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Inductors ECEN 1400 Introduction to Analog and Digital Electronics •Lecture 12: Inductors ECEN 1400 Introduction to Analog and Digital Electronics Inductors • Hydraulic analogy • Duality with capacitor • Charging and discharging Robert R. McLeod, University of Colorado http://hilaroad.com/camp/projects/magnet.html 99 •Lecture 12: Inductors ECEN 1400 Introduction to Analog and Digital Electronics The Inductor Packages http://www.electronicsandyou.com/electroni cs-basics/inductors.html Physics http://www.orble.com/userimages/user2207_1162388671.JPG Symbol Air core / generic Ferrite core Laminated iron core Robert R. McLeod, University of Colorado 100 •Lecture 12: Inductors ECEN 1400 Introduction to Analog and Digital Electronics Inductor hydraulics • The hydraulic analogy to an inductor is a frictionless waterwheel with mass. • Kinetic energy is stored in the wheel. • The finite mass makes the wheel resist changes in current. Wheel is initially Pump is turned on at t=0. stationary , that is, I(0)=0. …the wheel will be At a later time… turning with a finite current. If the pump belt was removed, current would continue to flow. Robert R. McLeod, University of Colorado https://ece.uwaterloo.ca/~dwharder/Analogy/Inductors/ 101 •Lecture 12: Inductors ECEN 1400 Introduction to Analog and Digital Electronics Inductor+resistor hydraulics “charging” phase Valve (switch) is open Wheel is initially stationary Pump is turned on at t=0. , that is, IINDUCTOR(0)=0. So all current initially goes through resistor according Pump is constant current to Ohm’s law. Valve (switch) is open At a later time… The wheel is turning, offering very little resistance. Thus a large current will go through the wheel. The same amount is still going through R (by Ohm’s law) but this is now a small fraction of the total current. Robert R. McLeod, University of Colorado https://ece.uwaterloo.ca/~dwharder/Analogy/Inductors/ 102 •Lecture 12: Inductors ECEN 1400 Introduction to Analog and Digital Electronics Inductor+resistor hydraulics “discharge” phase Valve (switch) is closed at t=0 Wheel is initially moving, that is, IINDUCTOR(0)>0. By conservation of current, this current must run through resistor, dissipating energy. Valve (switch) is closed At a later time… The kinetic energy in the wheel is gone and it is nearly stationary. Approximately no current is flowing. Robert R. McLeod, University of Colorado https://ece.uwaterloo.ca/~dwharder/Analogy/Inductors/ 103 •Lecture 12: Inductors ECEN 1400 Introduction to Analog and Digital Electronics RC circuit 0.2 ms 1 KHz Vsource V I C + VC - I • Energy is stored in the electric field of the capacitor. • Power is finite, so the energy does not change instantaneously. • The electric field is directly related to the voltage. • Thus capacitors resist changes in the voltage. • Capacitors act like open at DC, short at infinite frequency dV I C C RC 0.1 [ms] dt C Robert R. McLeod, University of Colorado 104 •Lecture 12: Inductors ECEN 1400 Introduction to Analog and Digital Electronics RL circuit 0.2 ms 1 KHz Vsource V I L + V L I - • Energy is stored in the magnetic field of the inductor. • Power is finite, so the energy does not change instantaneously. • The magnetic field is directly related to the current. • Thus inductors resist changes in the current. • Inductors act like short at DC, open at infinite frequency dI L V L GL 0.1 [ms] L dt L R Robert R. McLeod, University of Colorado 105 •Lecture 12: Inductors ECEN 1400 Introduction to Analog and Digital Electronics RL charge/discharge Discharge Charge • At t=0, the voltage source is • At t=0, a 12 V voltage source replaced by a short. replaces the short. • What is the current versus time? • What is the current versus time? Boundary conditions Boundary conditions I0 VSource R 1.2 A I0 0 I(t ) 0 I(t ) VSource R 1.2 A Time constant Time constant L GL 1 mH 10 0.1 ms L GL 1 mH 10 0.1 ms Discharging exponential function Charging exponential function t L t L It I0e It I0 1 e 1.2 1.2 1.0 1.0 0.8 0.8 0.6 0.6 [A] [A] I 0.4 I 0.4 0.2 0.2 0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5 t [mS] t [mS] Robert R. McLeod, University of Colorado 106 •Lecture 12: Inductors ECEN 1400 Introduction to Analog and Digital Electronics D2L 12.1 Q: A constant (“DC”) voltage is placed across an inductor on the left and a very high frequency time-varying (“AC”) voltage is placed across the inductor on the right. Large current will flow in which cases? A: No in the DC and no in the AC B: Yes in the DC and no in the AC C: No in the DC and yes in the AC D: Yes in the DC and yes in the AC E: It depends on the AC frequency. The inductor is a short at DC and an open at high frequency. Robert R. McLeod, University of Colorado 107 •Lecture 12: Inductors ECEN 1400 Introduction to Analog and Digital Electronics D2L 12.2 Q: At t=0, a switch is closed and the uncharged inductor L begins to charge. What is the current through the inductor at t=1 second? A: 0 L / R 1ms One second is 1000x the L/R time B: 1 m constant, so the inductor will be fully charged and operating like a short. C: 10 m The voltage across R is thus 10 V. D: 100 mA I = V / R = 10 mA E: I have no idea how to find this. Robert R. McLeod, University of Colorado 108 •Lecture 12: Inductors ECEN 1400 Introduction to Analog and Digital Electronics D2L 12.3 Q: A function generator is hooked to the series RL circuit above. The peak current through the inductor depends on A: The peak voltage of the source B: The frequency of the source C: The order of R and L in series D: A and B but not C • The system is linear, so the inductor current is E: A and C but not B proportional to the source voltage. • The current through the inductor will drop when the frequency is > 1/(L/R) • The order makes no difference Robert R. McLeod, University of Colorado 109 •Lecture 6: Capacitors ECEN 1400 Introduction to Analog and Digital Electronics D2L 12.4 Q: The current through an inductor of inductance L=2 H is I(t) = 1 + cos(500 t). The voltage on the inductor is: A: V(t)= -1000 sin(500 t) B: V(t)=2t + (1/250) sin(500 t) C: V(t)=1/2 + (1/2) cos(500 t) D: V(t)=2/(1 + cos(500 t)) E: V(t)=2 + 2 cos(500 t) dI V L 2 500sin500t 1000sin500t L dt Robert R. McLeod, University of Colorado 110 •Lecture 6: Capacitors ECEN 1400 Introduction to Analog and Digital Electronics D2L 12.5 Q: As the frequency of the function generator is increased from zero, the peak voltage across the inductor stays near zero, then begins to increase. The frequency where this begins to occur is about A: 5 mHz B: 200 Hz L / R 5ms C: 500 Hz 1 f 200 Hz D: 2 KHz T E: 200 MHz Robert R. McLeod, University of Colorado 111 •Lecture 6: Capacitors ECEN 1400 Introduction to Analog and Digital Electronics D2L 12.6 t L R It I0e t 1 I I e L R 4 0 0 L 1 t ln R 4 L 1 Q: A function generator is A : t ln hooked to the series RL R 4 circuit above. The function L 3 B : t ln generator is set to a square R 4 wave which alternates R 1 between V0 and 0V C : t ln (high/low) with a period >> L 4 RL. If a transition from V R 3 0 D : t ln to 0V occurs at t=0, when L 4 does the current through the 1 inductor drop to ¼ of its E : t e 4 value at t=0? Robert R. McLeod, University of Colorado 112.
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