ELL100: INTRODUCTION TO ELECTRICAL ENGG. Lecture 9 Course Instructors: J.-B. Seo, S. Srirangarajan, S.-D. Roy, and S. Janardhanan Department of Electrical Engineering, IITD

Impedance

Analysis with Impedance the ratio of voltage to current for exponential waveform extends the concept of resistance to AC circuits It has both magnitude and phase; unlike resistance, which has only magnitude. Impedances can be combined in Series and Parallel just like Resistances

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Equivalent Impedance  Impedance in series In parallel

Equivalent Impedance  Impedance in series In parallel

Equivalent Impedance  Impedance in series  Impedance in parallel

Equivalent Impedance  Impedance in series  Impedance in parallel

Example – 1

Example – 1

Example – 1

Example – 1

Example – 1

Poles and Zeros (1/2) Zero impedance implies that a current can exist with no external forcing voltage

Poles and Zeros (1/2) Zero impedance implies that a current can exist with no external forcing voltage

Poles and Zeros (1/2) Zero impedance implies that a current can exist with no external forcing voltage

Poles and Zeros (1/2) Zero impedance implies that a current can exist with no external forcing voltage

Poles and Zeros (1/2) - + + -

Poles and Zeros (1/2) - + + -

Poles and Zeros (1/2) - + + -

Poles and Zeros (1/2) - + + -

Poles and Zeros (2/2)

Poles and Zeros Example:

Poles and Zeros Example:

Natural response using impedance Write the impedance or admittance function for the terminals of interest Determine the poles and zeros For the terminals short-circuited, the natural behavior current is For the terminals open-circuited, the natural behavior voltage is Evaluate the coefficients from the initial conditions

Natural response using impedance Write the impedance or admittance function for the terminals of interest Determine the poles and zeros For the terminals short-circuited, the natural behavior current is For the terminals open-circuited, the natural behavior voltage is Evaluate the coefficients from the initial conditions

Example – 1 Switch is open at t=0. Find the open-circuit voltage across terminals ab

Example – 1 Switch is open at t=0. Find the open-circuit voltage across terminals ab

Example – 1 Switch is open at t=0. Find the open-circuit voltage across terminals ab

Example – 1 Switch is open at t=0. Find the open-circuit voltage across terminals ab

Example – 1 Switch is open at t=0. Find the open-circuit voltage across terminals ab

Example – 2 If terminals ab is short-circuited, find the current

Example – 2 If terminals ab is short-circuited, find the current

Example – 2 If terminals ab is short-circuited, find the current

Example – 2 If terminals ab is short-circuited, find the current

Forced response using Impedance

Forced response using Impedance

Forced response using Impedance

Forced response using Impedance

Forced response using Impedance

Forced response using Impedance

General solution method Transform time functions to phasor and convert element values to impedance/admittance Combine impedance/admittance to simplify circuit Determine the desired response in phasor form Draw phasor diagram to check calculation and display result Transform phase result to time function

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General solution method Transform time functions to phasor and convert element values to impedance/admittance Combine impedance/admittance to simplify circuit Determine the desired response in phasor form Draw phasor diagram to check calculation and display result Transform phase result to time function

Admittance

Admittance

Admittance

Admittance

Admittance

Admittance

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Dual circuit Duals ? When the set of transforms that converts one system into another also converts the second into the first, the systems are said to be duals.

Dual circuit Duals ? When the set of transforms that converts one system into another also converts the second into the first, the systems are said to be duals.

Dual circuit Duals ? When the set of transforms that converts one system into another also converts the second into the first, the systems are said to be duals.

Example

Example