AC Circuits

PHYS 3050 – Electronics I Chapter 2. AC Circuits

Earth, Moon, Mars, and Beyond

Dr. Jinjun Shan, Associate Professor of Space Engineering Department of Earth and Space Science and Engineering Room 255, Petrie Science and Engineering Building Tel: 416-736 2100 ext. 33854 Email: [email protected] Homepage: http://www.yorku.ca/jjshan

Introduction 

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For DC circuits, we can have steady voltages and currents. In this chapter, we will study the circuits with the steady-state analysis of AC circuits. The simplest and occur widely timevarying voltages and currents are sinusoidal. Special characteristic of sinusoids AC Circuits 2

Introduction

If a linear circuit is driven by a sinusoidal source, then all responses anywhere in the circuit are also sinusoidal. This applies only after all initial transients have died down and a steady-state is reached. This is referred to as steady-state AC analysis. AC Circuits 3

Sinusoidal Driving Functions

If the voltage or current source is sinusoidal, all voltages and currents anywhere in the linear circuit will also be sinusoidal.

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Sinusoidal Driving Functions

Out of phase

In phase

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Phasor Analysis

Phasor:

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Basis of Phasor Analysis

1) First, we recognize that we are dealing with a linear circuit. 2) The circuit equation is basically a linear differential equation (LDE) with constant coefficients. 3) Natural solutions to LDEs with constant coefficients are exponentials. All calculations will be in terms of complex numbers.

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Basis of Phasor Analysis

4) Let the real source be given by Vpcosωt=ReVp·exp(jωt) 5) The solution for the current I·exp(jωt), phasor I. 6) Convert phasor I to real-time current i(t) by simply multiplying I by exp(jωt) and take the real part, i.e. i(t) = ReI·exp(jωt). AC Circuits 8

Basis of Phasor Analysis

Example: Change the voltage source in RLC circuit to v(t) = Vpcos(ωt+ϕ), find current i(t) in the circuit.

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Impedance and Phasor Relationship

 For AC circuits, Ohm’s law becomes V=IZ, where Z is a complex number.  We can generalize and state that AC circuit analysis is DC analysis with complex numbers.  This is a powerful statement and means that all the circuit laws that were derived previously apply equally to AC circuits. AC Circuits 10

Impedance and Phasor Relationship

Example: Find voltage V2 in this figure when it is driven by V = cos2t.

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Admittance

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High-Pass and Low-Pass Filters 

RC Filters

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High-Pass and Low-Pass Filters 

High-Pass RC Filter

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High-Pass and Low-Pass Filters 

RL Filters

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High-Pass and Low-Pass Filters 

High-Pass RL Filter

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Resonance and Band-Pass Filters 

With RC and RL, we can have low-pass or high-pass filters. If we add both energy-storing elements to resistor, we can obtain band-pass or band-rejection action.

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Band-pass filters can be used as tuning circuits where they allow one station or more channel out of many to be selected. AC Circuits 17

Resonance and Band-Pass Filters 

Series Resonance

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Resonance and Band-Pass Filters 

Notch Filter

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Resonance and Band-Pass Filters 

Parallel Resonance

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Resonance and Band-Pass Filters 

Q-Factor and Bandwidth

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Power in AC and RF Circuits 

Reading: Section 2.5

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Transformers and Impedance Matching 

Reading: Section 2.6

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