LECTURE 8 RC AND RL FIRST-ORDER CIRCUITS (PART 1)

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1 CIRCUITS by Ulaby & Maharbiz LECTURE 8 RC AND RL FIRST-ORDER CIRCUITS (PART 1) 07/18/2013 ECE225 CIRCUIT ANALYSIS All rights reserved. Do not copy or distribute National Technology and Science Press Transient Response All rights reserved. Do not copy or distribute National Technology and Science Press 1

2 Non-Periodic Waveforms Step Function Ramp Function Square Pulse Exponential Non-Periodic Waveforms: Step Function 2

3 Non-Periodic Waveforms: Ramp Function Waveform synthesis as sum of two ramp functions All rights reserved. Do not copy or distribute National Technology and Science Press Non-Periodic Waveforms: Pulses 3

4 Waveform Synthesis 1. Pulse 2. Trapezoid All rights reserved. Do not copy or distribute National Technology and Science Press Non-Periodic Waveforms: Exponentials 4

5 Capacitors Passive element that stores energy in electric field 1 C t i dt t0 t o Parallel plate capacitor C A d For DC, capacitor looks like open circuit Voltage on capacitor must be continuous (no abrupt change) Various types of capacitors Energy Stored in Capacitor All rights reserved. Do not copy or distribute National Technology and Science Press 5

6 Tech Brief 11: Supercapacitors A new generation of capacitor technologies, termed supercapacitors or ultracapacitors, is narrowing the gap between capacitors and batteries. These capacitors can have sufficiently high energy densities to approach within 10 percent of battery storage densities, and additional improvements may increase this even more. Importantly, supercapacitors can absorb or release energy much faster than a chemical battery of identical volume. This helps immensely during recharging. Moreover, most batteries can be recharged only a few hundred times before they are degraded completely; supercapacitors can be charged and discharged millions of times before they wear out. Supercapacitors also have a much smaller environmental footprint than conventional chemical batteries, making them particularly attractive for green energy solutions. All rights reserved. Do not copy or distribute National Technology and Science Press Energy Storage Comparison Capacitor Response: Given v(t), determine i(t), p(t), and w(t) C = 6

7 RC Circuits at dc At dc no currents flow through capacitors: open circuits Capacitors in Series Use KVL, current same through each capacitor Capacitors in Parallel Use KCL, voltage same across each capacitor C C C C eq C N 7

8 Voltage Division Inductors Passive element that stores energy in magnetic field Solenoid Wound Inductor 1 i L t v t t At dc, inductor looks like a short circuit Current through inductor must be continuous (no abrupt change) o dt i t 0 2 N A L l Inductor Response to All rights reserved. Do not copy or distribute National Technology and Science Press 8

9 Inductors in Series Use KVL, current is same through all inductors Inductors in Parallel Voltage is same across all inductors Inductors add together in the same way resistors do All rights reserved. Do not copy or distribute National Technology and Science Press RL Circuits at dc At dc no voltage across inductors: short circuit 9

10 Summary 10

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