Saturation current density, Vbi Builtin voltage

	Variable	Description

	Js	Saturation current density
	L	Drawn mask length (PN Step Junctions), or
	L	Drawn gate length (NMOS Transistors), or
		Channel length (JFETs)
	Le	Effectives gate length
	NA	Pside doping (PN Step Junctions), or
	NA	Substrate doping (NMOS Transistors)
		Substrate doping (NMOS Transistors)
	ND	Nside doping (PN Step Junctions), or
	ND	Nchannel doping (JFETs)
		Nchannel doping (JFETs)

TTemperature

tox	Gate silicon dioxide thickness
Va	Applied voltage
VBC	Basetocollector voltage
VBE	Basetoemitter voltage
Vbi	Builtin voltage
VBS	Substrate voltage
VCEsat	Collectortoemitter saturation voltage
VDS	Applied drain voltage
VDsat	Saturation voltage
VGS	Applied gate voltage
Vt	Threshold voltage
Vt0	Threshold voltage (at zero substrate voltage)
W	Drawn mask width (PN Step Junctions), or
W	Drawn width (NMOS Transistors), or
	Channel width (JFETs)
We	Effective width
xd	Depletionregion width
xdmax	Depletionlayer width
xj	Junction depth

References: 5, 8.

Equation Reference 551

Page 487

Image 487

HP 48gII Graphing, 50g Graphing Saturation current density, Drawn mask length PN Step Junctions, or, Channel length JFETs

Contents

Advanced user’s reference manual HP 50g / 49g+ / 48gII graphing calculatorPage Printing History AcknowledgementsPage Contents Amort NamesAlgb Alog 317 COL→ DelalarmDelay →COL 359 Expand FindalarmEXP2POW Expan Iferr HaltIBP IDIV2 List Not MAXMaxr MIN Parsurface PA2B2Parametric Parity 3183 Rolld RNDRnrm Roll 3226 TAN Tabvar→TAG Tail Utpf WireframeUpdir Utpc Contents 514 →ALG Apeek ARM→ ASM ASM→ 610 Vpar AlrmdatCST Exited Expr Iopar MASD.INI Toff Tpar Understanding Programming Contents of a Program Examples of Program Actions Calculations in a ProgramProgram Results To store or name a program To enter commands and other objects in a programEntering and Executing Programs To enter a program @% @Ér # O4 /3 *!Ì Q3 @Ë@Ï To stop an executing program3Q!Ì*4`3/*@Ï 3Q!Ì*4#3/* @Ë@Ï Program Keys Comments LevelOsph K @%SPH% ˜ To switch between entry modesViewing and Editing Programs To view or edit a program `J!%SPH% @%SPH% ˜ Using Local VariablesCreating Programs on a Computer Creating Local Variables `OSPHLV K Program Comments Defining the Scope of Local Variables Evaluating Local Names Creating UserDefined Functions as Programs Compiled Local Variables To include a test in a program Using Tests and Conditional StructuresTesting Conditions Key Programmable Description Command TEST% L Using Logical FunctionsKeys Programmable Description Command Logical Functions To enter IFT in a program Using Conditional Structures and CommandsTo enter if then END in a program Press !%BRCH% !%IF% Press !%BRCH% L!%IFTE% To enter if then Else END in a programPress !%BRCH% @%#IF#% To enter Ifte in a program or in an algebraic Conditional Examples To enter Case END in a program 26 `52 J %TST% Otst K Using Definite Loop Structures Using Loop StructuresWhile … Repeat … END Press !%BRCH% !%START% Start Next Structure« … start finish Start loopclause Next … » To enter Start Next in a program Press ! %BRCH% … %START% Start Step Structure« … start finish Start loopclause increment Step … » To enter Start Step in a program Press !%BRCH% ! %FOR% For Next Structure« … start finish for counter loopclause Next … » To enter for Next in a program Press ! %BRCH% … %FOR% For Step Structure« … start finish for counter loopclause increment Step … » To enter for Step in a program To enter do Until END in a program Using Indefinite Loop StructuresDo Until END Structure « … do loopclause Until testclause END … » Duplicates n, stores the value into n Press !%BRCH% ! %WHILE% While Repeat END Structure« … While testclause Repeat loopclause END … » To enter While Repeat END in a program To enter Incr or Decr in a program Using Loop CountersPress ! #MEM# %ARITH% %INCR% or %DECR% ∑ j Using Summations Instead of Loops To set, clear, or test a flag Using FlagsSetting, Clearing, and Testing Flags Types of Flags Day.month.year format Recalling and Storing the Flag StatesExample Month/day/year format To change the current flag states Using SubroutinesTo recall the current flag states Execute Rclf !L %MODES% %FLAG% L%RCLF% Torsv K Torsa K` 8 J %TORSV% @·J6 `8 `O%TORSV% !LL%RUN% %DBUG% To singlestep from the start of a programTo turn off the Halt annunciator at any time Press !LL %RUN% %KILL% To singlestep from the middle of a program To singlestep when the next step is a subroutine@·J10 `12 O%TORSV% !LL%RUN% %DBUG% SingleStep Operations Trapping ErrorsCausing and Analyzing Errors To cause a userdefined error to occur in a program %ERROR% To artificially cause a builtin error to occur in a programTo analyze an error in a program Error Trapping Commands Iferr then END Structure Making an Error Trap« … Iferr trapclause then errorclause END … » Press !LL %ERROR% !%IFERR% Iferr then Else END Structure Press !LL %ERROR% @%IFERR%To enter Iferr then Else END in a program Input Data Input CommandsUsing PROMPT, Cont for Input Key Command Description @·J %TPROM% `OTPROMPT ‰ To enter Disp Freeze Halt in a program Using Disp Freeze HALT, Cont for InputTo respond to Halt while running a program To respond to Input while running a program Using INPUT, Enter for Input« … promptstring commandline Input OBJ→ … » To enter Input in a program %VSPH% Cursorposition Commandline cursorposition operatingoptionsTo design the commandline string for Input To include Input options Press @ Õ ! Ê a @ To process the result string from Input`O Tinput ‰ %TINPU% To set up an input form Using Inform and Choose for Input To set up a choose box `OPHONES ‰ To enter Wait in a program Using Wait for Keystroke InputBeeping to Get Attention To enter Beep in a program OUT% Using KEY for Keystroke InputData Output Commands Output %TTAG% 1.5 ˜1.85 ` Labeling Output with TagsLabeling and Displaying Output as Strings To label a result with a tag `OTSTRING ‰ Pausing to Display OutputUsing Msgbox to Display Output To set up a message box Using Menus for Input Using Menus with Programs SI% Using Menus to Run ProgramsTo create a menubased application Olst ‰ @·J%EIZ% To turn off the calculator in a program Turning Off the Calculator from a Program%% !Ü.37~@6 68 %%I%% !%%Z%% @%%I%% 2*%%I%% !%%E%%Page FIB1 Fibonacci Numbers, Recursive Version Fibonacci NumbersRPL Programming Examples %FIB1% FIB2 Fibonacci Numbers, Loop VersionFIB1% !Ü10 N %FIB2% FIB2 program listing10 %FIB2% Required Programs Fibt Comparing ProgramExecution TimeTechniques used in Fibt Structured programming. Fibt calls both FIB1 and FIB2 Techniques used in PAD Displaying a Binary IntegerPAD Pad with Leading Spaces 13 %FIBT% Techniques used in Preserve Preserve Save and Restore Previous StatusPAD program listing `OPAD K Preserve program listing Bdisp Binary Display`OPRESERVE K PAD Techniques used in Bdisp `OBDISP K Bdisp program listing Tile Percentile of a list Median of Statistics Data144 %BDISP% `O%TILE K Median Median of Statistics DataTechniques used in %TILE Tile program listing Required Program Techniques used in Median 11 `1 ` Expanding and Collecting Completely`OMEDIAN K 18 `12 `˜šš `OMULTI K Multi Multiple ExecutionTechniques used in Multi Multi program listing `OEXCO K Exco Expand and Collect CompletelyTechniques used in Exco Exco program listing User and system flags for logic control Minimum and Maximum Array ElementsMNX Minimum or Maximum Element-Version Ü4 *Y+Z + `OMNX K MNX program listing 12 `56 `˜šš 45 `1 ` MNX2 Minimum or Maximum Element-VersionTechniques used in MNX2 MNX2 program listing Aply program listing Applying a Program to an Array%MNX2% Techniques used in Aply Make sure the flag 1 is clear to begin Techniques used in nBASE Converting Between Number Bases`OAPLY K Ô3†2W†4` ‚Å 3 QA *7 `J %APLY% H#DISP ˜˜ NBASE program listing 1000 `23 J %NBASE% Verifying Program Arguments `ONAMES K Names Check List for Exactly Two NamesTechniques used in Names Names program listing Techniques used in VFY VFY Verify Program ArgumentVFY program listing %LIST% %²LIST% Converting Procedures from Algebraic to RPNOben ` Ojeff ` Osarah ` →RPN program listing Techniques used in →RPN XQ3 `%²RPN% Bessel FunctionsTechniques used in BER %BER% !Ü2 BER program listing`OBER K %BER% Sintp program listing Animation of Successive Taylor’s PolynomialsSintp Converting a Plot to a Graphics Object Techniques used in Sintp `OSETTS K Setts Superimposing Taylor’s polynomialsTechniques used in Setts Setts program listing `OTSA K TSA Animating Taylor’s PolynomialsTechniques used in TSA TSA program listing Temporary menu for data input Programmatic use of matrices and statistics commandsProgrammatic Use of Statistics and Plotting Techniques used in PIE Angle 983 %SLICE% 416 %SLICE% 85 %SLICE% `OPIE K ßENTER program listing Trace ModeTechniques used in αENTER and ßENTER ΑENTER program listing `OROOTR K InverseFunction SolverTechniques used in Rootr Rootr program listing Techniques used in Walk Animating a Graphical Image@Å@É x †O3.7 %X²FX% ` 599.5 ` 1 %ROOTR% `OWALK K Input/Output IntroductionAcos Type Other Provided Details How Commands Are AlphabetizedParallel Processing with Lists Classification of Operations Computer Algebra System Commands and Functions Binary integer Backup identifierRealnumber time or angle in hoursminutessecond s format Library identifier ABS AbcuvACK Type Description Ackall ASIN, ATAN, COS, Isol ACOS2S Symb ACOSHsymb AcoshASIN2C, ASIN2T, ATAN2S Acosh z Addtmod ADD 10z AddtorealAlgb Alog Principal Interest Balance AmortTVM, TVMBEG, TVMEND, Tvmroot ANS Animate Apply Access …µAPPLY Input/OutputARC ARG Archive →ARRY Access …µARRY→ Input/OutputArit ARRY→ Access !¼ ¼is the leftshift of the Skey ASIN2T ASIN2CAsinh ACOSH, ATANH, ISOL, Sinh ASNAsinh z Symb ASINHsymb Skey Access … ÃL BIT ASRASR Assume ADDTOREAL, Unassume Atan ACOS, ASIN, ISOL, TAN ATAN2SAtan z Symb ATANsymb Atanh z Access …µATICKAtanh Atick #n #m Access …µATTACH Input/OutputAttach Augment BAR Access …µAUTO Input/Output NoneAuto Axes Atick xaxis label yaxis label Access …µAXES Input/OutputAXL AXM AXL, AXM, GAUSS, QXA AXQBAR AXL, AXQ Baud Access …µBAR Input/Output NoneBarplot Basis Bestfit Access …µBESTFIT Input/Output NoneAccess … Ã BIN Beep BOX Access !L Pict BOX Is the leftshift of the NkeyBins Blank #n1 #m1 #n2 #m2 X1, y1 X2, y2 Access …µBUFLEN Input/OutputBuflen Bytes C2P Access … Ã B → RCascfg Case CascmdHelp FLOOR, IP, RND, Trnc CeilCentr Xunit Nunit Symb CEILsymb Cholesky Chinrem Choose Command ResultCHR REPL, SIZE, SUB CircCksm NUM, POS Closeio ClearClkadj Cllcd Cmplx CLΣClusr Clvar COL→ →COLCOL Symb1 Symb2 COL+Colct Collect Symb COMBsymb ,m COMBn, symb COMBsymb ,symb ColσComb CON IDN CondRarray constant Carray constant Name Conic Access …µCONIC Input/Output NoneConj Rarray Carray Symb CONJsymb ConlibConst Constants X1unitssource X2unitstarget X3unitstarget ContConvert Corr COV Access FlagsCOS Cosh …µCR CrdirCross Cswp COL+, COL-, Rswp CurlCyclotomic Cylin #n, #m →PXDarcy Date →date →DATEDATE+ Dbug « program » or program name DdaysDEC Decr Result See also DedicaceDEF Define Name=exp Namename Name =expname DelalarmDEG Degree CR, OLDPRT, PRLCD, PRST, PRSTC, PRVAR, PR1 DelayRCLALARM, Stoalarm Delkeys Xkey1, ... ,xkey n Access …µDEPND Input/OutputDepnd Depth Dervx DerivDesolve Attach Access …µDETACH Input/OutputDET Detach →DIAG DIAG→Diagmap Diffeq Diff DIR Access …µDIFFEQ Input/OutputDisp FREEZE, HALT, INPUT, Prompt DispxyDistrib Obj List CURL, Hess DIVDIV2 DIV2MOD DIV2 DivisDivmod Divpc END TAYLOR0, TAYLR, SeriesDERIV, DERVX, DESOLVE, ∂ Until testclause END Doerr ErrorDolist SIGNTAB, Tabvar List List n « program » Results Command Name List n+1Domain Dosubs CNRM, CROSS, DET, Rnrm List « program » Command NameDOT DOLIST, ENDSUB, NSUB, Stream DRAW3DMATRIX Access …µDRAWAccess …µDRAX Input/Output None Draw Lagrange DroiteDrop DROP2 DUP2 DropnDtag DUP Dupn Dupdup Editb EditEgcd END EGVEgvl Else Sign mantissa E sign exponent EndsubENG EPSX0 Erase EqnlibEQW EQ→ Euler ERR0Errm Errn →NUM EvalExlr Obj See above EXP EXP&LNEx,y = excosy + iexsiny EXP2POW EXP2HYPExpan Result X2+X ExpandExpandmod COLCT, EXPAND, ISOL, QUAD, Show Eyept ExpfitExpln Expm …µF0λ F0λFact Factor Factors FactormodModsto Fanning Access …µFANNINGFAST3D FC? Access …µFAST3D Input/Output NoneAccess ! Test LL FC ? C Fcoef Distrib FdistribFFT CF, FC?, FS? FS?C, SF Finish FindalarmAccess …µFINISH Filer Xunit Nunit Symb FLOORsymb FlashevalFloor FONT6 →FONT FONT7FONT8 FONT→ For Xunit Yunit Symb FPsymb FourierFree Freeze CLLCD, DISP, Halt FrootsFS? Display Area Value Code Function FS?CCF, FC?, FC?C, FS?C, SF Fxnd Access …µFUNCTIONExlr AXQ, QXA GammaGauss Gbasis GCDMOD, EGCD, IEGCD, LCM GCDGcdmod GET Objget GetiGETI, PUT, Puti #n #m Grob1 GORGrad GET, PUT, Puti DEG, RAD GramschmidtGraph Greduce →GROB Access …µGRIDMAP Input/Output NoneAccess …µ→GROB Gridmap →LCD, LCD→ GrobGrobadd Gxor GOR, REPL, SUB HadamardHalftan Halt Help HeadHEADER→ →HEADER CURL, DIV HermiteHess HEX Histogram Hilbert HMS+ Access …µHISTPLOT Input/Output NoneHistplot HMS … &9L HMS → HMS→→HMS … & 9L HMS + Horner HomeIabcuv ABCUV, Iegcd IbasisIbernoulli IBP Chinrem IchinremIDN Results See also Ax+by=c IDIV2Iegcd DIV2, Iquot Case IferrELSE, END, IFERR, then Ifft ∑ Y k e Obj It depends IFTIfte Ilap Rarray Carray Symb IMsymb ImageLAP, Lapl …ßIM Global Global xstart xend IncrIndep Inform Init ResetsTitle Format Resets Init → vals Input INT Stack prompt Commandline prompt ResultPROMPT, STR→ INTVX, Risch IntegerIntvx INV Invmod Command INVMOD2 ResultIquot Symb1 Global Symb2 IremainderIsol Isom NEXTPRIME, Prevprime ISPRIME?Jordan Mkisom BASIS, Image KERKerrm KEY Keyeval Access …µKEYEVAL Input/Output→KEYTIME Label KEYTIME→Kget Kill →LANGUAGE Access …µ→LANGUAGE Input/OutputLagrange LANGUAGE→ Objn Obj1 LAPLapl Last LCM LastargLCD→ →LCD Ldec Lcxm HERMITE, Tchebycheff LgcdLibeval Libs Title, nlib, nport, ...,title, nlib, nport LimLimit LIN Model Form of Expression LineΣline Linfit →LIST LininLinsolve LIST→ Πlist ListΣlist Access …¹ ¹is the rightshift of the Qkey Lncollect LnameLNP1 Symb LNP1symb LocalLOG Ln x + Logfit Access !Ø Input/Output Intercept x Slope x Access …µLR Input/OutputFull Command and Function Reference 3139 LSQ Lname LvarMAD DET, INV MAP Access …µMAP Input/OutputMain Mant Symb Symb symb Access …µ↓MATCH Input/OutputAccess …µ↑MATCH ↑MATCH Symb Symb , symb MathsMatr MAX Input/Output See also MaxrMaxσ Mcalc BINS, MAXΣ, MINΣ, SDEV, TOT, VAR MeanMEM Menu RCLMENU, Tmenu Menuxy MENU, Tmenu MergeMIN Minehunt Minr MINIFONT→→MINIFONT Minit 00000000000E-499 MinσMitm Mkisom Mod y MODModsto Modular Name Or xunit String MolwtMroot Msgbox Msolvr Mslv EQNLIB, MCALC, MINIT, MITM, MROOT, MSLV, Muser MultmodMuser →NDISP NEG Access …ß NEG ßis the rightshift of the 1keyNdist Ndupn Next NewobNextprime Noval Access ! Test L not Is the leftshift of the NkeyNIP Not …µNΣ Nsub→NUM NUM Numy NumxOBJ→ … &NL OBJ → OCTOFF Oldprt Access …µOPENIO Access …µOLDPRTOpenio Global1 ... globaln OrderOver Memory Directory Lorder is the leftshift of the Nkey Xmin, ymin, xmax, ymax, indep, res, axes, ptype, depend P2CPA2B2 Parametric Parity Access …µPARITY Input/Output Partfrac Parsurface Home directoryname 1 ... directoryname n PathPcar Pcoef Pcontour Access …µPCONTOUR Input/Output NonePcov Xmax, ymax PdimPerinfo Perm Pick PertblPeval Pgdir Pinit Pict Command Puts the name Pict on the stackPict Picture Pixon Access …µPKTPIX? Pixoff Pmin PlotPlotadd Pmax An nxn matrix a PminiPolar Finds the minimal polynomial of a matrix Form of Current Plotting Action Equation Access …µPOLARPolynomial POP Powexpand Input An expression raised to a powerPOS Potential PR1 Powmod Object PredvPredx …µPR1 Preval Predy Promptsto PrevprimePrlcd Prompt Prompt STO ProotPropfrac Global→ Name Name1 name2 Nport global PrstPrstc Prvar MEAN, PCOV, PVAR, SDEV, TOT, VAR PsdevPSI Psi Symb String or x or xunit or name PtaylPtprop Purge CLEAR, CLVAR, NEWOB, Pgdir PushPUT Global Global1 ... globaln Obj put List Name This command sequencePuti Obj put List Pvars PvarMEAN, PCOV, PSDEV, SDEV, VAR Pwrfit Access …µPVARS Input/OutputNport namebackup Memory Pview →Qπ PX→C+ c/d*i LQ, LSQ Quad̟ + c/ d* ̟ + c/ d Quotient of the Euclidean division QuotQuote Arithmetic, !ÞPOLYNOMIAL !« Rank QXARAD Rand LQ, LSQ, QR Access …µRATIORanm Ratio Steq RceqRCI Rcij RCL Rclalarm Rclmenu FINDALARM, StoalarmRclf Rclkeys RDM RclvxRclσ Rcws COMB, PERM, Rand RDZ…ßL RE REsymb RecnRect Recv New name Old name RemainderRename Quot END, While ReorderRepeat Repl String String result Plot Type Default IntervalRES String target Slopefield RestoreBackup To restore a Resultant Rewrite RevlistRisch Rkferr RKF Rkfstep Problem for a differential equationIs the rightshift 3key RNDsymb RLBRND RLB, RR, RRB Romupload RnrmRoll Rolld 3207 RootROT ROW ROW→ ROW+→ROW RL, RLB, RRB Access … ÃL Byte RRB Is the rightshift of the 3keyRPL RRB Rref Rref RRK Rrefmod Rrkstep − 2 t + t 2 RSD RsberrRKF, RKFERR, RKFSTEP, RRK, Rsberr DET, IDN Access … Ã R → BRswp Rules →Dsymb Same→R, IM, RE 180/̟x Scaleh Access …µSCALEH Input/OutputSbrk Scale Scatter ScatrplotAUTO, SCALEH, Xrng Sclσ Access …µSCATTER Input/Output NoneSchur SCI Send SconjScroll Sdev Series SEQDOSUBS, Stream Seval Server X1/cm3 ShowSidens Sigma Sign Access !ÖDERIV LAccess !ÖDERIV LL Sigmavx ABS, MANT, Xpon SigntabSIMP2 SIGNsymb Sin z SimplifySIN Sincos Sinh z SinhSinv Size Symb Grob SLBSlopefield String Integer List Vector Snrm SnegNEG, SCONJ, Sinv Solveqn Solve Solvevx SolverSort SQsymb SphereSrad Square Analytic Function Returns the square of the argument ASR, SL, SLB, SR SRBSrecv COND, SNRM, Trace SST↓ Access …µSRECVSrepl SST STD StartStep Stime Access …µSTIMEStep Steq Buflen StoalarmAccess Input/Output STO Óis the rightshift of the 9 key Access …µSTOFStof Stokeys Stovx StoreSTO+ STO/, + DTAG, EQ→, LIST→, OBJ→, →STR StoσSTR→ →STR List Obj Result StreamStrm Sturm Sturmab SturmabStws SUB CHR, GOR, GXOR, NUM, POS, REPL, Size SubstSubtmod X1, y1 X2, y2 DIAG→, MIN, SVL SVDSVL Swap Sylvester SysevalSYST2MAT Symb 1, symb Tabval100 y X, symb →ARRY Tabvar→TAG Tail Tan z TANTAN2CS2 TAN2SC TANHsymb TAN2SC2Tanh Tanh z HERMITE, Legendre TAYLOR0Taylr Tchebycheff TDELTAsymb1, symb2 TcollectTdelta Tests Then TevalTexpand Text Tinc TicksTime →TIME SIMPLIFY, TCOLLECT, Texpand TlinTline TINCsymb1, symb2 Tran TmenuTOT Trace BAUD, CKSM, Parity TransioTrig Effect Trigtan TrigcosTrigo Trigsin Trnc TRNCONJ, Tran TRNCsymb TruncTruth TRNCz Tsimp Access …µTRUTH Input/Output NoneTstr Tvmend TvarsTVM Tvmbeg Object Type Number User objects Builtin CommandsType Ubase Unassume UfactUFL1→MINIF Unassign →UNIT UnbindUnpick Utpc UnrotUntil Updir UTPC, UTPN, Utpt UtpfUtpn UTPF, UTPN, Utpt Uval UtptUVALsymb X1, x2, ..., xn Xn-2 Flag -16 clear Rectangular mode Flag -16 set Polar mode € yCoordinate System -16, Complex Mode X1, x2 VAR Vandermonde Version Access …µVERSION Input/OutputVars VER Visitb Variable name Contents opened in the command line EditorVariable name Contents opened in the most suitable Editor Visit Vtype Access ! L in Wait Is the leftshift of the NkeyWait While Repeat WireframeWhile While testclause Repeat loopclause END Wslog Log4 ... log1 Access …µWSLOGAccess …µΣX Input/Output ΣX2 Xmit ΣX2Xcol Xget Xnum Access …µXMITXOR MANT, Sign XponXput XPONsymb Xrng Command XQ.3658 Results 1829/5000Command XQ.3658 Results √19/142 Xrecv Input/Output RPN Access …µXSENDXsend Xserv ΣX*Y XvolXxrng ΣXY …µΣY ΣY2ΣY2 Ycol Yslice YrngAUTO, PDIM, PMAX, PMIN, Xrng EYEPT, XVOL, XXRNG, YYRNG, Zvol YvolYyrng Zeros Zvol PowerAccess Q Zfactor Symbz Where√ Square Root Zsymb SQ, , Isol Lower limit, upper limit, integrand, name Access …Á Áis the rightshift of the UkeyIntegrate ? Undefined Results -π/2 ∞ InfinitySummation Sigma Plus X 2, …, x m 1, …, x 1 m x n 1, … , x n m Access …µΣ+ Input/OutputAccess …µΣ Input/Output Sigma Minus Symb Name Xunit ∂ DerivativeFactorial 14159265359… Symb,x PercentUnit attachment Xy/100 Less than « » Program delimitersType Object Description #n1 #n2 ≤ Less than or Equal ≥ Greater than or Equal Greater than ≠ Not equal ≠ symb Multiply + Add Subtract Divide Y1/unit = Equal == Logical Equality … É Store→ Create Local DEFINE, RCL, →, STO CLEAR, DROP, DROPN, DROP2 Semicolon CAS directory, Casdir CAS SettingsSelecting CAS Settings Points to note when choosing settings Computer Algebra System Extending the CAS Using the CASExamples and Help Compatibility with Other Calculators Arithmetic Integer commands, !ÞINTEGER Computer algebra command categories listed by menuArithmetic commands Algebra commands, …× Arithmetic Permutation commands, !Þ Permutation Arithmetic Modulo commands, !Þ ModuloOther Arithmetic commands, !Þ Calculus commands Operations, !Ø Operations Exp and Lin commands, !ÐMatrixrelated commands Create, !Ø Create Eigenvectors, !Ø Eigenvectors Quadratic form, !Ø Quadratic FormLinear Systems, !Ø Linear Systems Linear Applications, !Ø Linear Appl Hyperbolic, …Ñ Hyperbolic Symbolic solve commands, !ÎTrigonometry commands Other Trigonometry commands, …Ñ Trigonometric conversions, !Ú Trig Conv Convert commands, !ÚUnit conversion tools, !Ú Units Tools Base conversion tools, !Ú Base Matrix convert, !Ú Matrix Convert Other CAS operations, …µ These commands display menus or lists of CAS operations CAS menu commands, …µCAS utility operations Equation Reference Equation Reference FLUIDS, 24 *********************3 Internal bending moment at Columns and BeamsVariable Description Σcr Critical stress Σmax Maximum stress Example Elastic Buckling 1Eccentric Columns 1 Equations Simple Slope 1 Simple Deflection 1Equation Simple Moment 1 Solution V=624.387lbfSimple Shear 1 Cantilever Slope 1 Cantilever Deflection 1Cantilever Moment 1 Cantilever Shear 1 Solution V=200lbf Equation Reference Relative permittivity ElectricityRelative permeability Coulomb’s Law 2 Ohm’s Law and Power 2 Voltage Divider 2 Wire Resistance 2Solution V1=80V Solution I1=5.6250A Series and Parallel R 2 Solution R=0.175Series and Parallel C 2 Inductive Energy 2 Solution V=50VSeries and Parallel L 2 Capacitive Energy 2 Capacitor Charge 2 RLC Current Delay 2Solution q=0.0020C Equation Reference DC Capacitor Current 2 RL Transient 2 Solution V=3.2968VDC Inductor Voltage 2 RC Transient 2 Cylindrical Capacitor 2,19 Solution I=0.0072AResonant Frequency 2 Plate Capacitor 2 Toroid Inductance 2 Solenoid Inductance 2 Sinusoidal Voltage 2 FluidsSinusoidal Current 2 Initial and final velocities Pressure at Depth 3Bernoulli Equation 3 Reynolds number Flow with Losses 3 Flow in Full Pipes 3 Forces and Energy Linear Mechanics 4 Centripetal Force 4 Angular Mechanics 4Hooke’s Law 4 MassEnergy Relation 4 1D Elastic Collisions 4Drag Force 4 Law of Gravitation 4 Ideal Gas Law 5 Gases Polytropic Processes 5 Solution Vf=21Ideal Gas State Change 5 Isothermal Expansion 5 Real Gas State Change 5 Real Gas Law 5 Kinetic Theory 5 Heat Transfer Thermal Expansion 6 Heat Capacity 6Conduction 6 Conduction + Convection 6 Convection 6 Ia, Ib MagnetismBlack Body Radiation 6 Fba Force between Wires 7 Straight Wire 7 Magnetic B Field in Solenoid 7 Solution B=0.0785TMagnetic B Field in Toroid 7 Motion Object in Free Fall 8 Linear Motion 8Projectile Motion 8 Escape Velocity 8 Angular Motion 8Circular Motion 8 Terminal Velocity 8 Law of Refraction 9 Optics Brewster’s Law 9 Critical Angle 9 Thin Lens 9 Solution n2=1.5000Spherical Reflection 9 Spherical Refraction 9 Oscillations Simple Pendulum 10 MassSpring System 10Example Given L=15cm Torsional Pendulum 10 Conical Pendulum 10Simple Harmonic 10 Plane Geometry Ellipse 11 Circle 11Equations Example Regular Polygon 11 Rectangle 11 Triangle 11 Circular Ring 11 Cone 12 Solid Geometry Parallelepiped 12 Cylinder 12 Sphere 12 Solid State Devices Channel length JFETs Saturation current densityDrawn mask length PN Step Junctions, or Drawn gate length Nmos Transistors, or PN Step Junctions 13 VDS Nmos Transistors 13 JFETs 13 Bipolar Transistors 13 Xdmax = ⋅ Vbi VGS + VDS Maximum principal normal stress Stress AnalysisMinimum principal normal stress Shear Stress 14 Normal Stress 14Stress on an Element 14 Example Mohr’s Circle 14 Transverse Waves 15,1 WavesLongitudinal Waves 15 Sound Waves 15 References Page Development Library Development Library Development Library Command ReferenceObj String Obj1 … objn Symb Obj1, ...,objn Code String BetaTestingString Obj Debug string Error list String Obj Library Object String String Error list Edited stringLibrary n Ey,z.Et LC~C Obj … obj Obj 1, ...,obj n →LST Obj 1 … obj n Obj 1, ...,obj n Pokearm String Global →S2String1 String2 Returns Xlib Crlib Create Library Command Extension program Modes Masd The Machine Language and System RPL CompilerIntroduction Starting Masd Format of the error list ErrorsError messages Message Description Labels Links Constants Extable Expressions Macros and includes Operator Priority Compilation directive Filename conventionsDirective Description Docstr !DBGINF directive CPU architecture Saturn ASM modeBit registers New instructions Other notesSkips These instructions Are equivalent to Skips instructions Equivalents Tests Syntax Example Saturn instructions syntax Syntax Example DReg=hh See above. This is only valid in emulated Saturn Places the value of Exp in the code, on x nibbles CARRY0 003AA Autousertest ARM architecture ARM mode Description Form Instruction set Operation Assembler Action Flags REG B Armsat instructionOffset Element REG a REG C REG D REG R0 REG R1 REG R2 REG R3 REG R4 Unnamed local variables System RPL modeInstructions Reals and system binary Tokens DefinesToken Description Code LC 001 Gosbvl Outcinrtn ?CBIT=1.6 Turnmenuoff LC 80100 Armsat Level Disassemblers String String 1, ...,string n Entry Point Library ExtableLibrary Nop C0C Error and Status Messages A1Messages Listed Alphabetically Message Meaning # hex A2 Error and Status Messages Error and Status Messages A3 Σdat A4 Error and Status Messages Error and Status Messages A5 A6 Error and Status Messages C0D Error and Status Messages A7C0E C0B A8 Error and Status Messages # hex Message General Messages Error and Status Messages A9 # hex Message A10 Error and Status Messages OutofMemory Prompts Error and Status Messages A11 Equation Writer Application Messages Stack Errors and MessagesA12 Error and Status Messages Object Editing Messages Statistics Messages # hex Message FloatingPoint ErrorsError and Status Messages A13 Array Messages A14 Error and Status Messages Mode and Plot Input Form Prompts # hex Message 70F Error and Status Messages A15 73F A16 Error and Status Messages 75F Error and Status Messages A17 78F A18 Error and Status Messages Error and Status Messages A19 Advanced Statistics Messages A20 Error and Status Messages 80F Error and Status Messages A21 82F A22 Error and Status Messages 85F Error and Status Messages A23 87F A24 Error and Status Messages Statistics Help Messages Error and Status Messages A25HP Solve Application Messages Programmer’s Doerr # hex Message Unit ManagementPrinting Time Messages Error and Status Messages A27 System Flags Choose Box Prompts A28 Error and Status Messages Error and Status Messages A29 A30 Error and Status Messages Error and Status Messages A31 Prompts A32 Error and Status Messages Error and Status Messages A33 A34 Error and Status Messages Statistics Prompts Error and Status Messages A35 A36 Error and Status Messages Time and Alarm Prompts Error and Status Messages A37 A38 Error and Status Messages Symbolic Application Prompts Plot Application Prompts Error and Status Messages A39 A40 Error and Status Messages Error and Status Messages A41 Solve Application Prompts A42 Error and Status Messages Error and Status Messages A43 A44 Error and Status Messages CAS Messages Error and Status Messages A45 A46 Error and Status Messages Error and Status Messages A47 DF1A DF1B DF1C DF1D DF1E DF1F A48 Error and Status MessagesFiler Application Messages DF0A DF0B DF0C DF0D DF0E DF0F Constants Library Messages Error and Status Messages A49 MultipleEquation Solver Messages A50 Error and Status MessagesEquation Library Messages Minehunt Game Prompts Development Library and Miscellaneous Messages Error and Status Messages A51Periodic Table Messages Financial Solver Messages A52 Error and Status Messages Tables of Units and Constants B1 Units B2 Tables of Units and Constants Tables of Units and Constants B3 B4 Tables of Units and Constants Constant Full Name Value in SI Units Tables of Units and Constants B5 B6 Tables of Units and Constants Properties of Elements System Flags C1 System FlagsFlag Description Not used C2 System Flags System Flags C3 C4 System Flags System Flags C5 C6 System Flags System Flags C7 C8 System Flags Internal use only /0 occurred System Flags C9 User FlagsPage Reserved Variables D1 Contents of the System Reserved Variables Reserved Variables D3 ΒENTER D4 Reserved Variables Exited Reserved Variables D5 Nmines MHparMpar N1, n2 Reserved Variables D7 BAR, etc D8 Reserved Variables Prtpar Reserved Variables D9 S1, s2 D10 Reserved Variables Parameter Description Default Value CommandTo use for input into the table NUMX, Numy Statistical Matrix for Variables 1 to m Var1 var2 … varmReserved Variables D11 D12 Reserved Variables EXPFIT, PWRFIT, or Logfit Casdir Reserved Variables D14 Reserved Variables Modulo Object Type Size bytes Object SizeTechnical Reference E1 Pattern Antiderivative Symbolic IntegrationE2 Technical Reference Technical Reference E3 E4 Technical Reference →DEF Expansions Technical Reference E5 Order Operation E6 Technical Reference International Standard publication No. ISO 31/l197 8 E Parallel Processing with Lists F1 Group 1 Commands that cannot parallel processGroup 2 Commands that must use Dolist to parallel process General rules for parallel processing F2 Parallel Processing with Lists Group 5 Commands that set modes / statesGroup 6 Oneargument, oneresult commands Group 4 ADD and + Group 10 Quirky commands Group 7 Two argument, one result commandsGroup 8 Multipleargument, oneresult commands Group 9 Multipleresult commands F4 Parallel Processing with Lists Using Dolist for Parallel Processing $ & + $ & C$ & D $ & F ~@ & O Keycode Keystroke Definition¥ ! &I @ & ³ @ & O @%VARNAME% = varname ~@ & Í @ &†Keyboard Shortcuts G3 G4 Keyboard Shortcuts Syntax Example Menu NumbersMenuNumber Table H1 H2 The MenuNumber Table Menus 0 through MenuNumber Table H3 H4 The MenuNumber Table Menus 118 through BuiltIn Library Menus Menus 178 throughMenuNumber Table H5 Page Key ALPHARS2 MTH NXT Prob Command MenuPath Table+ key I2 The Command MenuPath Table Command Type Library Size Keys Menu First CAT Algb MTH ListArith Modul «MODULAR» Addtoreal I4 The Command MenuPath Table CHR LS&MODE FlagPRG Test NXT NXT PRG NXT Modes Flag Chinrem PRG NXT I6 The Command MenuPath Table PRG NXT NXT Time NXT CAT DelalarmPRG NXT NXT Time Alrm Delay RS&TIME NXT I8 The Command MenuPath Table Else PRG NXT NXT Error Iferr«POLYNOMIAL» EGV MTH Matrx NXT I10 The Command MenuPath Table I11 I12 The Command MenuPath Table «DIFF» NXT NXT Calc Deriv NXT«INTEGER» PRG Brch NXT I14 The Command MenuPath Table I15 I16 The Command MenuPath Table I17 I18 The Command MenuPath Table I19 I20 The Command MenuPath Table I21 I22 The Command MenuPath Table I23 I24 The Command MenuPath Table I25 I26 The Command MenuPath Table I27 I28 The Command MenuPath Table XLIB~ Matrices Creat NXT NXT MTH Matrx Make NXT NXTDUP Menuxy Version CAT Vtype MTH NXT Const «CONSTANTS» I30 The Command MenuPath TableSLV NXT Alphalse →ALG ΣlineΣlist PRG Test «TESTS» NXT I32 The Command MenuPath Table Character Codes Code DescriptionAscii Character Codes and Translations J1 J2 Ascii Character Codes and Translations Code Trans. Description Index Alpha keyboard Calculator 59, 531 375 Preserving calculator status Flags 132 Last argument Memory Nested structures 545 Programs Range 3115 Serial communications 237, D3 Tagged objects UPs

HP 48gII Graphing manual Saturation current density, Drawn mask length PN Step Junctions, or

Models: 50g Graphing 48gII Graphing

Variable

Saturation current density

Drawn mask length (PN Step Junctions), or

Drawn gate length (NMOS Transistors), or

Channel length (JFETs)

Effectives gate length

Pside doping (PN Step Junctions), or

Substrate doping (NMOS Transistors)

Nside doping (PN Step Junctions), or

Nchannel doping (JFETs)

tox

Gate silicon dioxide thickness

Applied voltage

Basetocollector voltage

Basetoemitter voltage

Vbi

Builtin voltage

Substrate voltage

VCEsat

Collectortoemitter saturation voltage

VDS

Applied drain voltage

VDsat

Saturation voltage

Applied gate voltage

Threshold voltage

Equation Reference 551