Cho mạng hai cửa:

In the provided circuit diagrams, the following mathematical relationships can be established:

### Circuit Analysis

**1. Circuit with Two Ports (Part 4)**
- **Matrix Z Determination**:
The impedance matrix \( Z \) relates the voltage and current at the ports. For a two-port network, it is defined as:

\[
\begin{bmatrix}
V_1 \\
V_2
\end{bmatrix}
=
\begin{bmatrix}
Z_{11} & Z_{12} \\
Z_{21} & Z_{22}
\end{bmatrix}
\begin{bmatrix}
I_1 \\
I_2
\end{bmatrix}
\]

- **For the T Configuration**:
The resistors \( R_1, R_2, \) and \( R_3 \) would need to be combined appropriately to derive \( Z_{11}, Z_{12}, Z_{21}, \) and \( Z_{22} \).

**2. Finding Impedance and Admittance**
- **Impedance (Z)**:
Use KVL (Kirchhoff's Voltage Law) and KCL (Kirchhoff's Current Law) to find \( Z \) values in the respective circuit configurations.

- **Admittance (Y)**:
The admittance matrix \( Y \) is the inverse of the impedance matrix:

\[
Y = Z^{-1}
\]

### Important Equations:
- **For Resistors in Series**:
\[
Z = R_1 + R_2 + R_3
\]

- **For Resistors in Parallel**:
\[
Y = Y_1 + Y_2 + Y_3 = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}
\]

### Specific Tasks:
- **Task (a)**: Determine the \( Z \) matrix for the given configurations:
- Calculate \( Z_{11}, Z_{12}, Z_{21}, Z_{22} \) using node or mesh analysis.

- **Task (b)**: Derive transfer functions \( K_{u} \) based on provided relationships:

\[
K_{u} = \frac{U_2}{U_1}, \quad K_{u1} = \frac{U_1}{I_1}, \quad K_{u2} = \frac{U_2}{I_2}
\]

**Final Tasks**:
- Solve each part using the given voltage and current relations within the circuits shown. This will involve substituting the impedance or admittance values as necessary.

If you need detailed steps for calculations or specific numerical examples, feel free to ask!