Question

Resonant circuits are used to select a signal (e.gr, a radio station or 'TV channel) from among other competing signals. Resonant circuits are characterized by the frequency response shown in the figure below. The resonant frequency response is completely described by three parameters: the resonant frequency, \(\omega_{\mathrm{o}}\) the bandwidth, \(B\), and the gain at the resonant frequency, \(k\). Two simple resonant circuits are shown in the figure below, The circuit in (a) is called a parallel resonant circuit. The circuit in (b) is called a series resonant circuit. Both resonant circuits consist of a resistor having resistance \(R\), a capacitor having capacitance \(C\), and an inductor having inductance \(L\). These circuits are designed by determining values of \(R, C\), and \(L\) that cause the resonant frequency response to be described by specified values of \(m_{o}, B\), and \(k\). The design equations for the parallel resonant circuit are: $$ R=k, \quad C=\frac{1}{B R}, \text { and } \quad L=\frac{1}{\omega_{0}^{2} C} $$ Similarly, the design equations for the series resonant circuit are: $$ R=\frac{1}{k}, L=\frac{R}{B}, \text { and } C=\frac{1}{\omega_{\mathrm{o}}^{2} L} $$ Write a Python program that represents ResonantCircuit as a superclass and represents the SeriesResonantCircuit and FarallelResonantCircuit as subclasses. Give the superclass thrce instance variables representing the parameters \(\omega_{\mathrm{o}}, B\), and \(k\) of the resonant frequency response. The superclass should provide public methods to get and set cach of these variables. The superclass should also provide a display method that prints a description of the resonant frequency response. Each subclass should provide a method that designs the corresponding resonant circuit. The subclasses should also override the display method of the superclass to print descriptions of both the frequency response (the values of \(\omega_{\mathrm{o}} B\), and \(k\) ) and the circuit (the values of \(R, C\), and \(L\) ). All classes should provide appropriate constructors. Supply a program that demonstrates that the subclasses all work properly.

Short answer

Create three classes: `ResonantCircuit`, `SeriesResonantCircuit`, `ParallelResonantCircuit`, and override methods to calculate and display circuit parameters.

Step-by-step solution

Define the ResonantCircuit superclass

Start by defining a Python class named `ResonantCircuit` that will serve as the superclass. This class should initialize with three instance variables: `omega_o`, `B`, and `k`. Implement getter and setter methods for each of these variables to allow modifications. Also, include a `display` method that prints out the frequency response values: `omega_o`, `B`, and `k`.

Define subclass SeriesResonantCircuit

Create a subclass named `SeriesResonantCircuit` that inherits from `ResonantCircuit`. Define a method named `design_circuit` that calculates the resistance `R`, capacitance `C`, and inductance `L` using the given formulas: \[ R = \frac{1}{k}, \quad L = \frac{R}{B}, \quad C = \frac{1}{\omega_\mathrm{o}^{2} \times L} \]Override the `display` method to include a description of the circuit parameters alongside the frequency response.

Define subclass ParallelResonantCircuit

Develop another subclass called `ParallelResonantCircuit` inheriting from `ResonantCircuit`. Implement the `design_circuit` method to calculate `R`, `C`, and `L` using:\[ R = k, \quad C = \frac{1}{B \times R}, \quad L = \frac{1}{\omega_{0}^{2} \times C} \]Override the `display` method to display both the frequency response and the circuit parameter values.

Write constructor functions

Ensure all classes (superclass and subclasses) have appropriate constructor functions (`__init__`) that initialize their respective variables. The `ResonantCircuit` class should initialize the basic frequency parameters, while the subclasses will set up more specific details including method calls for designing the circuits.

Demonstrate the program

Create a program that instantiates objects from the `SeriesResonantCircuit` and `ParallelResonantCircuit` classes. Use the methods provided to set values for `omega_o`, `B`, and `k`. Call the `display` methods to show that each class correctly calculates and displays its respective circuit and frequency response.

Key concepts

Class Inheritance

In Python, class inheritance is a fundamental concept that allows a class to derive properties and methods from another class. This is an integral part of object-oriented programming.
When you create a new class, you can build it upon an existing class. The new class, known as the subclass, inherits all the attributes and methods of the parent class, also known as the superclass. However, it can also have additional attributes and methods or can override existing ones. This allows you to :

• Reuse code without duplication, which saves time and effort.
• Implement polymorphism where a common interface is used for different data types.
• Extend and customize the behavior of base classes.

In our exercise, `ResonantCircuit` acts as the superclass. It provides basic functionalities related to resonant circuits, like managing frequency response parameters. The `SeriesResonantCircuit` and `ParallelResonantCircuit` are subclasses. They inherit the structure and behavior of the `ResonantCircuit` class but add specific methods to calculate unique circuit parameters. By overriding the `display` method, these subclasses can showcase polymorphism, providing different implementations for displaying their data.

Circuit Design

Circuit design plays a crucial role in creating functional electronics. It involves determining the right components and values that allow a circuit to perform its intended function. Resonant circuits are particularly interesting because they focus on selecting specific frequencies from a range of signals, making them essential in applications like radio communication.
Resonant circuits utilize resistors, capacitors, and inductors to achieve a particular frequency response, defined by:

• Resonant Frequency (\( \omega_o \))
• Bandwidth (\( B \))
• Gain (\( k \))

The formulas for the circuit parameters (R, C, L) largely depend on whether the circuit is series or parallel.
In a **series resonant circuit**, the calculations involve:

• \( R = \frac{1}{k} \)
• \( L = \frac{R}{B} \)
• \( C = \frac{1}{\omega_{o}^{2} \times L} \)

For a **parallel resonant circuit**, you use:

• \( R = k \)
• \( C = \frac{1}{B \times R} \)
• \( L = \frac{1}{\omega_{0}^{2} \times C} \)

Understanding these equations is vital for designing circuits that possess the desired frequency attributes, enabling effective signal selection and amplification.

Python Programming Concepts

When tackling the problem of designing resonant circuits, Python offers a flexible and powerful way to implement object-oriented features.
**Classes and Objects:** Python allows you to define classes as blueprints for creating objects. An object is an instance of a class. In this exercise, the `ResonantCircuit` class establishes the framework for the circuit's frequency response attributes: \( \omega_o \), \( B \), and \( k \). These attributes are initialized and managed within the class.
**Methods:** Inside classes, you define methods, which are functions that belong to an object. Methods like `display` and `design_circuit` provide functionality related to the circuit's characteristics.
**Constructors:** The constructor method `__init__` allows you to initialize an object's properties when it is first created. Each class in our problem uses this method to set up initial values.
**Encapsulation:** The use of getter and setter methods is a way to implement encapsulation. This concept involves restricting access to an object's components, which ensures controlled manipulation of attributes, enhancing the robustness and security of your code.
Together, these programming concepts allow the effective modeling of complex systems in Python, demonstrating how theoretical designs can be translated into functional software applications.