LockedFP Block Diagram

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Equation

ブロックダイアグラムを連立方程式であらわし, ν_1を求めます .

Numerator of ν_1

まず, 求めたν_1の分子のうち, ν_INの係数を求めます . それをCoeffNuINとし, それで他の項を割ることで, ν_INと比較できます . まずν_INの係数を求めます .

CoeffNuIN = Simplify[Coefficient[Numerator[ν_1], ν_IN]]

C_0 C_IN (C_EOM H_EOM + C_PZT H_PZT) P_IN H_ (IN, PD) (C_FA + C_MC P_MC H_ (MC, END) H_ (MC, PD))

次にN_INの係数を求めます .

Simplify[Coefficient[Numerator[ν_1]/CoeffNuIN, N_IN ]]

-1/(P_IN H_ (IN, PD))

次にN_MCの係数を求めます .

Simplify[Coefficient[Numerator[ν_1]/CoeffNuIN, N_MC ]]

-1/(C_IN P_IN H_ (IN, PD) (C_FA + C_MC P_MC H_ (MC, END) H_ (MC, PD)))

最後にν_MCの係数を求めます .

Simplify[Coefficient[Numerator[ν_1]/CoeffNuIN, ν_MC ]]

(P_MC H_ (MC, PD))/(C_IN P_IN H_ (IN, PD) (C_FA + C_MC P_MC H_ (MC, END) H_ (MC, PD)))

Denominator of ν_1

1 + C_0 (C_EOM H_EOM + C_PZT H_PZT) (C_FA C_IN P_MC H_ (IN, PD) + (1 + C_IN C_MC P_MC^2 H_ (IN, PD) H_ (MC, END)) H_ (MC, PD))

Parameter1

CLIOの基本的なパラメ - タ - です . 仮定を多く含みます .

Feedback Circuit

Feedback Circuitの伝達関数です .

MC Servo Loop Gain

[Graphics:HTMLFiles/CLIOLFPindex_30.gif]

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[Graphics:HTMLFiles/CLIOLFPindex_32.gif]

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Primary Cavity Servo Loop Gain

[Graphics:HTMLFiles/CLIOLFPindex_36.gif]

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[Graphics:HTMLFiles/CLIOLFPindex_38.gif]

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Secondary Cavity Servo Loop Gain

[Graphics:HTMLFiles/CLIOLFPindex_42.gif]

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[Graphics:HTMLFiles/CLIOLFPindex_44.gif]

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Noise Contributions(Lock Acquire Gain)

G_IN = C_IN * P_IN * H_ (IN, PD) * (C_FA/H_ (MC, PD) + P_MC * C_MC * H_ (MC, END))

[Graphics:HTMLFiles/CLIOLFPindex_50.gif]

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Noise Contributions(After GainUP)

G_IN = C_IN * P_IN * H_ (IN, PD) * (C_FA/(P_MCH_ (MC, PD)) + C_MC * H_ (MC, END)) ;

[Graphics:HTMLFiles/CLIOLFPindex_55.gif]

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