使用者:Shenyileirob/測試

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數學公式

以下是數學公式的測試。

$R_{eq}=50\,\Omega$

$R_{eq}/[R_{eq}+X_{s}(n\omega _{0})]$

$X_{p}(n\omega _{0})/[X_{p}(n\omega _{0})+X_{s}(n\omega _{0})+R_{eq}]$

$X_{p}(\omega _{0})/[X_{p}(\omega _{0})+X_{s}(\omega _{0})+R_{eq}]$

1 $I_{out}(t)=I_{a}\cos {(\omega _{0}t+\phi )}$

2 $V_{1}(t_{1})=0$

3 ${\frac {dV_{1}(t_{1})}{dt}}=0$

4 $C_{eq}=C_{0}+C_{1}//C_{2}=C_{0}+{\frac {C_{1}C_{2}}{C_{1}+C_{2}}}$

5 $\alpha ={\frac {C_{1}}{C_{1}+C_{2}}}$

6 $\beta ={\frac {C_{0}}{C_{eq}}}$

7 $q={\frac {1}{\omega _{0}{\sqrt {L_{0}C_{eq}}}}}$

8 $V_{DD}-V_{1}(t)=L_{0}{\frac {di_{L}(t)}{dt}}$

9 $i_{L}(t)=C_{0}{\frac {dV_{1}(t)}{dt}}+C_{1}\left({\frac {dV_{1}(t)}{dt}}-{\frac {dV_{2}(t)}{dt}}\right)$

10 $C_{1}\left({\frac {dV_{1}(t)}{dt}}-{\frac {dV_{2}(t)}{dt}}\right)=C_{2}{\frac {dV_{2}(t)}{dt}}+I_{a}\cos {(\omega _{0}t+\phi )}$

11 $V_{DD}=L_{0}{\frac {di_{L}(t)}{dt}}$

12 $(C_{1}+C_{2}){\frac {dV_{2}(t)}{dt}}=-I_{a}\cos {(\omega _{0}t+\phi )}$

13 $V_{1}(t)=A_{1}V_{DD}\cos {(\omega _{1}t)}+A_{2}V_{DD}\sin {(\omega _{1}t)}+\kappa V_{DD}{\frac {1}{q^{2}-1}}\sin {(\omega _{0}t+\phi )}+V_{DD}$

14 $V_{2}(t)={\frac {C_{1}}{C_{1}+C_{2}}}V_{1}(t)-{\frac {I_{a}}{(C_{1}+C_{2})\omega _{0}}}\sin {(\omega _{0}t+\phi )}$

15 $i_{L}(t)=C_{eq}q\omega _{0}[A_{2}V_{DD}\cos {(q\omega _{0}t)}-A_{1}V_{DD}\sin {(q\omega _{0}t)}]+\kappa V_{DD}C_{eq}\omega _{0}{\frac {q^{2}}{q^{2}-1}}\cos {(\omega _{0}t+\phi )}$

16 $\kappa ={\frac {\alpha I_{a}}{C_{eq}\omega _{0}V_{DD}}}$

17 $V_{2}=-{\frac {I_{a}}{(C_{1}+C_{2})\omega _{0}}}\sin {(\omega _{0}t+\phi )}+A_{3}V_{DD}$

18 $i_{L}(t)={\frac {V_{DD}}{L_{0}}}t+i_{L}(t_{1})$

19 $A_{1}={\frac {q(\sin {a_{2}}-\sin {a_{1}}+\sin {a_{3}}-\sin {a_{4}})+\sin {a_{1}}+\sin {a_{2}}}{q\sin {a_{1}}-q\sin {a_{2}}-2q\sin {\phi }-\sin {a_{2}}-\sin {a_{1}}}}$

20 $A_{2}={\frac {q(\cos {a_{1}}-\cos {a_{2}}+\cos {a_{4}}-\cos {a_{3}})-\cos {a_{1}}-\cos {a_{2}}+2\cos {a_{5}}}{q\sin {a_{1}}-q\sin {a_{2}}-2q\sin {\phi }-\sin {a_{2}}-\sin {a_{1}}}}$

21 $\kappa ={\frac {-q(\cos {(2q\pi (1-D))}q^{2}-\cos {(2q\pi (1-D))-q^{2}+1})}{k_{1}+k_{2}+k_{3}+k_{4}+k_{5}}}$

22 $\phi =\pi D+\pi +\arctan {\left({\frac {g_{n1}+g_{n2}+g_{n3}+g_{n4}}{g_{d1}+g_{d2}+g_{d3}+g_{d4}+g_{d5}}}\right)}$

23 $V_{2}(t)=V_{2\_0}+V_{2\_1}\cos {(\omega _{0}+\phi _{1})}+V_{2\_2}\cos {(2\omega _{0}+\phi _{2})}+V_{2\_3}\cos {(3\omega _{0}+\phi _{3})}+\cdots$

24 $Z_{out}={\frac {V_{2\_1}}{I_{a}}}\exp {[(\phi _{1}-\phi )j]}=Z_{out\_real}+j\cdot Z_{out\_imag}$

25 $Z_{out}=\left(R_{0}//{\frac {1}{C_{3}\omega _{0}j}}\right)+L_{1}\omega _{0}j={\frac {R_{0}}{1+(R_{0}C_{3}\omega _{0})^{2}}}+\left(L_{1}\omega _{0}-{\frac {R_{0}^{2}C_{3}\omega _{0}}{1+(R_{0}C_{3}\omega _{0})^{2}}}\right)j$

26 $L_{1}\omega _{0}=Z_{out\_imag}+{\frac {R_{0}^{2}C_{3}\omega _{0}}{1+(R_{0}C_{3}\omega _{0})^{2}}}$

27 $C_{3}\omega _{0}={\sqrt {({\frac {1}{Z_{out\_real}R_{0}}}-{\frac {1}{R_{0}^{2}}})}}$

28 $L_{xn}=L_{x}\cdot \omega _{0}$

29 $C_{xn}=C_{x}\cdot \omega _{0}$

30 $P_{out}=V_{DD}\cdot {\frac {1}{T}}\int _{0}^{T}i_{L_{0}}(t)dt=V_{DD}^{2}C_{eqn}h(q,D)$

31 $P_{out}\approx (p_{O_{3}}q^{3}+p_{O_{2}}q^{2}+p_{O_{1}}q+p_{O_{0}})C_{eqn}V_{DD}^{2}$

32 $L_{in}\approx p_{L_{3}}q^{3}+p_{L_{2}}q^{2}+p_{L_{1}}q+p_{L_{0}}$

33 $C_{3n}\approx p_{C_{3}}q^{3}+p_{C_{2}}q^{2}+p_{C_{1}}q+p_{C_{0}}$

34 $P_{Loss\_M1\_norm}(t)={\frac {P_{Loss\_M1}(t)}{P_{DC,PA}}}$

35 $P_{ACC\_M1\_norm}(t)={\frac {1}{T}}\int _{0}^{t}P_{Loss\_M1\_norm}(t)dt$