### Transfer Function for the Circuit#### Problem Statement:1. **Find the transfer function for the circuit**: a. Plot Amplitude and phase spectrum using MATLAB. b. Identify the type of filter it is.#### Circuit Diagram:The circuit consists of the following components:- **Resistor \( R_1 = 1 \Omega \)** connected in series with the input voltage \( V_{in} \).- **Capacitor \( C = 0.4 F \)** connected to the junction between \( R_1 \) and \( R_2 \), leading to the ground.- **Resistor \( R_2 = 2 \Omega \)** connected in series with an inductor \( L = 1 H \), forming the right branch of the circuit.- The output voltage \( V_o \) is measured across the parallel combination of \( R_2 \) and \( L \).#### Solution:**Steps to find the transfer function \( H(\omega) \):**1. **Write Node equation at point \( a \)**: - This is determined by analyzing the node with the capacitor connected, considering the currents entering and leaving the node.2. **Write Node equation at point \( b \)**: - This involves formulating the equation at the node where \( R_2 \) and \( L \) meet.3. **Apply the second equation into the first equation**: - Solve the system of equations to relate \( V_o \) and \( V_{in} \).4. **Simplify and find \( H(\omega) = \frac{V_o(\omega)}{V_{in}(\omega)} \)**: - The final transfer function will express the ratio of the output voltage to the input voltage as a function of angular frequency \( \omega \).**Note**: The exact method of solving these equations and determining the simplified form of the transfer function involves standard circuit analysis techniques like Kirchhoff's Current Law (KCL), Kirchhoff's Voltage Law (KVL), and impedance analysis in the frequency domain.The type of filter (Low-pass, High-pass, Band-pass, or Band-stop) can be determined from the form of the transfer function and its response characteristics.This concludes the explanation and steps to find the transfer function for the given circuit. Use MATLAB for plotting the amplitude and phase spectrum of the transfer function to further analyze the frequency response of the

SOLUTION -Plot amplitude and phase spectrum using H(s) and bode command in Matlab. Below is the…

1. Find the transfer function for the circuit a. Plot Amplitude and phase spectrum using MATLAB. b. What the type of filter is it? Solution: R₁ www 102 +4li 0.4 F R₂ www 20 b L V₂ 1 H Steps to find transfer function: 1. Write Node equation (a), 2. Write Node equation (b). 3. Appy second equation into equation 1. Simplify and find H(w) =Vow) Vin(w)

1. Find the transfer function for the circuit a. Plot Amplitude and phase spectrum using MATLAB. b. What the type of filter is it? Solution: R₁ www 102 +4li 0.4 F R₂ www 20 b L V₂ 1 H Steps to find transfer function: 1. Write Node equation (a), 2. Write Node equation (b). 3. Appy second equation into equation 1. Simplify and find H(w) =Vow) Vin(w)

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Question

### Transfer Function for the Circuit

#### Problem Statement:
1. **Find the transfer function for the circuit**:
a. Plot Amplitude and phase spectrum using MATLAB.
b. Identify the type of filter it is.

#### Circuit Diagram:
The circuit consists of the following components:
- **Resistor \( R_1 = 1 \Omega \)** connected in series with the input voltage \( V_{in} \).
- **Capacitor \( C = 0.4 F \)** connected to the junction between \( R_1 \) and \( R_2 \), leading to the ground.
- **Resistor \( R_2 = 2 \Omega \)** connected in series with an inductor \( L = 1 H \), forming the right branch of the circuit.
- The output voltage \( V_o \) is measured across the parallel combination of \( R_2 \) and \( L \).

#### Solution:

**Steps to find the transfer function \( H(\omega) \):**

1. **Write Node equation at point \( a \)**:
- This is determined by analyzing the node with the capacitor connected, considering the currents entering and leaving the node.

2. **Write Node equation at point \( b \)**:
- This involves formulating the equation at the node where \( R_2 \) and \( L \) meet.

3. **Apply the second equation into the first equation**:
- Solve the system of equations to relate \( V_o \) and \( V_{in} \).

4. **Simplify and find \( H(\omega) = \frac{V_o(\omega)}{V_{in}(\omega)} \)**:
- The final transfer function will express the ratio of the output voltage to the input voltage as a function of angular frequency \( \omega \).

**Note**: The exact method of solving these equations and determining the simplified form of the transfer function involves standard circuit analysis techniques like Kirchhoff's Current Law (KCL), Kirchhoff's Voltage Law (KVL), and impedance analysis in the frequency domain.

The type of filter (Low-pass, High-pass, Band-pass, or Band-stop) can be determined from the form of the transfer function and its response characteristics.

This concludes the explanation and steps to find the transfer function for the given circuit. Use MATLAB for plotting the amplitude and phase spectrum of the transfer function to further analyze the frequency response of the

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