Slide 1

  • Topic: Equivalent Circuits
  • Introduction to Equivalent Circuits
  • Understanding the concept of equivalent circuits
  • Why do we use equivalent circuits?
  • Importance of equivalent circuits in understanding complex systems

Slide 2

  • Defining Equivalent Circuits
  • Equivalent circuits defined as simplifications of complex circuits
  • Circuits that have the same behavior as the original circuit
  • Equivalent circuits help in analyzing and understanding circuit behavior

Slide 3

  • Types of Equivalent Circuits
  • Two commonly used equivalent circuit models: Thevenin and Norton
  • Thevenin Equivalent Circuit: Voltage source in series with a resistor
  • Norton Equivalent Circuit: Current source in parallel with a resistor

Slide 4

  • Thevenin Equivalent Circuit
  • Defined by an equivalent voltage source and an equivalent resistance
  • Thevenin voltage (Vth) and Thevenin resistance (Rth)
  • Example equation: Vth = Voc (open circuit voltage)

Slide 5

  • Norton Equivalent Circuit
  • Defined by an equivalent current source and an equivalent resistance
  • Norton current (In) and Norton resistance (Rn)
  • Example equation: In = Isc/Rsc (short circuit current)

Slide 6

  • Steps to Find Equivalent Circuits
  • Method for Thevenin Equivalent Circuits:
    • Calculate open-circuit voltage (Voc)
    • Find Thevenin resistance (Rth) when all independent sources are turned off
  • Method for Norton Equivalent Circuits:
    • Calculate short-circuit current (Isc)
    • Find Norton resistance (Rn) when all independent sources are turned off

Slide 7

  • Example 1: Thevenin Equivalent Circuit
  • Given circuit with independent sources and resistors
  • Step 1: Calculate open-circuit voltage (Voc)
  • Step 2: Find Thevenin resistance (Rth) when sources are turned off
  • Provide numerical calculations and example circuit diagram

Slide 8

  • Example 2: Norton Equivalent Circuit
  • Given circuit with independent sources and resistors
  • Step 1: Calculate short-circuit current (Isc)
  • Step 2: Find Norton resistance (Rn) when sources are turned off
  • Provide numerical calculations and example circuit diagram

Slide 9

  • Applications of Equivalent Circuits
  • Equivalent circuits help in simplifying complex circuits
  • Useful in analyzing and predicting circuit behavior
  • Application in analysis of electrical networks, digital systems, and power systems

Slide 10

  • Summary
  • Equivalent circuits are simplifications of complex circuits
  • Two commonly used equivalent circuit models: Thevenin and Norton
  • Steps to find equivalent circuits for a given circuit
  • Applications of equivalent circuits in various fields of electrical engineering
  1. Thevenin’s Theorem
  • Thevenin’s theorem is a powerful theorem in circuit analysis.
  • It states that any linear electrical network can be replaced by an equivalent circuit consisting of a voltage source (Vth) in series with a resistor (Rth).
  • This equivalent circuit has the same output current-voltage characteristics at any pair of terminals.
  1. Steps to Find Thevenin Equivalent Circuit
  1. Identify the terminals across which you want to find the Thevenin equivalent.
  1. Remove all the loads connected to these terminals.
  1. Calculate the open-circuit voltage (Voc) by finding the voltage across the terminals when no current is flowing.
  1. Calculate the Thevenin resistance (Rth) by determining the resistance seen from the terminals with all the independent sources turned off.
  1. Construct the Thevenin equivalent circuit by connecting Vth in series with Rth.
  1. Example: Thevenin Equivalent Circuit
  • Given circuit with a dependent source, independent sources, and resistors.
  • Step 1: Identify the terminals for Thevenin equivalent.
  • Step 2: Remove the load connected to these terminals.
  • Step 3: Calculate the open-circuit voltage (Voc) across the terminals.
  • Step 4: Determine the Thevenin resistance (Rth) seen from the terminals.
  • Step 5: Assemble the Thevenin equivalent circuit.
  1. Norton’s Theorem
  • Norton’s theorem is another important theorem in circuit analysis.
  • It states that any linear electrical network can be replaced by an equivalent circuit consisting of a current source (In) in parallel with a resistor (Rn).
  • This equivalent circuit has the same output current-voltage characteristics at any pair of terminals.
  1. Steps to Find Norton Equivalent Circuit
  1. Identify the terminals for which you want to find the Norton equivalent.
  1. Remove all the loads connected to these terminals.
  1. Calculate the short-circuit current (Isc) by connecting a short circuit across the terminals.
  1. Determine the Norton resistance (Rn) seen from the terminals with all the independent sources turned off.
  1. Construct the Norton equivalent circuit by connecting In in parallel with Rn.
  1. Example: Norton Equivalent Circuit
  • Given circuit with independent sources and resistors.
  • Step 1: Identify the terminals for the Norton equivalent.
  • Step 2: Remove the load connected to these terminals.
  • Step 3: Calculate the short-circuit current (Isc) across the terminals.
  • Step 4: Determine the Norton resistance (Rn) seen from the terminals.
  • Step 5: Assemble the Norton equivalent circuit.
  1. Superposition Theorem
  • The superposition theorem simplifies the analysis of linear circuits with multiple sources.
  • According to this theorem, the total response in a circuit is equal to the sum of individual responses caused by each source acting alone.
  • This theorem can be applied to any circuit which can be described by linear differential equations.
  1. Steps to Apply Superposition Theorem
  1. Turn off all the sources except one.
  1. Analyze the circuit using the techniques you are familiar with.
  1. Repeat the above steps for each source separately.
  1. Add the individual responses algebraically to obtain the total response.
  1. Example: Superposition Theorem
  • Given circuit with independent sources and resistors.
  • Step 1: Turn off all the sources except one.
  • Step 2: Analyze the circuit for one source.
  • Step 3: Repeat steps 1 and 2 for other sources.
  • Step 4: Add the individual responses to obtain the total response.
  1. Node-Voltage Method
  • The node-voltage method is a powerful technique to solve circuit problems.
  • It involves selecting the node voltages as unknowns and writing equations based on Kirchhoff’s current law (KCL) at each node.
  • These equations can then be solved simultaneously to find the unknown node voltages and other circuit parameters.
  1. Node-Voltage Method (Continued)
  • Steps to Apply Node-Voltage Method:
    1. Select a reference node (usually the one with the most connections).
    2. Assign a variable for each node voltage relative to the reference node.
    3. Write Kirchhoff’s current law (KCL) equations for each node (except the reference node).
    4. Solve the resulting system of equations for the unknown node voltages.
  • Example: Node-Voltage Method
    • Given circuit with resistors and current/voltage sources.
    • Step 1: Select the reference node and assign variables for each node voltage.
    • Step 2: Write KCL equations for each node (excluding the reference node).
    • Step 3: Solve the equations to find the unknown node voltages.
  1. Circuit Analysis with Capacitors and Inductors
  • Introduction to Circuit Analysis with Capacitors and Inductors
  • Capacitors store energy in an electric field, while inductors store energy in a magnetic field.
  • Analyzing circuits with capacitors and inductors requires the use of differential equations.
  • Kirchhoff’s laws still apply, but with additional equations for the behavior of capacitors and inductors.
  1. Capacitor Behavior in DC Circuits
  • Capacitors in DC Circuits
  • Capacitors appear as open circuits (infinite resistance) to direct current (DC).
  • Charge build-up and voltage across the capacitor occurs gradually over time.
  • Time constant (τ) determines the rate at which a capacitor charges or discharges.
  • Charging equation: Vc = V(1 - e^(-t/τ))
  • Discharging equation: Vc = V e^(-t/τ)
  1. Inductor Behavior in DC Circuits
  • Inductors in DC Circuits
  • Inductors appear as short circuits (zero resistance) to direct current (DC).
  • Magnetic field builds up gradually when current flows, causing an opposing voltage (back EMF).
  • Time constant (τ) determines the rate at which an inductor’s magnetic field builds up.
  • Charging equation: IL = I(1 - e^(-t/τ))
  • Discharging equation: IL = I e^(-t/τ)
  1. Capacitor and Inductor Behavior in AC Circuits
  • Capacitor and Inductor Behavior in AC Circuits
  • Capacitors and inductors behave differently in AC circuits compared to DC circuits.
  • Capacitors allow high-frequency signals to pass but block low-frequency signals.
  • Inductors allow low-frequency signals to pass but block high-frequency signals.
  • Impedance (Z) is used to represent the opposition to the flow of AC current in capacitors and inductors.
  • Capacitor impedance (Zc): Zc = 1/(jωC) where ω = 2πf (angular frequency)
  1. Introduction to Complex Impedance
  • Complex Impedance
  • Complex impedance (Z) is used to represent the opposition to the flow of AC current in circuits.
  • Complex impedance combines the resistance (R) and reactance (X) of a circuit element.
  • Z = R + jX (where j = √(-1))
  • The real part (R) represents the resistance, while the imaginary part (X) represents the reactance.
  1. RC Circuits
  • RC Circuits
  • RC circuits consist of resistors (R) and capacitors (C) connected in series or parallel.
  • Time constant (τ) determines the rate at which a capacitor charges or discharges in an RC circuit.
  • Charging equation: Vc = V(1 - e^(-t/τ))
  • Discharging equation: Vc = V e^(-t/τ)
  • RC circuits can be used as low-pass filters, high-pass filters, or integrators, depending on the configuration.
  1. RL Circuits
  • RL Circuits
  • RL circuits consist of resistors (R) and inductors (L) connected in series or parallel.
  • Time constant (τ) determines the rate at which the magnetic field builds up or collapses in an RL circuit.
  • Charging equation: IL = I(1 - e^(-t/τ))
  • Discharging equation: IL = I e^(-t/τ)
  • RL circuits can be used as low-pass filters, high-pass filters, or differentiators, depending on the configuration.
  1. RLC Circuits
  • RLC Circuits
  • RLC circuits consist of resistors (R), capacitors (C), and inductors (L) connected in different configurations.
  • Resonance occurs when capacitive and inductive reactance cancel each other out.
  • Resonant frequency (fr): fr = 1 / (2π√(LC))
  • Quality factor (Q): Q = ω0L/R (where ω0 = 2πfr)
  • RLC circuits are used in filters, oscillators, and voltage/current amplification circuits.
  1. Summary
  • Recap of Key Concepts
  • Equivalent circuits: Thevenin and Norton models
  • Node-voltage method for circuit analysis
  • Capacitor and inductor behavior in DC and AC circuits
  • Complex impedance and RC, RL, and RLC circuits
  • Importance of understanding these concepts for circuit analysis applications
  • Encouragement for further exploration and practice with circuit analysis techniques.