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me365.TXT
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me365.TXT
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\START92\
\COMMENT=
\NAME=me365
\FILE=main.me365.89p
()
Prgm
Disp ""
ClrIO
Lbl top
Toolbar
Title "Quit",quit
Title "Cal."
Item "Def.",def
Item "Hysteresis",hy
Item "Resolution",res
Title "ADC"
Item "Prob.",pro
Item "Q",q
Item "V\->\Q",vtq
Item "Q\->\V",qtv
Item "T[a],F,n",tfn
Item "True Input",ti
Item "MinBitsNeeded",mbn
Title "Stat."
Item "Gauss",gauss
Item "\mu\ & \sigma\",mx
Item "pdf",pdf
Item "C.I.",ci
Item "Prop. of Err",prop
Item "Least\^2\",ls
Title "Sys."
Item "\diff\ & \integral\",id
Item "y[ss]",yss
Item "y[trans]",yt
Title "ODE"
Item "1st & 2nt",fso
Item "Characteristics",cha
Item "1st ID",fid
Item "2nt ID",sid
Item "2nt ID,2",sidt
Title "FLO"
Item "Filters",fil
Item "Loading",loa
Item "Op-Amp",oa
Item "Reduce Loading",rl
Title "Per."
Item "Frequency",frequ
Item "A[k] & B[k]",akbk
Item "M[k] & \theta\[k]",mk\theta\k
Item "M[k] & \psi\[k]",mkyk
Item "Complex Form",comfo
Item "Complex Form",comfo2
Item "Amp. Spectra",asps
Item "Odd & Even",oe
Title "StrainG"
Item "Equation",sge
EndTBar
\(C)\\(C)\\(C)\\(C)\\(C)\\(C)\\(C)\\(C)\\(C)\
Lbl tx
ClrIO
Goto top
\(C)\\(C)\\(C)\\(C)\\(C)\\(C)\\(C)\\(C)\\(C)\
Lbl sge
ClrIO
Disp "(Z1*Z3-Z2*Z4)/","((Z1+Z4)(Z2+Z3))"
Goto top
\(C)\
Lbl oe
ClrIO
Disp "Odd: No cos() Terms"
Disp "Even: No sin() Terms"
Goto top
\(C)\
Lbl comfo2
ClrIO
Disp "|c[k]|=1/2*M[k]"
Disp "\/_\c[k]=\(-)\\theta\[k]"
Disp "2*real(c[k])"
Disp "\(-)\2*imag(c[k])"
Goto top
\(C)\
Lbl comfo
ClrIO
Disp "x(t)=c[0]+","\Sigma\(c[k]*\e\^(\i\k\omega\t),k,1,\infinity\)+","\Sigma\(c[k]*\e\^(\i\k\omega\t),k,\(-)\1,\(-)\\infinity\)"
Disp "c[k]=1/T*\integral\(x*\e\^(\(-)\\i\k\omega\t),t)"
Goto top
\(C)\
Lbl asps
ClrIO
Disp "Amplitude & Phase Spectra"
Disp "M[k] vs. \omega\[k]=k*\omega\[1]"
Disp "&"
Disp "\theta\[k] vs. \omega\[k]=k*\omega\[1]"
Disp "\theta\[k] is in the range of","\^+\\pi\ NOT \^+\\pi\/2"
Goto top
\(C)\
Lbl mkyk
ClrIO
Disp "x(t)=A[0]/2+","\Sigma\(M[k]*sin(k*\omega\1*t+\psi\[k])"
Disp "M[k]=\root\(A[k]\^2\+B[k]\^2\)"
Disp "\psi\[k]=tan\^-1\(A[k]/B[k])"
Disp "A[k]=M[k]*sin(\psi\[k])"
Disp "B[k]=M[k]*cos(\psi\[k])"
Goto top
\(C)\
Lbl mk\theta\k
ClrIO
Disp "x(t)=\->\A[0]/2+","\Sigma\(M[k]*cos(k*\omega\1*t-\theta\[k])"
Disp "M[k]=\root\(A[k]\^2\+B[k]\^2\)"
Disp "\theta\[k]=tan\^-1\(B[k]/A[k])"
Disp "A[k]=M[k]*cos(\theta\[k])"
Disp "B[k]=M[k]*sin(\theta\[k])"
Goto top
\(C)\
Lbl akbk
ClrIO
Disp "x(t)=","A[0]/2+\Sigma\(A[k]*cos(k*\omega\1*t)"," +\Sigma\(B[k]*sin(k*\omega\1*t)"
Disp "A[0]=2/T*\integral\(x)"
Disp "A[k]=2/T*\integral\(x*cos(k*\omega\1*t)"
Disp "B[k]=2/T*\integral\(x*sin(k*\omega\1*t)"
Goto top
\(C)\
Lbl frequ
ClrIO
Disp "Fundamental Frequency:"
Disp "\omega\[1]=2\pi\*f[1]=2\pi\/T"
Disp "k^th requency"
Disp "\omega\[k]=2\pi\k*f[1]=2\pi\k/T"
Goto top
\(C)\
Lbl rl
ClrIO
Disp "Passive:choose R2>>R1"
Disp "Active: Use Volt follower"
Goto top
\(C)\
Lbl oa
ClrIO
Disp "High\->\Z[out],Low\->\Z[in]"
Disp "A\->\very large,1\ee\5V/V"
Disp "Input impedance is just","R[in]"
Goto top
\(C)\
Lbl loa
ClrIO
Disp "L[i,i+1]=Z[in,i+1]/","(Z[in,i+1]+Z[out,i])"
Disp "Z[in]\->\Look in"
Disp "Z[out]\->\Look from out"
Disp "Short all V"
Goto top
\(C)\
Lbl fil
ClrIO
Disp "LP=K/(1+\i\RC\omega\)"
Disp "HP=RC\i\\omega\/(1+\i\RC\omega\)"
Disp "BP=LP*HP"
Disp "BS=LP+HP"
Disp "\omega\[c]=1/\tau\ 1st order"
Goto top
\(C)\
Lbl sidt
ClrIO
Disp "T[rise]=(\pi\-\beta\)/\omega\[d]"
Disp "\beta\=tan\^-1\(\root\(1-\zeta\\^2\)/(\zeta\))"
Disp "%OS=100*\e\^(\(-)\\pi\*\zeta\/\root\(1-\zeta\\^2\))"
Disp "2% T[s]=4/(\zeta\*\omega\[n])"
Disp "1% T[s]=5/(\zeta\*\omega\[n])"
Goto top
\(C)\
Lbl sid
ClrIO
Disp "T[d]=2\pi\/\omega\[d]"
Disp "\omega\[d]=\omega\[n]\root\(1-\zeta\\^2\)"
Disp "\zeta\=ln((yi-yf)/(y[i+n]-yf))"," *1/(2*\pi\*n)"
Disp "\zeta\=1/\pi\*ln((yf-y0)/OS)"
Disp "OS=Peak[1]-yf"
Goto top
\(C)\
Lbl fid
ClrIO
Disp "y=yf+(y0-yf)\e\^(\(-)\t/\tau\)"
Disp "ln((yf-y0)/(yf-y)), m=\tau\\^-1\"
Disp "0\<=\\phi\\<=\\(-)\90"
Goto top
\(C)\
Lbl cha
ClrIO
Disp "Peak @ \omega\[res]"
Disp "\omega\[res]=\root\(1+2\zeta\^2)*\omega\[n]"
Disp "if \zeta\>1/2, no peak"
Disp "If K>0"
Disp "\phi\=\(-)\tan\^-1\(2\zeta\\omega\[n]\omega\/"," (\omega\[n]\^2\-\omega\\^2\))"
Goto top
\(C)\
Lbl fso
ClrIO
Disp "\tau\*y'+y=K*x"
Disp "y''/\omega\^2+2*\zeta\*y'/\omega\+y=K*x"
Disp "y=y[ss]+y[transient]"
Disp "Roll off=20dB*order"
Goto top
\(C)\
Lbl yt
ClrIO
Goto top
\(C)\
Lbl yss
ClrIO
Disp "x(t)=A*sin(\omega\t)"
Disp "x(t)=\e\^(\i\\omega\t)"
Disp "y(t)=T1*\e\^(\i\\omega\t)"
Disp "Solve for T1"
Disp "y[ss]=A|T1|*sin(\omega\t+\/_\T1)"
Goto top
\(C)\
Lbl id
ClrIO
Disp "\diff\(\e\^(\i\\omega\t))/\diff\t=\i\\omega\\e\^(\i\\omega\t)"
Disp "\integral\(\e\^(\i\\omega\t))=1/(\i\\omega\)"
Goto top
\(C)\
Lbl ls
ClrIO
Disp "y=Aa+n"
Disp "f=a0+a1*x"
Disp "Derivate w/each var"
Disp "Dev in fit"
Disp "\sigma\[n]=1/[N-2]*\Sigma\(n[i])\^2\"
Disp "2\o\ of free"
Disp "v=N-2"
Goto top
\(C)\
Lbl prop
ClrIO
Disp "y=f(a,b)"
Disp "a\^+\\Delta\a,b\^+\\Delta\b,c\^+\\Delta\c"
Disp ""
Disp "\ymean\=f(a,b)"
Disp "\Delta\y=\root\((\delta\f\delta\a/\delta\a)\^2\+(\delta\f\Delta\b/\delta\b)\^2\"
Disp "y=\ymean\\^+\\Delta\y"
Goto top
\(C)\
Lbl ci
ClrIO
Disp "Confidence Interval"
Disp "s[\xmean\]=s[x]/\root\(N)"
Disp "\sigma\[\xmean\]=\sigma\[x]/\root\(N)"
Disp "N>60 - Normal"
Disp "\mu\\^+\z[n]*\sigma\[x] | \xmean\\^+\z[n]*s[x]"
Disp "N<60 - Student T"
Disp "\mu\\^+\t[v]*\sigma\[x] | \xmean\\^+\t[v]*s[x]"
Disp "v=N-1"
Goto top
\(C)\
Lbl pro
ClrIO
Disp "Aliasing"
Disp "f[s]>2*f[highest]"
Disp "f[c]<<f[s]/2"
Goto top
\(C)\
Lbl qtv
ClrIO
Disp "C*Q+Offset=V"
Goto top
\(C)\
Lbl vtq
ClrIO
Disp "C=(V[in]-VADC[min]*2^n/"," (Nominal Span)"
Goto top
\(C)\
Lbl res
ClrIO
Disp "Out. Dev. Res.=\Delta\O"
Disp "Resolution=\Delta\I"
Disp "K=Sensitivity=Slope"
Disp "\Delta\I=\Delta\O/K"
Goto top
\(C)\
Lbl hy
ClrIO
Disp "max hysteresis="
Disp "max(|O[inc]-O[dec]|)/"," (O[max]-O[min]"
Goto top
\(C)\
Lbl def
ClrIO
Disp "Out=K*In+B"
Disp "K=slope=Sensitivity"
Disp "B=y-intercept=Bias"
Disp "Non-Lin=line - data"
Disp "max nonlin%=max(|K*I+B-O/"
Disp " max(O)-min(O)"
Goto top
\(C)\
Lbl pdf
ClrIO
Disp "p(x)==PDF"
Disp "1=\integral\(p(x),x,\(-)\\infinity\,\infinity\)"
Disp "\mu\=\integral\(x*p(x),x,\(-)\\infinity\,\infinity\)"
Disp "Prob btw a & b is:"
Disp "\integral\(p(x),x,a,b)"
Goto top
\(C)\
Lbl ti
ClrIO
Disp "Nominal range"
Disp "\(-)\x to x"
Disp "True range"
Disp "\(-)\x to (x-Q)"
Goto top
\(C)\
Lbl gauss
ClrIO
Disp "p(x)=1/(\sigma\*\root\(2*\pi\))*"," \e\^((x-\mu\)^2/(2*\sigma\^2))"
Goto top
\(C)\
Lbl mx
ClrIO
Disp "E[g(x)]=\integral\(g(x)*p(x))"
Disp "\mu\=\xmean\=1/N*\Sigma\(X[i])"
Disp "\sigma\[x]\^2\=1/N*\Sigma\(x-\mu\)^2"
Disp "S[x]\^2\=1/(N-1)*\Sigma\(x-\xmean\)^2"
Goto top
\(C)\
Lbl mbn
ClrIO
Disp "Calc. Min Bits needed"
Disp "Resolution=Nom.Span/2^n"
Disp "Round Up"
Goto top
\(C)\
Lbl tfn
ClrIO
Disp "t[a]\<=\1/(2^n*\pi\*f)"
Disp "f\<=\1/(2^n*\pi\*t[a])"
Disp "2^n\<=\1/(f*\pi\*t[a])"
Disp "Do not round bits"
Goto top
\(C)\
Lbl q
ClrIO
Disp "Q=Nominal Span/2^n"
Disp "Q=True Span/(2^n-1)"
Disp "Max.Q Err=Q/2"
Goto top
\(C)\
Lbl quit
ClrIO
ClrDraw
ClrGraph
setGraph("Axes","On")
DispHome
EndPrgm
\STOP92\