Learn · Basic Electrical Circuits
Lecture 46 of 143Week 4: Nodal analysis
Nodal analysis with independent voltage sources
Prof. Gajendranath Chowdary · IIT Madras
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- Basic Electrical Circuits, IIT Madras (at NPTEL)
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- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
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All the lectures
- Preliminaries
- Current
- Voltage
- Electrical elements and circuits
- Kirchhoff's current law(KCL)
- Kirchhoff's voltage law(KVL)
- Voltage source
- Current source
- Resistor
- Capacitor
- Inductor
- Mutual inductor
- Linearity of elements
- Series connection-Voltage sources in series
- Series connection of R, L, C, current source
- Elements in parallel
- Current source in series with an element; Voltage source in parallel with an element
- Extreme cases: Open and short circuits
- Summary
- Voltage controlled voltage source(VCVS)
- Voltage controlled current source(VCCS)
- Current controlled voltage source(CCVS)
- Current controlled current source(CCCS)
- Realizing a resistance using a VCCS or CCCS
- Scaling an element's value using controlled sources
- Example calculation
- Power and energy absorbed by electrical elements
- Power and energy in a resistor
- Power and energy in a capacitor
- Power and energy in an inductor
- Power and energy in a voltage source
- Power and energy in a current source
- Goals of circuit analysis
- Number of independent KCL equations
- Number of independent KVL equations and branch relationships
- Analysis of circuits with a single independent source
- Analysis of circuits with multiple independent sources using superposition
- Superposition: Example
- What is nodal analysis
- Setting up nodal analysis equations
- Structure of the conductance matrix
- How elements appear in the nodal analysis formulation
- Completely solving the circuit starting from nodal analysis
- Nodal analysis example
- Matrix inversion basics
- Nodal analysis with independent voltage sources
- Supernode for nodal analysis with independent voltage sources
- Nodal analysis with VCCS
- Nodal analysis with VCVS
- Nodal analysis with CCVS
- Nodal analysis with CCCS
- Nodal analysis summary
- Planar circuits
- Mesh currents and their relationship to branch currents
- Mesh analysis
- Mesh analysis with independent current sources-Supermesh
- Mesh analysis with current controlled voltage sources
- Mesh analysis with current controlled current sources
- Mesh analysis using voltage controlled sources
- Nodal analysis versus Mesh analysis
- Superposition theorem
- Pushing a voltage source through a node
- Splitting a current source
- Substitution theorem: Current source
- Substitution theorem: Voltage source
- Substituting a voltage or current source with a resistor
- Extensions to Superposition and Substitution theorem
- Thevenin's theorem
- Worked out example: Thevenin's theorem
- Norton's theorem
- Worked out example: Norton's theorem
- Maximum power transfer theorem
- Preliminaries
- Two port parameters
- y parameters
- y parameters: Examples
- z parameters
- z parameters: Examples
- h parameters
- h parameters: Examples
- g parameters
- g parameters: Examples
- Calculations with a two-port element
- Calculations with a two-port element
- Degenerate cases
- Relationships between different two-port parameters
- Equivalent circuit representation for two ports
- Reciprocity
- Proof of reciprocity of resistive two-ports
- Proof for 4-terminal two-ports
- Reciprocity in terms of different two-port parameters
- Reciprocity in circuits containing controlled sources
- Examples
- Feedback amplifier using an opamp
- Ideal opamp
- Negative feedback around the opamp
- Finding opamp signs for negative feedback
- Example: Determining opamp sign for negative feedback
- Analysis of circuits with opamps
- Inverting amplifier
- Summing amplifier
- Instrumentation amplifier
- Negative resistance and Miller effect
- Finding opamp signs for negative feedback-circuits with multiple opamps
- Opamp supply voltages and saturation
- KCL with an opamp and supply currents
- More on opamps: Example circuits and additional topics
- Circuits with storage elements(capacitors and inductors)
- First order circuit with zero input-natural response
- First order RC circuit with zero input-Example
- First order circuit with a constant input
- General form of the first order circuit response
- First order RC circuit with a constant input-Example
- First order circuit with piecewise constant input
- First order circuit with piecewise constant input-Example
- First order circuit-Response of arbitrary circuit variables
- Summary: Computing first order circuit response
- Does a capacitor block DC?
- Finding the order of a circuit
- First order RC circuits with discontinuous capacitor voltages
- Summary: Computing first order circuit response with discontinuities
- First order RL circuits
- First order RL circuit with discontinuous inductor current-Example
- First order RC circuit with an exponential input
- First order RC response to its own natural response
- First order RC response to a sinusoidal input
- First order RC response to a sinusoidal input-via the complex exponential
- Summary: Linear circuit response to sinusoidal input via the complex exponential
- Three methods of calculating the sinusoidal steady state response
- Calculating the total response including initial conditions
- Why are sinusoids used in measurement?
- Second order system natural response
- Second order system as a cascade of two first order systems
- Second order system natural response-critically damped and underdamped
- Generalized form of a second order system
- Numerical example
- Series and parallel RLC circuits
- Forced response of a second order system
- Steady state response calculation and Phasors
- Phasors cont'd
- Magnitude and Phase plots
- Magnitude and phase plotes of a second order system
- Maximum power transfer and Conjugate matching