ECEN 1400 - Introduction to Digital and Analog Electronics
Peter Mathys, Spring 2013

Lab 5: Inductors and How to Light White LEDs from 1 Volt
Quick Links * Goals of this Lab * Prelab * Lab Experiments

Goals of this Lab * Wind a toroidal inductor. * Measure the inductance and the resistance of an inductor. * Use an inductor to step up the voltage of a battery. * Build a circuit for lighting up white LEDs from a 1 Volt battery.

This lab is a group activity. The current group assignments are given here. One lab report per group needs to be turned in on D2L. The responsibilites for the successful completion of the lab consist of three parts: The prelab, the actual lab measurements, and the writing of the report. The report will be graded according to three criteria: Correctness, completion, and clarity. On the cover page you must clearly state which group member had the main responsibility for the prelab, for the lab measurements, and for the report writing. All group members need to be knowledgeable for all three parts, but each member has a specific role in the group. The responsibilities must be rotated for future labs so that each group member will have experienced all three roles.
Prelab
An inductor is a passive device that can store energy in its magnetic field. Two examples of inductors (solenoid on the left, toroid on the right) are shown in the figure below.

The i-v relationship for an inductor is:

Compare this to the i-v relationship for a capacitor:

We say that inductors and capacitors are duals of each other since the roles of voltage and current are exchanged between them.
Inductance L is measured in henry (H). Typically, L of an inductor made from a wire-wound coil is proportional to number of turns N squared. For a solenoidal inductor wound (in a single layer) on a core with permeability u, L can be computed as:

(Ideal) inductors do not dissipate power, but they can store energy by absorbing power and then release it again by delivering power. The formulas for instantaneous inductor power pL(t) and stored energy wL(t) are:

When inductors are used with sinusoidal signals, they act like frequency dependent resistors, similar to what we have already observed for capacitors. It is instructive to use phasors and impedances to compare the behavior of inductors and capacitors for sinusoidal waveforms. We start out by defining a sinusoidal current i(t) and its complex phasor representation I. Then we will use the same current for a capacitor and an inductor and observe the resulting phasor voltages VC and VL.

Integrating this current results in the capacitor voltage vC(t) (lagging behind the capacitor current by 90o) and voltage phasor VC as shown below. Defining the impedance of a capacitor by the complex number ZC = 1/(j*w*C), a relationship between the capacitor voltage and current phasors similar to Ohm's is established for sinusoidal waveforms.

To obtain the inductor voltage vL(t) (leading the inductor current by 90o) and voltage phasor VL, the derivative of the current i(t) is taken as shown below. The impedance of the inductor, which relates the inductor voltage and current phasors for sinusoidal signals, is obtained as ZL = j*w*L.

Combining resistors, capacitors, and inductors results in interesting circuits that exhibit resonant behavior, similar to the behavior of strings in musical instruments. Resonant circuits are widely used as filters in radio transmitters and receivers and in other signal processing applications. The figure below shows a series combination of R, L, and C. Note that in practice all inductors have some amount of resistance. Thus, R in the figure can either be thought of as a separate element or as being part of a (real) inductor.

The interesting result for the equivalent impedance Zeq is that it is just equal to R at the resonant frequency w0 = 1/sqrt(L*C). Thus, if w0 and C are known, then an unknown inductor can be characterized in terms of L and R (resistance of inductor) at frequency w0. Note that for practical inductors L and R are generally frequency dependent. The inductor resistance R includes the wire resistance and losses in the core around which the inductor is wound.
P1. Wind a Toroidal Inductor. Use about 9" of #24 magnet wire to wind 11 (eleven) turns on a Amidon FT-37-77 toroidal core as shown in the picture below (click to enlarge).

When you wind the inductor, place one turn next to the previous turn (don't wind turns on top of each other). Avoid scraping the enamel from the magnet wire when you pull it through the toroid. The number of teruns is determined the the number of times the wire passes through the inside of the toroid. When the inductor is complete, the windings should approximately evenly cover 2/3 to 3/4 of the circumference of the toroid. Trim the wire ends to about 1" from the toroid. To be able to use the inductor, the enamel of the magnet wire has to be completely removed from the ends, e.g., by scraping it off with a knife or by sanding it off with sandpaper. A good test to see if all the enamel has been removed is to tin the the ends with solder, using a soldering iron.
P2. How to Measure an Inductor. Use the following setup in Mutlisim for measuring R (R2 in the schematic) and L (L1 in the schematic) of an unknown inductor.

Assume that the values of R1 (the 50 ohm series resistance of a real waveform generator) and C1 are known. To determine the resistance R2 and the inductance L1 of the inductor, proceed as follows. * Set the waveform generator to generate a sinewave with a frequency of about 48 kHz and an amplitude of about 1 Vpp. * Increase the frequency until the amplitude of the sinusoid at the top of capacitor C1 is minimum. Write down the (resonant) frequency f0 at which this happens and write down the amplitude (in volts peak-to-peak) of the sinusoid at the top of capacitor C1. * Use the formulas shown below to compute L1, R2, and the quality factor Q. Hint: Use voltage division to determine the value of R2.

P3. Step Up Converter Using an Inductor. Build the circuit shown below in Multisim.

The intended operation of the circuit is that transistor Q1 is driven by a rectangular waveform so that it turns on and off periodically with a duty cycle of approximately 50%. When Q1 is on (closed switch between emitter and collector) then the current through inductor L1 increases linearly up to some maximum value, thereby storing energy wL(t) = (L/2)*[iL(t)]2 in its magnetic field. When Q1 turns off (open switch between emitter and collector) then the resulting decrease in current results in a reversal of the voltage across the inductor (making the right side more positive than the left side) through vL(t) = L*diL(t)/dt. Now current can flow through diode D2 to charge capacitor C1. The voltage produced by the inductor is proportional to the inductance L and proportional to the speed with which Q1 turns off. Thus, the voltage produced across C1 can be made much larger than the input voltage from battery V1. Diode D1 and capacitor C2 are included in the circuit to control the voltage oscillations produced by the inductor once it has delivered (most of) the stored energy to C1.
The component values shown in the circuit above have been optimized for operation at a frequency of about 50 kHz. To simulate the circuit in Multisim at this frequency it is necessary to compute sufficiently many sample points along the time axis. To achieve this, click on "Simulate" on the menu bar in Multisim and then choose "Interactive Simulation Settings". Then change the maximum time step (TMAX) setting to 1e-007 s as ahown below.

Set the waveform generator to produce a rectangular waveform with 50% duty cycle and a frequency of 50 kHz. Set the amplitude to 1 Vpp and set the dc offset to 0.5 Vdc. The current probe that is connected to input 1 of the oscilloscope is set for a voltage to current ratio of 1V/mA as shown below.

The following figure shows the waveforms that you should see on the oscilloscope when the circuit operates correctly.

The oscilloscope screen below shows the current through inductor L1 (yellow trace) in response to the output from the waveform generator (blue trace). The waveform generator outputs a 50 kHz, 50% duty cycle rectangular waveform that switches between 0 V and 1 V. When the rectangular waveform is at 1 V (=> Q1 is on), then the inductor current increases linearly from 0 to about 90 mA (88.7 mA). When the rectangular waveform is 0 V (=> Q1 is off), then the inductor current decreases rapidly (within about 1 us) to 0 and then oscillates around 0 until the rectangular input goes high again.

The next screen shows the inductor current (yellow trace) and the voltage (purple trace) on the right side of the inductor (where it connects to Q1 and D2). During the time when the inductor current decreases, the voltage peaks at around 14.6V and then oscillates with about 2 Vpp. The voltage is approximately zero when Q1 is on (rectangular input high).

Finally, looking at the voltage on the right side of the inductor (purple trace) and the voltage across capacitor C1 (green trace), we see how C1 gets charged to an average voltage of 13.5V from the peaks of the voltage at the inductor (max 14.6V). Note that part of the voltage difference comes from the forward voltage drop across D2 (approx 0.7V) and part comes from averaging.

Use the graphs that you obtain from the Multisim simulation to determine (i) the approximate amount of energy stored in inductor L1 and (ii) the approximate efficiency of the step up converter. For (ii) you will have to compute the average output power and the average input power and then take the ratio.

Lab Experiments
E1. The Solar-Powered Tone Generator (E3 from Lab 4). Add the 2-stage amplifier to the output of the multivibrator as shown in the circuit below. Use the resistor and capacitor values for a frequency of approximately 2 kHz that you found in P2 and E2 of lab 4. Check the datasheet for the 2N2222 Transistor and the 2N2907 Transistor to identify the Emitter, Base, and Collector pins on the TO-92 package of the transistors you have in your lab kit.

Replace the 100 ohm resistor at the collector of Q4 by a speaker. Check that the circuit works with the power supply. Look at the signal across the speaker with the oscilloscope. What is the frequency of this signal? What is the smallest power supply voltage for which the circuit produces an audible tone? Connect the solar cell instead of the power supply. Go outside or use an incandescent light source (fluorescent lamps don't work well because the wavelength of the light they generate is too short) to power the circuit and verify that it produces a sound. Note:You will use the same circuit with some minor modifications in experiment E4, so you may want to keep it on your breadboard.
E2. Measure your Inductor. Use the following setup to measure the inductance of the toroidal inductor you wound in P1.

Use the same procedure to determine R, L, and Q of the inductor as you did in prelab problem P2. Note: When you use voltage division to determine R, you need to know the amplitude of the sinewave that the waveform generator generates internally (before the 50 ohm resistor). An easy way to do this is to measure the output of the waveform generator with the oscilloscope when no other load is connected to the output.
E3. Step Up Converter. Build the circuit from P3, repeated below for convenience, on your breadboard.

Use the inductor that you wound in P1 for L1. Set the waveform generator to the values given in P2 (50 kHz, rectangular, 1Vpp amplitude, 0.5V dc offset). Then use the oscilloscope to display and measure the voltage on the right side of the inductor, and the voltage across C1. Discuss the similarities and differences between the Multisim simulation and the real circuit implementation. Note tha measuring the current through L1 is not very easy in the lab (you could use a 1 ohm resistor in series with L1, but then you would need two probes to measure the voltage on both sides of the resistor.
E4. White LEDs Powered by 1 Volt. Build the following mutlivibrator driven step up circuit for white (or blue) LEDs on your breadboard.

The goal of the circuit is to produce a high enough voltage from a 1...1.5 V battery to light up three white (or blue) LEDs connected in series. Note that this circuit is a combination of the circuits that you built in E1 and E3, with only minor modifications. The capacitors in the multivibrator were changed from 10 nF to 100 pF to increase the frequency. The speaker in E1 has been replaced by inductor L1 and the base of Q4 is driven with a higher current by selecting a 220 ohm resistor for R7. Finally, D2, C1, R2 in the step up circuit in E3 are replaced by 3 white (or blue) LEDs.
To check that the circuit works properly, use the oscilloscope as indicated in the schematic above to measure the waveform produced at the collector of Q3 and the waveform that drives the three LEDs. Look at both the amplitudes and the timing of these waveforms. What is the frequency that is generated by the multivibrator for this circuit? Why do you think a higher frequency was chosen here than for the tone generator in E1?

©2008, 2013, P. Mathys. Last revised: 02-15-13, PM.