双端口网络

Two-Port Networks

A two-port network is an electrical network with two separate ports for input and output.

Impedance Parameters

$$\begin{array}{rl}{\mathbf{V}}_1& ={\mathbf{z}}_{11}{\mathbf{I}}_1+{\mathbf{z}}_{12}{\mathbf{I}}_2\\ {\mathbf{V}}_2& ={\mathbf{z}}_{21}{\mathbf{I}}_1+{\mathbf{z}}_{22}{\mathbf{I}}_2\end{array}$$$$\begin{array}{rlrl}{\mathbf{z}}_{11}& =\frac{{\mathbf{V}}_1}{{\mathbf{I}}_1}{|}_{{\mathbf{I}}_2=0},& {\mathbf{z}}_{12}& =\frac{{\mathbf{V}}_1}{{\mathbf{I}}_2}{|}_{{\mathbf{I}}_1=0}\\ {\mathbf{z}}_{21}& =\frac{{\mathbf{V}}_2}{{\mathbf{I}}_1}{|}_{{\mathbf{I}}_2=0},& {\mathbf{z}}_{22}& =\frac{{\mathbf{V}}_2}{{\mathbf{I}}_2}{|}_{{\mathbf{I}}_1=0}\end{array}$$

• ${\mathbf{z}}_{11}=$ Open-circuit input impedance
• ${\mathbf{z}}_{12}=$ Open-circuit transfer impedance from port 2 to port 1
• ${\mathbf{z}}_{21}=$ Open-circuit transfer impedance from port 1 to port 2
• ${\mathbf{z}}_{22}=$ Open-circuit output impedance

Admittance Parameters

$$\begin{array}{rl}{\mathbf{I}}_1& ={\mathbf{y}}_{11}{\mathbf{V}}_1+{\mathbf{y}}_{12}{\mathbf{V}}_2\\ {\mathbf{I}}_2& ={\mathbf{y}}_{21}{\mathbf{V}}_1+{\mathbf{y}}_{22}{\mathbf{V}}_2\end{array}$$$$\begin{array}{rlrl}{\mathbf{y}}_{11}& =\frac{{\mathbf{I}}_1}{{\mathbf{V}}_1}{|}_{{\mathbf{V}}_2=0},& {\mathbf{y}}_{12}& =\frac{{\mathbf{I}}_1}{{\mathbf{V}}_2}{|}_{{\mathbf{V}}_1=0}\\ {\mathbf{y}}_{21}& =\frac{{\mathbf{I}}_2}{{\mathbf{V}}_1}{|}_{{\mathbf{V}}_2=0},& {\mathbf{y}}_{22}& =\frac{{\mathbf{I}}_2}{{\mathbf{V}}_2}{|}_{{\mathbf{V}}_1=0}\end{array}$$

• ${\mathbf{y}}_{11}=$ Short-circuit input admittance
• ${\mathbf{y}}_{12}=$ Short-circuit transfer admittance from port 2 to port 1
• ${\mathbf{y}}_{21}=$ Short-circuit transfer admittance from port 1 to port 2
• ${\mathbf{y}}_{22}=$ Short-circuit output admittance

Hybrid Parameters

$$\begin{array}{rl}{\mathbf{V}}_1& ={\mathbf{h}}_{11}{\mathbf{I}}_1+{\mathbf{h}}_{12}{\mathbf{V}}_2\\ {\mathbf{I}}_2& ={\mathbf{h}}_{21}{\mathbf{I}}_1+{\mathbf{h}}_{22}{\mathbf{V}}_2\end{array}$$$$\begin{array}{rlrl}{\mathbf{h}}_{11}& =\frac{{\mathbf{V}}_1}{{\mathbf{I}}_1}{|}_{{\mathbf{V}}_2=0},& {\mathbf{h}}_{12}& =\frac{{\mathbf{V}}_1}{{\mathbf{V}}_2}{|}_{{\mathbf{I}}_1=0}\\ {\mathbf{h}}_{21}& =\frac{{\mathbf{I}}_2}{{\mathbf{I}}_1}{|}_{{\mathbf{V}}_2=0},& {\mathbf{h}}_{22}& =\frac{{\mathbf{I}}_2}{{\mathbf{V}}_2}{|}_{{\mathbf{I}}_1=0}\end{array}$$

• ${\mathbf{h}}_{11}=$ Short-circuit input impedance
• ${\mathbf{h}}_{12}=$ Open-circuit reverse voltage gain
• ${\mathbf{h}}_{21}=$ Short-circuit forward current gain
• ${\mathbf{h}}_{22}=$ Open-circuit output admittance

Inverse Hybrid Parameters

$$\begin{array}{rl}{\mathbf{I}}_1& ={\mathbf{g}}_{11}{\mathbf{V}}_1+{\mathbf{g}}_{12}{\mathbf{I}}_2\\ {\mathbf{V}}_2& ={\mathbf{g}}_{21}{\mathbf{V}}_1+{\mathbf{g}}_{22}{\mathbf{I}}_2\end{array}$$$$\begin{array}{rlrl}{\mathbf{g}}_{11}& =\frac{{\mathbf{I}}_1}{{\mathbf{V}}_1}{|}_{{\mathbf{I}}_2=0},& {\mathbf{g}}_{12}& =\frac{{\mathbf{I}}_1}{{\mathbf{I}}_2}{|}_{{\mathbf{V}}_1=0}\\ {\mathbf{g}}_{21}& =\frac{{\mathbf{V}}_2}{{\mathbf{V}}_1}{|}_{{\mathbf{I}}_2=0},& {\mathbf{g}}_{22}& =\frac{{\mathbf{V}}_2}{{\mathbf{I}}_2}{|}_{{\mathbf{V}}_1=0}\end{array}$$

• ${\mathbf{g}}_{11}=$ Open-circuit input admittance
• ${\mathbf{g}}_{12}=$ Short-circuit reverse current gain
• ${\mathbf{g}}_{21}=$ Short-circuit forward voltage gain
• ${\mathbf{g}}_{22}=$ Short-circuit output impedance

Transmission Parameters

$$\begin{array}{rl}{\mathbf{V}}_1& =\mathbf{A}{\mathbf{V}}_2-\mathbf{B}{\mathbf{I}}_2\\ {\mathbf{I}}_1& =\mathbf{C}{\mathbf{V}}_2-\mathbf{D}{\mathbf{I}}_2\end{array}$$$$\begin{array}{rlrl}\mathbf{A}& =\frac{{\mathbf{V}}_1}{{\mathbf{V}}_2}{|}_{{\mathbf{I}}_2=0},& \mathbf{B}& =-\frac{{\mathbf{V}}_1}{{\mathbf{I}}_2}{|}_{{\mathbf{V}}_2=0}\\ \mathbf{C}& =\frac{{\mathbf{I}}_1}{{\mathbf{V}}_2}{|}_{{\mathbf{I}}_2=0},& \mathbf{D}& =-\frac{{\mathbf{I}}_1}{{\mathbf{I}}_2}{|}_{{\mathbf{V}}_2=0}\end{array}$$

• $\mathbf{A}=$ Open-circuit voltage ratio
• $\mathbf{B}=$ Negative short-circuit transfer impedance
• $\mathbf{C}=$ Open-circuit transfer admittance
• $\mathbf{D}=$ Negative short-circuit current ratio

Inverse Transmission Parameters

$$\begin{array}{rl}{\mathbf{V}}_2& =\mathbf{a}{\mathbf{V}}_1-\mathbf{b}{\mathbf{I}}_1\\ {\mathbf{I}}_2& =\mathbf{c}{\mathbf{V}}_1-\mathbf{d}{\mathbf{I}}_1\end{array}$$$$\begin{array}{rlrl}\mathbf{a}& =\frac{{\mathbf{V}}_2}{{\mathbf{V}}_1}{|}_{{\mathbf{I}}_1=0},& \mathbf{b}& =-\frac{{\mathbf{V}}_2}{{\mathbf{I}}_1}{|}_{{\mathbf{V}}_1=0}\\ \mathbf{c}& =\frac{{\mathbf{I}}_2}{{\mathbf{V}}_1}{|}_{{\mathbf{I}}_1=0},& \mathbf{d}& =-\frac{{\mathbf{I}}_2}{{\mathbf{I}}_1}{|}_{{\mathbf{V}}_1=0}\end{array}$$

• $\mathbf{a}=$ Open-circuit voltage gain
• $\mathbf{b}=$ Negative short-circuit transfer impedance
• $\mathbf{c}=$ Open-circuit transfer admittance
• $\mathbf{d}=$ Negative short-circuit current gain

参数转换表