243 Thermisches Rauschen

Needs["ErrorBarPlots`"]

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, zimmer])=Quantity[{24.7,0.1},"Celsius"]

background=Quantity[{1.3981, 0.00467/(Sqrt[101])},"Millivolts"]

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/casimir/Dropbox/uniself/AP2/2.2/243/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[{bla=laber},NonlinearModelFit[fit,(1000/((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]

TODO: Mit festem und variablem V fitten!

frequenzgang[f_]=Normal[fml]

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

Berechnung der Boltzmannkonstante

data

data2=data//QuantityMagnitude

data2[[All,1]]

Boltzfit1=LinearModelFit[data2[[All,1]],x,x]

Parameters1=Boltzfit1["ParameterTableEntries"]

c=Quantity[Parameters1[[2,1]],"Millivolts"/"Kiloohms"]//UnitConvert

(Subscript[T, zimmer2])=(Subscript[T, zimmer])//QuantityMagnitude

(Subscript[T, Zimmerreal])=Quantity[{First[(Subscript[T, zimmer2])]+273.15,Last[(Subscript[T, zimmer2])]},"Kelvins"]

c

(Subscript[k, B])=UnitConvert[(c/(4*(Subscript[T, Zimmerreal])*B)),"BoltzmannConstant"]

Quantity["BoltzmannConstant"]