二端口网络参数#

阻抗参数(Z参数)#

$$ \left\{\begin{array}{l} U_1 = Z_{11}I_1 + Z_{12}I_2\\ U_2 = Z_{21}I_1 + Z_{22}I_2 \end{array}\right. $$

导纳参数(Y参数)#

$$ \begin{cases} I_1 = Y_{11}U_1 + Y_{12}U_2 \\ I_2 = Y_{21}U_1 + Y_{22}U_2 \end{cases} $$

混合参数(H参数)#

$$ \begin{cases} U_1 = h_{11}I_1 + h_{12}U_2 \\ I_2 = h_{21}I_1 + h_{22}U_2 \end{cases} $$

传输参数(ABCD参数/T参数)#

$$ \begin{cases} U_1 = AU_2 - BI_2 \\ I_1 = CU_2 - DI_2 \end{cases} $$

参数转换关系#

Z参数与Y参数互转#

$$ [Z] = [Y]^{-1} \quad \Leftrightarrow \quad [Y] = [Z]^{-1} $$ $$ 注:H型、T型由Z或Y变换即可 $$

测量公式#

开路阻抗#

$$ Z_{11} = \left.\frac{V_1}{I_1}\right|_{I_2=0} \qquad Z_{22} = \left.\frac{V_2}{I_2}\right|_{I_1=0}\\ \ \\ Z_{21} = \left.\frac{U_2}{I_1}\right|_{I_2=0} \qquad Z_{12} = \left.\frac{U_1}{I_2}\right|_{I_1=0} $$

短路导纳#

$$ Y_{11} = \left.\frac{I_1}{U_1}\right|_{U_2=0} \qquad Y_{22} = \left.\frac{I_2}{U_2}\right|_{U_1=0}\\ \ \\ Y_{21} = \left.\frac{I_1}{U_2}\right|_{U_1=0} \qquad Y_{12} = \left.\frac{I_2}{U_1}\right|_{U_2=0} $$ $$ 注:下标与测量统一逻辑 $$