【Practical Exercise】Basic High-Frequency Electronic Circuit Simulation Using MATLAB

# 2.1 Fundamental Concepts of High-Frequency Circuits

### 2.1.1 Impedance and Admittance

Impedance is a significant concept in high-frequency circuits, indicating the circuit's opposition to alternating current. It consists of resistance, inductance, and capacitance and is expressed as:

Z = R + j(XL - XC)

Where:

* Z is impedance
* R is resistance
* XL is inductive reactance
* XC is capacitive reactance

Admittance is the reciprocal of impedance and represents the circuit's capability to pass alternating current. It is expressed as:

Y = 1/Z = G + j(B)

Where:

* Y is admittance
* G is conductance
* B is susceptance

# 2. Basic Theoretical Foundations of High-Frequency Electronic Circuit Simulation

### 2.1 Fundamental Concepts of High-Frequency Circuits

#### 2.1.1 Impedance and Admittance

In high-frequency circuits, impedance and admittance are two essential concepts. Impedance (Z) signifies the degree of opposition to alternating current, determined by resistance (R), inductance (L), and capacitance (C). Admittance (Y) is the reciprocal of impedance, indicating the circuit's ability to pass alternating current.

The relationship between impedance and admittance is:

Y = 1 / Z

Impedance and admittance can be represented as complex numbers, where the real part denotes resistance, and the imaginary part denotes inductance or capacitance.

#### 2.1.2 Resonance and Quality Factor

Resonance refers to the phenomenon where a circuit exhibits maximum impedance or admittance at a specific frequency. The resonant frequency (f0) is determined by the circuit's inductance and capacitance:

f0 = 1 / (2π√LC)

The quality factor (Q) signifies the frequency selectivity of a resonant circuit, which is determined by the resonant frequency and the bandwidth (BW):

Q = f0 / BW

The higher the quality factor, the better the frequency selectivity of the resonant circuit.

### 2.2 Analysis Methods of High-Frequency Electronic Circuits

#### 2.2.1 S-Parameters and Transmission Line Theory

S-parameters are a set of parameters describing the transmission characteristics of high-frequency circuits. They represent the power transmission, reflection, and isolation between different ports of the circuit. Transmission line theory is used to analyze the propagation and reflection of signals on transmission lines in high-frequency circuits.

#### 2.2.2 Equivalent Circuit Models

Equivalent circuit models simplify high-frequency circuits into a configuration composed of resistors, inductors, and capacitors. These models can be used to analyze the frequency response, stability, and other characteristics of the circuit.

**Code Block 1: Analyzing Transmission Lines Using S-Parameters**

% Define transmission line parameters
length = 0.1;   % Length (m)
epsilon_r = 4.4;   % Dielectric constant
conductor_loss = 0.001;   % Conductor loss (S/m)

% Calculate the transmission line S-parameters
[S11, S12, S21, S22] = s_parameters(length, epsilon_r, conductor_loss);

% Plot S-parameter curves
figure;
plot(S11, 'b');
hold on;
plot(S12, 'r');
plot(S21, 'g');
plot(S22, 'k');
legend('S11', 'S12', 'S21', 'S22');
xlabel('Frequency (GHz)');
ylabel('Magnitude (dB)');
title('Transmission Line S-Parameters');

**Logical Analysis:**

This code block uses S-parameters to analyze a transmission line. It defines the parameters of the transmission line (length, dielectric constant, and conductor loss), then calculates the S-parameters. Finally, it plots the S-parameter curves, showing the power transmission, reflection, and isolation of the transmission line at different frequencies.

**Parameter Description:**

* `length`: Length of the transmission line (m)
* `epsilon_r`: Dielectric constant of the transmission line
* `conductor_loss`: Conductor loss of the transmission line (S/m)
* `S11`: Input reflection coefficient of the transmission line
* `S12`: Reverse transmission coefficient of the transmission line
* `S21`: Forward transmission coefficient of the transmission line
* `S22`: Output reflection coefficient of the transmission line

# 3. MATLAB High-Frequency Electronic Circuit Simulation Practice

### 3.1 Simulation of Basic Circuit Components

#### 3.1.1 Resistors, Capacitors, Inductors

In MATLAB, the `resistor`, `capacitor`, and `inductor` functions are used to simulate resistors, capacitors, and inductors, respectively. These functions accept resistance, capacitance, or inductance as parameters and return a circuit component object.

% Create a 100-ohm resistor
R = resistor(100);

% Create a 1μF capacitor
C = capacitor(1e-6);

% Create a 1mH inductor
L = inductor(1e-3);

#### 3.1.2 Transmission Lines and Microstrip Lines

MATLAB provides the `transmissionline` and `microstrip` functions to simulate transmission lines and microstrip li