243 Thermisches Rauschen

Needs["ErrorBarPlots`"]

Messung des Frequenzgangs des Verstärkers und des Bandfilters

{Decrease,ΔDecrease}= 0.001*{1,0.002}

Uin=Quantity[0.2,"Volts"]

ν=Quantity[100,"Hertz"]

Einstellungen
Vertical Scale: 5 db/div
V-Range: 0.1 V
Frequency Range: 1 MHz
Frequency Start: 100 Hz
Frequency Step Size: 20%
Automatic Voltage Scale

data2 = StringSplit@StringSplit[Import["/Users/jannis/Dropbox/uniself/AP2/2.2/243 Thermisches Rauschen/Meßwerte.txt"],"\n"][[2;;]]//ToExpression;

Uout=data2[[All,2]];

Max[Uout]

ListLogLogPlot[data2[[All,{1,2}]]]

ν=Quantity[#,"Hertz"]&@data2[[All,1]];

{g,Δg}=Table[Transpose[{QuantityMagnitude[ν],(1/Decrease)*(Uout/(QuantityMagnitude[Uin]))*f}],{f,{1,((ΔDecrease)/Decrease)}}];

ListLogLogPlot[{g,g[[20;;137]]},ImageSize->Full,Joined->True];

{fit,Δfit}=With[{start=20,end=137},{g[[start;;end]],Δg[[start;;end]]}];

fml=With[{V=1000},NonlinearModelFit[fit,(V/((Sqrt[1+(1/((((f/(Ω1))))^(2n1)))])(Sqrt[1+((((f/(Ω2))))^(2n2))]))),{{Ω1,1000},{Ω2,50000},{n1,5},{n2,5}},f,VarianceEstimatorFunction->(1&),Weights->(1/((Δfit[[All,2]])^2))]]

fml["ParameterTable"]

LogLogPlot[fml[x],{x,10,1000000},PlotRange->{{100,1000000},{1,1200}}]

Show[ListLogLogPlot[g],LogLogPlot[fml[x],{x,300,150000}],ImageSize->Full]

frequenzgang[f_]=Normal[fml]

B=Quantity[NIntegrate[((frequenzgang[f])^2),{f,0,1000000}],"Hertz"]

ΔB=0.02*B

Messung der Rausch-Spannung als Funktion des ohmschen Widerstandes

data = {
{Quantity[ 5*{1,0.005},"Kiloohms"], Quantity[{2.4320, 0.00851/(Sqrt[107])},"Millivolts"]},{Quantity[10*{1,0.005},"Kiloohms"], Quantity[{3.1366, 0.0115/(Sqrt[106])},"Millivolts"]},{Quantity[15*{1,0.005},"Kiloohms"], Quantity[{3.7130, 0.0119/(Sqrt[105])},"Millivolts"]},{Quantity[20*{1,0.005},"Kiloohms"], Quantity[{4.2193, 0.0161/(Sqrt[104])},"Millivolts"]},{Quantity[25*{1,0.005},"Kiloohms"], Quantity[{4.6808, 0.0174/(Sqrt[103])},"Millivolts"]},
{Quantity[30*{1,0.005},"Kiloohms"], Quantity[{5.0737, 0.0237/(Sqrt[186])},"Millivolts"]}
}

{(Subscript[T, Raum]),(Subscript[ΔT, Raum])}={UnitConvert[Quantity[24.7,"Celsius"],"Kelvins"],Quantity[0.1,"Kelvins"]}

Verstärkerrauschen:

{(Subscript[U, V]),(Subscript[ΔU, V])}=Quantity[{1.3981, 0.00467/(Sqrt[101])},"Millivolts"]

{TR,(Subscript[TU, aus])}=Transpose[data]

{R,ΔR}=Transpose[TR]

{(Subscript[U, aus]),(Subscript[ΔU, aus])}=Transpose[(Subscript[TU, aus])]

G=((Subscript[U, aus])^2)-((Subscript[U, V])^2)

ΔG=(Sqrt[(((2(Subscript[U, aus])(Subscript[ΔU, aus])))^2)+(((2(Subscript[U, V])(Subscript[ΔU, V])))^2)])

gplot=ErrorListPlot[Table[
With[
{
r=R[[i]]//QuantityMagnitude,
Δr=ΔR[[i]]//QuantityMagnitude,
g=G[[i]]//QuantityMagnitude,
Δg=ΔG[[i]]//QuantityMagnitude
},
{{r,g},ErrorBar[Δr,Δg]}],{i,Length[G]}],ImageSize->Full,AxesLabel->{"R [kΩ]","(Subscript[U, aus]^2)-(Subscript[U, V]^2) [(mV^2)]"}];

lmf=LinearModelFit[Transpose[QuantityMagnitude/@{R,G}],x,x,VarianceEstimatorFunction->(1&),Weights->(1/(((QuantityMagnitude[ΔR])^2)+((QuantityMagnitude[ΔG])^2))),IncludeConstantBasis->False]

Show[gplot,Plot[lmf[x],{x,0,100}]]

lmf["RSquared"]

{{c,Δc}}=Quantity[lmf["ParameterTableEntries"][[All,1;;2]],((("Millivolts")^2)/("Kiloohms"))]

{k,(Subscript[Δk, stat])}=UnitConvert[(({c,Δc})/(4(Subscript[T, Raum])B)),(("Joules")/("Kelvins"))]

(Subscript[Δk, syst])=UnitConvert[(Sqrt[(((((c ΔB)/(4(Subscript[T, Raum])(B^2)))))^2)+(((((c (Subscript[ΔT, Raum]))/(4((Subscript[T, Raum])^2)B))))^2)]),(("Joules")/("Kelvins"))]