itype=11
More informationLesson Plan. Recode: They will do a graphic organizer to sequence the steps of scientific method.
Lessn Plan Reach: Ask the students if they ever ppped a bag f micrwave ppcrn and nticed hw many kernels were unppped at the bttm f the bag which made yu wnder if ther brands pp better than the ne yu are
More informationAP Statistics Practice Test Unit Three Exploring Relationships Between Variables. Name Period Date
AP Statistics Practice Test Unit Three Explring Relatinships Between Variables Name Perid Date True r False: 1. Crrelatin and regressin require explanatry and respnse variables. 1. 2. Every least squares
More informationENG2410 Digital Design Sequential Circuits: Part B
ENG24 Digital Design Sequential Circuits: Part B Fall 27 S. Areibi Schl f Engineering University f Guelph Analysis f Sequential Circuits Earlier we learned hw t analyze cmbinatinal circuits We will extend
More informationALE 21. Gibbs Free Energy. At what temperature does the spontaneity of a reaction change?
Name Chem 163 Sectin: Team Number: ALE 21. Gibbs Free Energy (Reference: 20.3 Silberberg 5 th editin) At what temperature des the spntaneity f a reactin change? The Mdel: The Definitin f Free Energy S
More informationChapter 3: Cluster Analysis
Chapter 3: Cluster Analysis } 3.1 Basic Cncepts f Clustering 3.1.1 Cluster Analysis 3.1. Clustering Categries } 3. Partitining Methds 3..1 The principle 3.. K-Means Methd 3..3 K-Medids Methd 3..4 CLARA
More informationMath Foundations 20 Work Plan
Math Fundatins 20 Wrk Plan Units / Tpics 20.8 Demnstrate understanding f systems f linear inequalities in tw variables. Time Frame December 1-3 weeks 6-10 Majr Learning Indicatrs Identify situatins relevant
More informationAerodynamic Separability in Tip Speed Ratio and Separability in Wind Speed- a Comparison
Jurnal f Physics: Cnference Series OPEN ACCESS Aerdynamic Separability in Tip Speed Rati and Separability in Wind Speed- a Cmparisn T cite this article: M L Gala Sants et al 14 J. Phys.: Cnf. Ser. 555
More informationDataflow Analysis and Abstract Interpretation
Dataflw Analysis and Abstract Interpretatin Cmputer Science and Artificial Intelligence Labratry MIT Nvember 9, 2015 Recap Last time we develped frm first principles an algrithm t derive invariants. Key
More information3.4 Shrinkage Methods Prostate Cancer Data Example (Continued) Ridge Regression
3.3.4 Prstate Cancer Data Example (Cntinued) 3.4 Shrinkage Methds 61 Table 3.3 shws the cefficients frm a number f different selectin and shrinkage methds. They are best-subset selectin using an all-subsets
More informationPressure And Entropy Variations Across The Weak Shock Wave Due To Viscosity Effects
Pressure And Entrpy Variatins Acrss The Weak Shck Wave Due T Viscsity Effects OSTAFA A. A. AHOUD Department f athematics Faculty f Science Benha University 13518 Benha EGYPT Abstract:-The nnlinear differential
More information[COLLEGE ALGEBRA EXAM I REVIEW TOPICS] ( u s e t h i s t o m a k e s u r e y o u a r e r e a d y )
(Abut the final) [COLLEGE ALGEBRA EXAM I REVIEW TOPICS] ( u s e t h i s t m a k e s u r e y u a r e r e a d y ) The department writes the final exam s I dn't really knw what's n it and I can't very well
More informationDepartment of Economics, University of California, Davis Ecn 200C Micro Theory Professor Giacomo Bonanno. Insurance Markets
Department f Ecnmics, University f alifrnia, Davis Ecn 200 Micr Thery Prfessr Giacm Bnann Insurance Markets nsider an individual wh has an initial wealth f. ith sme prbability p he faces a lss f x (0
More information