0:00:00.000,0:00:03.300 >> This is Dr. Cynthia Furse[br]of the University of Utah. 0:00:03.300,0:00:05.865 Today, I'd like to talk about inductors. 0:00:05.865,0:00:08.400 We're going to talk about[br]what is inductance and how 0:00:08.400,0:00:10.540 does it relate to[br]the magnetic field and current? 0:00:10.540,0:00:13.280 We'll explain the effect of[br]different inductor parameters, 0:00:13.280,0:00:16.364 and finally what it does to a voltage[br]and current in the circuit. 0:00:16.364,0:00:20.235 An inductor is a passive element that[br]stores energy in the magnetic field. 0:00:20.235,0:00:23.430 Passive means that whether or not[br]it's connected to a voltage source, 0:00:23.430,0:00:24.690 it's still an inductor. 0:00:24.690,0:00:26.820 An inductor is basically a coil of wire. 0:00:26.820,0:00:29.040 You can just take a wire 0:00:29.040,0:00:31.410 and wrap it around your pencil[br]and you have an inductor. 0:00:31.410,0:00:33.630 When you drive current[br]through it as shown here, 0:00:33.630,0:00:36.750 you have the effect of the inductance. 0:00:36.750,0:00:39.900 The inductance is given in[br]Henries and its N squared. 0:00:39.900,0:00:41.190 That's the number of turns, 0:00:41.190,0:00:45.740 the number of coil squared times[br]the magnetic permeability times the area, 0:00:45.740,0:00:47.675 that's the surface area of this core, 0:00:47.675,0:00:49.145 divided by the total length. 0:00:49.145,0:00:50.705 Again, it is given in Henries. 0:00:50.705,0:00:54.935 The magnetic permeability is a property[br]of the material of the core. 0:00:54.935,0:00:58.100 It's given by the magnetic permeability 0:00:58.100,0:01:00.845 constant times the relative permeability. 0:01:00.845,0:01:02.900 For air mu.R is one. 0:01:02.900,0:01:06.620 The core is generally made out[br]of ferrite or magnetic material, 0:01:06.620,0:01:09.080 and that's because it increases[br]the total inductance. 0:01:09.080,0:01:12.845 So ferrite is typically the material[br]that's used in this core. 0:01:12.845,0:01:16.380 This is how you can tell which direction[br]the magnetic field goes. 0:01:16.380,0:01:18.890 Take your fingers and wrap them[br]in the direction of current, 0:01:18.890,0:01:20.870 the fingers of your right[br]hand and your thumb 0:01:20.870,0:01:23.240 will show you which direction[br]the magnetic field goes. 0:01:23.240,0:01:25.550 In this case, wrap your fingers[br]in the direction of 0:01:25.550,0:01:28.700 the core and you'll see that[br]the magnetic field comes out of the top, 0:01:28.700,0:01:31.250 and because magnetic field lines[br]are always closed lines, 0:01:31.250,0:01:32.795 it comes back in the bottom. 0:01:32.795,0:01:38.410 The magnetic field for this solenoid[br]inductor, is basically doughnut-shaped. 0:01:38.410,0:01:41.990 Here's an example of a wire wound inductor. 0:01:41.990,0:01:44.495 The core is a non magnetic ceramic. 0:01:44.495,0:01:46.040 So it's more or less like air, 0:01:46.040,0:01:49.940 except the ceramic holds it[br]together and also dissipates heat. 0:01:49.940,0:01:53.210 A very thin wire, thin like is[br]about as thick as your hair, 0:01:53.210,0:01:55.100 is wrapped around the ceramic[br]and then attached on 0:01:55.100,0:01:58.810 either side to electrodes with[br]a resin coating over the top. 0:01:58.810,0:02:00.675 Here's a multi-layer inductor. 0:02:00.675,0:02:03.385 The electrodes or connections[br]are on either side, 0:02:03.385,0:02:05.195 and you can see that you can just print 0:02:05.195,0:02:07.850 a series of loops and you[br]connect them by vias. 0:02:07.850,0:02:10.445 Here's an example of[br]a via, here's another via. 0:02:10.445,0:02:13.370 A via is where you drill a hole[br]and fill it with solder, 0:02:13.370,0:02:17.555 and that basically connects two different[br]layers of your multilayer inductor. 0:02:17.555,0:02:21.440 Here's a thin-film inductor made[br]a very similar way where you have 0:02:21.440,0:02:27.420 several layers of coils to[br]make the total inductance. 0:02:27.420,0:02:31.295 Now, let's talk about[br]the electrical properties of the inductor. 0:02:31.295,0:02:34.760 Remember, it's a passive element that[br]stores energy in the magnetic field. 0:02:34.760,0:02:36.485 Again, here's a solenoid. 0:02:36.485,0:02:40.310 The voltage is given by the inductance[br]times the derivative of the current. 0:02:40.310,0:02:42.215 That means, that at DC when there is 0:02:42.215,0:02:44.990 no change in the inductance[br]that the voltage will be zero. 0:02:44.990,0:02:49.070 That effectively means that the inductor[br]looks like a short circuit at DC. 0:02:49.070,0:02:50.900 Here's the equation for the current. 0:02:50.900,0:02:54.215 It's the integral of the voltage[br]divided by the inductance. 0:02:54.215,0:02:57.330 Here's the equation for the energy. 0:02:57.940,0:03:00.785 This is what happens to the inductor. 0:03:00.785,0:03:03.470 The current basically[br]starts out at zero and 0:03:03.470,0:03:06.815 gradually rises to[br]its full total value for current. 0:03:06.815,0:03:08.240 The total value for current, 0:03:08.240,0:03:11.495 remember that the inductor would[br]be a short circuit in that case, 0:03:11.495,0:03:16.605 would simply be V over[br]R in its final state. 0:03:16.605,0:03:18.770 The voltage on the other hand,[br]does change quickly. 0:03:18.770,0:03:21.410 It goes from zero to all[br]of a sudden going up 0:03:21.410,0:03:24.320 to a maximum value and[br]then dropping on down. 0:03:24.320,0:03:28.325 The maximum value of this voltage[br]is the source voltage. 0:03:28.325,0:03:30.620 So we can see the time t equals zero, 0:03:30.620,0:03:34.050 the current is zero, and the voltage[br]across the resistor is zero. 0:03:34.050,0:03:37.060 But the voltage across the inductor[br]is the source voltage. 0:03:37.060,0:03:39.695 At time equal infinity or[br]late time steady state, 0:03:39.695,0:03:42.470 the current is Vb over R[br]as if the inductor were 0:03:42.470,0:03:46.699 a short circuit and the voltage[br]across the resistor goes to Vb, 0:03:46.699,0:03:49.460 where as the voltage across[br]the inductor would be zero. 0:03:49.460,0:03:51.590 This is all controlled by a time constant. 0:03:51.590,0:03:53.419 The time constant for this circuit, 0:03:53.419,0:03:56.180 is L over R. Time constant tells us how 0:03:56.180,0:04:00.540 quickly the voltage drops[br]or the current rises. 0:04:00.650,0:04:02.720 So the way this works, 0:04:02.720,0:04:04.490 is current begins to flow in the inductor 0:04:04.490,0:04:07.045 and it starts to create a magnetic field. 0:04:07.045,0:04:08.790 At time t equals zero, 0:04:08.790,0:04:09.960 this acts like an open circuit. 0:04:09.960,0:04:12.035 The voltage is high and the current is low. 0:04:12.035,0:04:15.035 But very quickly as soon as[br]the magnetic field is established, 0:04:15.035,0:04:16.370 the current flows freely. 0:04:16.370,0:04:17.750 So at time t equal infinity, 0:04:17.750,0:04:21.730 it acts like a short circuit where the[br]voltage is low and the current is high. 0:04:21.730,0:04:24.750 So what does the inductor do in a circuit? 0:04:24.750,0:04:28.505 Here basically is the equation for[br]the voltage considering the time constant. 0:04:28.505,0:04:32.150 This is a picture of the current[br]for this particular example, 0:04:32.150,0:04:35.740 where we have a 1K resistor[br]and a one millihenry inductor. 0:04:35.740,0:04:42.460 The current rises reaching[br]66 percent of its value at time tau. 0:04:42.950,0:04:45.315 This is what happens to the voltage, 0:04:45.315,0:04:46.370 it starts at zero, 0:04:46.370,0:04:48.290 it jumps up to the source voltage, 0:04:48.290,0:04:52.475 and at tau it's 36 percent[br]of its original value. 0:04:52.475,0:04:57.330 So this is what the inductor does to[br]the voltage and current in the circuit. 0:04:57.740,0:05:02.150 This is what it would look like if you[br]hit an inductor with a square wave. 0:05:02.150,0:05:04.715 The voltage would rise and fall, 0:05:04.715,0:05:06.350 and then when the square wave drop, 0:05:06.350,0:05:08.760 it would fall and rise. 0:05:09.250,0:05:13.400 This is basically acting[br]like a device that gives you 0:05:13.400,0:05:17.645 the derivative of the voltage that[br]was initially put on the inductor. 0:05:17.645,0:05:20.015 Inductors in series and parallel. 0:05:20.015,0:05:23.720 Inductors that are in series add just[br]like they did if they were resistors, 0:05:23.720,0:05:26.570 and inductors in parallel add[br]as if they were resistors. 0:05:26.570,0:05:28.640 So here's how we can use inductors. 0:05:28.640,0:05:31.385 There are many applications for inductors. 0:05:31.385,0:05:34.100 Inductive coupling is[br]a very cool thing where you 0:05:34.100,0:05:36.995 use the current to[br]produce a magnetic field, 0:05:36.995,0:05:40.910 the magnetic field moves to another coil[br]right here where it is picked up, 0:05:40.910,0:05:43.960 and a current comes out of this coil. 0:05:43.960,0:05:47.870 Here's an example of inductive coupling[br]on the University of Utah campus. 0:05:47.870,0:05:50.270 Wave has created an electric powered bus. 0:05:50.270,0:05:53.030 Underneath, there's a coil[br]of wire in the bottom of 0:05:53.030,0:05:56.480 the Wave bus and then in the concrete[br]underneath is another coil. 0:05:56.480,0:05:59.570 The current is induced in[br]the coil on the concrete, 0:05:59.570,0:06:01.130 which is picked up in[br]the coil of the bus in 0:06:01.130,0:06:03.715 order to charge its batteries at a stop. 0:06:03.715,0:06:06.370 Blackrock Microsystems has created 0:06:06.370,0:06:09.790 an inductively coupled brain stimulator 0:06:09.790,0:06:11.920 where you have a 100 electrodes[br]shown right here, 0:06:11.920,0:06:13.630 very small needle electrodes, 0:06:13.630,0:06:16.930 and this coil right here with[br]a lot of different turns, 0:06:16.930,0:06:20.620 is used to couple to power[br]outside through the skin. 0:06:20.620,0:06:23.260 Here's a picture of a passive ID chip. 0:06:23.260,0:06:29.965 This is often used in theft detection[br]devices in commercial sales. 0:06:29.965,0:06:31.960 Here's a little circuit right there, 0:06:31.960,0:06:35.920 and here's the inductor that[br]is picking up the current, 0:06:35.920,0:06:40.750 that's picking up the magnetic field[br]from an externally generated source. 0:06:40.750,0:06:45.295 Here's a picture of the passive ID[br]that's normally used to tag animals, 0:06:45.295,0:06:47.435 and there's the coil inside. 0:06:47.435,0:06:50.145 Here's an application of a transformer. 0:06:50.145,0:06:52.100 On one side on the primary winding, 0:06:52.100,0:06:55.375 you'll have a number of windings N1, 0:06:55.375,0:06:57.560 and they will generate[br]a magnetic field which is 0:06:57.560,0:06:59.700 going to go through[br]this transformer core shown here. 0:06:59.700,0:07:02.270 This doughnut-shaped thing.[br]Then on the other side, 0:07:02.270,0:07:05.345 you can have a different number[br]of windings and two, 0:07:05.345,0:07:09.470 to pick up the magnetic flux[br]that's going through there. 0:07:09.470,0:07:11.570 What will happen, is you will change 0:07:11.570,0:07:12.860 the current on this side and you'll get 0:07:12.860,0:07:14.390 out actually less current on this side, 0:07:14.390,0:07:18.860 less voltage so that you're able to change[br]the voltage across the transformer. 0:07:18.860,0:07:22.025 Here are several places that you[br]might have seen transformers; 0:07:22.025,0:07:23.330 upon a power pole, 0:07:23.330,0:07:25.145 as a charger for your devices, 0:07:25.145,0:07:28.840 as a taser or on top of[br]an electric power system. 0:07:28.840,0:07:32.840 Inductors can be used as[br]both high and low pass filters. 0:07:32.840,0:07:34.910 Here's a picture of a low pass filter, 0:07:34.910,0:07:36.920 where the inductor is here[br]and we're reading the voltage 0:07:36.920,0:07:39.320 across the resistor. So what happens? 0:07:39.320,0:07:41.960 If a DC signal goes through, 0:07:41.960,0:07:45.190 the inductor acts like a short-circuit, 0:07:45.190,0:07:48.695 and so a large voltage is[br]read across the resistor. 0:07:48.695,0:07:50.660 But if a high frequency goes through, 0:07:50.660,0:07:52.205 the inductor acts like 0:07:52.205,0:07:55.720 an open circuit and so no voltage[br]makes it through to the resistor. 0:07:55.720,0:07:58.049 Here is the high pass configuration, 0:07:58.049,0:08:00.310 and that's just the opposite. 0:08:01.030,0:08:03.860 So I'm sure you're very curious[br]about where the picture 0:08:03.860,0:08:07.250 was from the introductory slide. 0:08:07.250,0:08:10.800 This is in White Canyon, in American Fork.