# Lecture 24. Inductance and Switching Power Supplies (how your solar charger voltage converter works)

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1 Lecture 24 Inductance and Switching Power Supplies (how your solar charger voltage converter works) Copyright 2014 by Mark Horowitz 1

2 Roadmap: How Does This Work? 2

3 Processor Board 3

4 More Detailed Roadmap For This Week In the last week of lectures we will introduce a new device, an inductor, and then use it and capacitors to take an energy source at one voltage, and convert it to produce energy at another voltage. While this might seem like a funny thing to do, you use a ton of these every day. They are the little wall warts that you use to charge your cell phone, your tablet, laptop, and are built into most of the lighting that we use today. These wall warts used to be big and clunky, but now they are much smaller, light weight, and, of course, cheaper. These lectures will explain what happened 4

5 Roadmap For Today What is an inductor Introduction to a simple step down voltage converter Use impedance to analyze this converter 5

6 Learning Objectives Understand what an inductor is V=L di/dt It is a device that tries to keep current constant Generates voltage (in either direction) to resist current changes Understand that ideal inductors and capacitor are lossless They store energy, and don t dissipate it Energy that goes into an LC circuit, must come out We can use this to convert energy from one voltage to another Size of the components is related to the energy they can store Be able to use impedance to Solve for the output voltage of a buck converter Determine the needed switching freq given L,C (or vice versa) 6

7 PREVIOUSLY IN E40M 7

8 ECG Measurement Need to measure the difference between L1 and L2 We think the circuit looks like 8

9 The Circuit Really Looks Like This: There are many unwanted signals coupling into our circuit Both capacitive (stray E fields) and inductive (B fields) These signals can be larger than what we want to measure! How to prevent them from obscuring our signal? 9

10 Balanced Amplifier This is a completely differential system Good for reducing noise coupling 10

11 Why Does the ECG Circuit Look Like This? 11

12 12

13 INDUCTORS 13

14 Inductors An inductor is a new type of two terminal device It is linear Double V, you will double I Like a capacitor it stores energy Ideal inductors don t dissipate energy But unlike a capacitor Its current determines the stored energy In a capacitor the capacitor voltage sets the energy stored Defining equation: If the input is a sinewave, Z = 2 f L 14

15 Energy Flow in Inductors Power flow into a device is always iv Power flow into an inductor is iv = i Ldi/dt Total energy that flows into the inductor Assumes current starts at 0A ends at i final The energy stored in the inductor is Li 2 /2 This energy is returned when the current ramps to zero. 15

16 What This Means The current flowing through an inductor sets its stored energy The only way to change this energy Is to pull power out of the device Is to push power into the device Power is iv So a rapid change in current (a.k.a energy) Requires large power, But i is set by the inductor So it will generate a very large voltage Inductors try to keep their current from changing rapidly And look like current sources for short time periods 16

17 Inductor Info, if You Know Physics E&M Models the energy stored in magnetic fields An inductor is just a wire. In the idea case the wire has zero resistance But current through a wire causes a magnetic field Changing magnetic flux induces a voltage Size of flux/i depends on the length of the wire Faraday s Law is what generates the voltage 17

18 Transformers The energy is stored in the magnetic field And the field is generated by the current If you have two coils of wire around the same magnetic material Both wires will see the same magnetic material You can transfer power between the two coils Drive one with a sinewave to create changing magnetic field The other coil will develop a voltage across it The voltage depends on the relative inductance 18

19 Ideal vs. Real Inductors Ideal inductors Have no loss Can store energy by letting the stored current circulate Real Inductors Are not that idea (unless they are superconducting) They have significant resistance from the wire Can by modeled by an ideal inductor in series with a resistor The resistance causes a voltage across the ideal inductor Since the voltage across the ideal inductor is negative The current decreases 19

20 BREAKING BREAK 20

21 Take Apart A GFI Outlet 21

22 BUCK CONVERTER FREQUENCY ANALYSIS 22

23 Problem: Convert 12V to 1V Your laptop / tablet adapter generates around 12V Its internal battery is probably around 8V But the processor requires a Vdd of around 1V And it can draw up to 30W in a laptop That is 30A at 1V So we need to convert the energy from battery/wall To 1V And we don t want to waste energy 23

24 Basic Buck Converter What happens if I drive a power inverter from a 12V supply? 12V How do we analyze this? Assume R = 0.1 1V) 24

25 Let s Use Impedance

26 Bode Plot Frequency 0 db 26

27 Some Reasonable Values L = 5 H; C=600 F If the input square wave was at 200kHz 2 = 5000, So the signal at 200kHz would be very small A couple of mv! So what is left? Average value of the input The DC component Set by the duty cycle! 27

28 BUCK CONVERTER ENERGY ANALYSIS 28

29 Setting The Output Voltage 29

30 Is This Energy Efficient? Ideal C, L don t dissipate power Can make the R of the transistors small So it doesn t seem to dissipate much energy 12V If it is energy efficient 12V supply ~ But this means = 12 Is this possible? 30

31 How Can This Work? Remember inductor current changes slowly 12V 31

32 32

33 Learning Objectives Understand what an inductor is V=L di/dt It is a device that tries to keep current constant Generates voltage (in either direction) to resist current changes Understand that ideal inductors and capacitor are lossless They store energy, and don t dissipate it Energy that goes into an LC circuit, must come out We can use this to convert energy from one voltage to another Size of the components is related to the energy they can store Be able to use impedance to Solve for the output voltage of a buck converter Determine the needed switching freq given L,C (or vice versa) 33

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### 12. The current in an inductor is changing at the rate of 100 A/s, and the inductor emf is 40 V. What is its self-inductance?

12. The current in an inductor is changing at the rate of 100 A/s, and the inductor emf is 40 V. What is its self-inductance? From Equation 32-5, L = -E=(dI =dt) = 40 V=(100 A/s) = 0.4 H. 15. A cardboard