Musical keyboard as a signal generator
PARTS AND MATERIALS- Electronic "keyboard" (musical)
- "Mono" (not stereo) headphone-type plug
- Impedance matching transformer (1k Ω to 8 Ω ratio; Radio Shack catalog # 273-1380)
- 10 kΩ resistor
The "impedance matching transformer" is a small-size transformer easily obtained from an electronics supply store. One may be scavenged from a small, junk radio: it connects between the speaker and the circuit board (amplifier), so is easily identifiable by location. The primary winding is rated in ohms of impedance (1000 Ω), and is usually center-tapped. The secondary winding is 8 Ω and not center-tapped. These impedance figures are not the same as DC resistance, so don't expect to read 1000 Ω and 8 Ω with your ohmmeter -- however, the 1000 Ω winding will read more resistance than the 8 Ω winding, because it has more turns.
If such a transformer cannot be obtained for the experiment, a regular 120V/6V step-down power transformer works fairly well, too.
CROSS-REFERENCES
Lessons In Electric Circuits, Volume 2, chapter 1: "Basic AC Theory"
Lessons In Electric Circuits, Volume 2, chapter 7: "Mixed-Frequency AC Signals"
LEARNING OBJECTIVES
- Difference between amplitude and frequency
- Measuring AC voltage, current with a meter
- Transformer operation, step-up
SCHEMATIC DIAGRAM
ILLUSTRATION
INSTRUCTIONS
Normally, a student of electronics in a school would have access to a device called a signal generator, or function generator, used to make variable-frequency voltage waveforms to power AC circuits. An inexpensive electronic keyboard is a cheaper alternative to a regular signal generator, and provides features that most signal generators cannot match, such as producing mixed-frequency waves.
To "tap in" to the AC voltage produced by the keyboard, you'll need to insert a plug into the headphone jack (sometimes just labeled "phone" on the keyboard) complete with two wires for connection to circuits of your own design. When you insert the plug into the jack, the normal speaker built in to the keyboard will be disconnected (assuming the keyboard is equipped with one), and the signal that used to power that speaker will be available at the plug wires. In this particular experiment, I recommend using the keyboard to power the 8 Ω side of an audio "output" transformer to step up voltage to a higher level. If using a power transformer instead of an audio output transformer, connect the keyboard to the low-voltage winding so that it operates as a step-up device. Keyboards produce very low voltage signals, so there is no shock hazard in this experiment.
Using an inexpensive Yamaha keyboard, I have found that the "panflute" voice setting produces the truest sine-wave waveform. This waveform, or something close to it (flute, for example), is recommended to start experimenting with since it is relatively free of harmonics (many waveforms mixed together, of integer-multiple frequency). Being composed of just one frequency, it is a less complex waveform for your multimeter to measure. Make sure the keyboard is set to a mode where the note will be sustained as any key is held down -- otherwise, the amplitude (voltage) of the waveform will be constantly changing (high when the key is first pressed, then decaying rapidly to zero).
Using an AC voltmeter, read the voltage direct from the headphone plug. Then, read the voltage as stepped up by the transformer, noting the step ratio. If your multimeter has a "frequency" function, use it to measure the frequency of the waveform produced by the keyboard. Try different notes on the keyboard and record their frequencies. Do you notice a pattern in frequency as you activate different notes, especially keys that are similar to each other (notice the 12-key black-and-white pattern repeated on the keyboard from left to right)? If you don't mind making marks on your keyboard, write the frequencies in Hertz in black ink on the white keys, near the tops where fingers are less likely to rub the numbers off.
Ideally, there should be no change in signal amplitude (voltage) as different frequencies (notes on the keyboard) are tried. If you adjust the volume up and down, you should discover that changes in amplitude should have little or no impact on frequency measurement. Amplitude and frequency are two completely independent aspects of an AC signal.
Try connecting the keyboard output to a 10 kΩ load resistance (through the headphone plug), and measure AC current with your multimeter. If your multimeter has a frequency function, you can measure the frequency of this current as well. It should be the same as for the voltage for any given note (keyboard key).
PC Oscilloscope
PARTS AND MATERIALS- IBM-compatible personal computer with sound card, running Windows 3.1 or better
- Winscope software, downloaded free from internet
- Electronic "keyboard" (musical)
- "Mono" (not stereo) headphone-type plug for keyboard
- "Mono" (not stereo) headphone-type plug for computer sound card microphone input
- 10 kΩ potentiometer
CROSS-REFERENCES
Lessons In Electric Circuits, Volume 2, chapter 7: "Mixed-Frequency AC Signals"
Lessons In Electric Circuits, Volume 2, chapter 12: "AC Metering Circuits"
LEARNING OBJECTIVES
- Computer use
- Basic oscilloscope function
SCHEMATIC DIAGRAM
ILLUSTRATION
INSTRUCTIONS
The oscilloscope is an indispensable test instrument for the electronics student and professional. No serious electronics lab should be without one (or two!). Unfortunately, commercial oscilloscopes tend to be expensive, and it is almost impossible to design and build your own without another oscilloscope to troubleshoot it! However, the sound card of a personal computer is capable of "digitizing" low-voltage AC signals from a range of a few hundred Hertz to several thousand Hertz with respectable resolution, and free software is available for displaying these signals in oscilloscope form on the computer screen. Since most people either have a personal computer or can obtain one for less cost than an oscilloscope, this becomes a viable alternative for the experimenter on a budget.
One word of caution: you can cause significant hardware damage to your computer if signals of excessive voltage are connected to the sound card's microphone input! The AC voltages produced by a musical keyboard are too low to cause damage to your computer through the sound card, but other voltage sources might be hazardous to your computer's health. Use this "oscilloscope" at your own risk!
Using the keyboard and plug arrangement described in the previous experiment, connect the keyboard output to the outer terminals of a 10 kΩ potentiometer. Solder two wires to the connection points on the sound card microphone input plug, so that you have a set of "test leads" for the "oscilloscope." Connect these test leads to the potentiometer: between the middle terminal (the wiper) and either of the outer terminals.
Start the Winscope program and click on the "arrow" icon in the upper-left corner (it looks like the "play" arrow seen on tape player and CD player control buttons). If you press a key on the musical keyboard, you should see some kind of waveform displayed on the screen. Choose the "panflute" or some other flute-like voice on the musical keyboard for the best sine-wave shape. If the computer displays a waveform that looks kind of like a square wave, you need to adjust the potentiometer for a lower-amplitude signal. Almost any waveshape will be "clipped" to look like a square wave if it exceeds the amplitude limit of the sound card.
Test different instrument "voices" on the musical keyboard and note the different waveshapes. Note how complex some of the waveshapes are, compared to the panflute voice. Experiment with the different controls in the Winscope window, noting how they change the appearance of the waveform.
As a test instrument, this "oscilloscope" is quite poor. It has almost no capability to make precision measurements of voltage, although its frequency precision is surprisingly good. It is very limited in the ranges of voltage and frequency it can display, relegating it to the analysis of low- and mid-range audio tones. I have had very little success getting the "oscilloscope" to display good square waves, presumably because of its limited frequency response. Also, the coupling capacitor found in sound card microphone input circuits prevents it from measuring DC voltage: it is as though the "AC coupling" feature of a normal oscilloscope were stuck "on."
Despite these shortcomings, it is useful as a demonstration tool, and for initial explorations into waveform analysis for the beginning student of electronics. For those who are interested, there are several professional-quality oscilloscope adapter devices manufactured for personal computers whose performance is far beyond that of a sound card, and they are typically sold at less cost than a complete stand-alone oscilloscope (around $400, year 2002). Radio Shack sells one made by Velleman, catalog # 910-3914. Having a computer serve as the display medium brings many advantages, not the least of which is the ability to easily store waveform pictures as digital files.
Waveform analysis
PARTS AND MATERIALS- IBM-compatible personal computer with sound card, running Windows 3.1 or better
- Winscope software, downloaded free from internet
- Electronic "keyboard" (musical)
- "Mono" (not stereo) headphone-type plug for keyboard
- "Mono" (not stereo) headphone-type plug for computer sound card microphone input, with wires for connecting to voltage sources
- 10 kΩ potentiometer
CROSS-REFERENCES
Lessons In Electric Circuits, Volume 2, chapter 7: "Mixed-Frequency AC Signals"
LEARNING OBJECTIVES
- Understand the difference between time-domain and frequency-domain plots
- Develop a qualitative sense of Fourier analysis
SCHEMATIC DIAGRAM
ILLUSTRATION
INSTRUCTIONS
The Winscope program comes with another feature other than the typical "time-domain" oscilloscope display: "frequency-domain" display, which plots amplitude (vertical) over frequency (horizontal). An oscilloscope's "time-domain" display plots amplitude (vertical) over time (horizontal), which is fine for displaying waveshape. However, when it is desirable to see the harmonic constituency of a complex wave, a frequency-domain plot is the best tool.
If using Winscope, click on the "rainbow" icon to switch to frequency-domain mode. Generate a sine-wave signal using the musical keyboard (panflute or flute voice), and you should see a single "spike" on the display, corresponding to the amplitude of the single-frequency signal. Moving the mouse cursor beneath the peak should result in the frequency being displayed numerically at the bottom of the screen.
If two notes are activated on the musical keyboard, the plot should show two distinct peaks, each one corresponding to a particular note (frequency). Basic chords (three notes) produce three spikes on the frequency-domain plot, and so on. Contrast this with normal oscilloscope (time-domain) plot by clicking once again on the "rainbow" icon. A musical chord displayed in time-domain format is a very complex waveform, but is quite simple to resolve into constituent notes (frequencies) on a frequency-domain display.
Experiment with different instrument "voices" on the musical keyboard, correlating the time-domain plot with the frequency-domain plot. Waveforms that are symmetrical above and below their centerlines contain only odd-numbered harmonics (odd-integer multiples of the base, or fundamental frequency), while nonsymmetrical waveforms contain even-numbered harmonics as well. Use the cursor to locate the specific frequency of each peak on the plot, and a calculator to determine whether each peak is even- or odd-numbered.
Inductor-capacitor "tank" circuit
PARTS AND MATERIALS- Oscilloscope
- Assortment of non-polarized capacitors (0.1 µF to 10 µF)
- Step-down power transformer (120V / 6 V)
- 10 kΩ resistors
- Six-volt battery
CROSS-REFERENCES
Lessons In Electric Circuits, Volume 2, chapter 6: "Resonance"
LEARNING OBJECTIVES
- How to build a resonant circuit
- Effects of capacitor size on resonant frequency
- How to produce antiresonance
SCHEMATIC DIAGRAM
ILLUSTRATION
INSTRUCTIONS
If an inductor and a capacitor are connected in parallel with each other, and then briefly energized by connection to a DC voltage source, oscillations will ensue as energy is exchanged from the capacitor to inductor and vice versa. These oscillations may be viewed with an oscilloscope connected in parallel with the inductor/capacitor circuit. Parallel inductor/capacitor circuits are commonly known as tank circuits.
Important note: I recommend against using a PC/sound card as an oscilloscope for this experiment, because very high voltages can be generated by the inductor when the battery is disconnected (inductive "kickback"). These high voltages will surely damage the sound card's input, and perhaps other portions of the computer as well.
A tank circuit's natural frequency, called the resonant frequency, is determined by the size of the inductor and the size of the capacitor, according to the following equation:
Many small power transformers have primary (120 volt) winding inductances of approximately 1 H. Use this figure as a rough estimate of inductance for your circuit to calculate expected oscillation frequency.
Ideally, the oscillations produced by a tank circuit continue indefinitely. Realistically, oscillations will decay in amplitude over the course of several cycles due to the resistive and magnetic losses of the inductor. Inductors with a high "Q" rating will, of course, produce longer-lasting oscillations than low-Q inductors.
Try changing capacitor values and noting the effect on oscillation frequency. You might notice changes in the duration of oscillations as well, due to capacitor size. Since you know how to calculate resonant frequency from inductance and capacitance, can you figure out a way to calculate inductor inductance from known values of circuit capacitance (as measured by a capacitance meter) and resonant frequency (as measured by an oscilloscope)?
Resistance may be intentionally added to the circuit -- either in series or parallel -- for the express purpose of dampening oscillations. This effect of resistance dampening tank circuit oscillation is known as antiresonance. It is analogous to the action of a shock absorber in dampening the bouncing of a car after striking a bump in the road.
COMPUTER SIMULATION
Schematic with SPICE node numbers:
Rstray is placed in the circuit to dampen oscillations and produce a more realistic simulation. A lower Rstray value causes longer-lived oscillations because less energy is dissipated. Eliminating this resistor from the circuit results in endless oscillation.
Netlist (make a text file containing the following text, verbatim):
tank circuit with loss l1 1 0 1 ic=0 rstray 1 2 1000 c1 2 0 0.1u ic=6 .tran 0.1m 20m uic .plot tran v(1,0) .end
Signal coupling
PARTS AND MATERIALS- 6 volt battery
- One capacitor, 0.22 µF (Radio Shack catalog # 272-1070 or equivalent)
- One capacitor, 0.047 µF (Radio Shack catalog # 272-134 or equivalent)
- Small "hobby" motor, permanent-magnet type (Radio Shack catalog # 273-223 or equivalent)
- Audio detector with headphones
- Length of telephone cable, several feet long (Radio Shack catalog # 278-872)
CROSS-REFERENCES
Lessons In Electric Circuits, Volume 2, chapter 7: "Mixed-Frequency AC Signals"
Lessons In Electric Circuits, Volume 2, chapter 8: "Filters"
LEARNING OBJECTIVES
- How to "couple" AC signals and block DC signals to a measuring instrument
- How stray coupling happens in cables
- Techniques to minimize inter-cable coupling
SCHEMATIC DIAGRAM
ILLUSTRATION
INSTRUCTIONS
Connect the motor to the battery using two of the telephone cable's four conductors. The motor should run, as expected. Now, connect the audio signal detector across the motor terminals, with the 0.047 µF capacitor in series, like this:
You should be able to hear a "buzz" or "whine" in the headphones, representing the AC "noise" voltage produced by the motor as the brushes make and break contact with the rotating commutator bars. The purpose of the series capacitor is to act as a high-pass filter, so that the detector only receives the AC voltage across the motor's terminals, not any DC voltage. This is precisely how oscilloscopes provide an "AC coupling" feature for measuring the AC content of a signal without any DC bias voltage: a capacitor is connected in series with one test probe.
Ideally, one would expect nothing but pure DC voltage at the motor's terminals, because the motor is connected directly in parallel with the battery. Since the motor's terminals are electrically common with the respective terminals of the battery, and the battery's nature is to maintain a constant DC voltage, nothing but DC voltage should appear at the motor terminals, right? Well, because of resistance internal to the battery and along the conductor lengths, current pulses drawn by the motor produce oscillating voltage "dips" at the motor terminals, causing the AC "noise" heard by the detector:
Use the audio detector to measure "noise" voltage directly across the battery. Since the AC noise is produced in this circuit by pulsating voltage drops along stray resistances, the less resistance we measure across, the less noise voltage we should detect:
You may also measure noise voltage dropped along either of the telephone cable conductors supplying power to the motor, by connecting the audio detector between both ends of a single cable conductor. The noise detected here originates from current pulses through the resistance of the wire:
Now that we have established how AC noise is created and distributed in this circuit, let's explore how it is coupled to adjacent wires in the cable. Use the audio detector to measure voltage between one of the motor terminals and one of the unused wires in the telephone cable. The 0.047 µF capacitor is not needed in this exercise, because there is no DC voltage between these points for the detector to detect anyway:
The noise voltage detected here is due to stray capacitance between adjacent cable conductors creating an AC current "path" between the wires. Remember that no current actually goes through a capacitance, but the alternate charging and discharging action of a capacitance, whether it be intentional or unintentional, provides alternating current a pathway of sorts.
If we were to try and conduct a voltage signal between one of the unused wires and a point common with the motor, that signal would become tainted with noise voltage from the motor. This could be quite detrimental, depending on how much noise was coupled between the two circuits and how sensitive one circuit was to the other's noise. Since the primary coupling phenomenon in this circuit is capacitive in nature, higher-frequency noise voltages are more strongly coupled than lower-frequency noise voltages.
If the additional signal was a DC signal, with no AC expected in it, we could mitigate the problem of coupled noise by "decoupling" the AC noise with a relatively large capacitor connected across the DC signal's conductors. Use the 0.22 µF capacitor for this purpose, as shown:
The decoupling capacitor acts as a practical short-circuit to any AC noise voltage, while not affecting DC voltage signals between those two points at all. So long as the decoupling capacitor value is significantly larger than the stray "coupling" capacitance between the cable's conductors, the AC noise voltage will be held to a minimum.
Another way of minimizing coupled noise in a cable is to avoid having two circuits share a common conductor. To illustrate, connect the audio detector between the two unused wires and listen for a noise signal:
There should be far less noise detected between any two of the unused conductors than between one unused conductor and one used in the motor circuit. The reason for this drastic reduction in noise is that stray capacitance between cable conductors tends to couple the same noise voltage to both of the unused conductors in approximately equal proportions. Thus, when measuring voltage between those two conductors, the detector only "sees" the difference between two approximately identical noise signals.
END OF CHAPTER 4
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