13 December 2002

Build the Optical Synthesizer

Craig Kendrick Sellen
Birch hills residence
25 reservoir Street
Simpson PA 18407-1300

With you at the controls of this oscilloscope add-on, an enormous variety of seemingly three-dimensional traces can be displayed.

Anyone with a new or old oscilloscope has observed a Lissajous figure, which is a line pattern that is generated by various harmonically related waveforms applied to an oscilloscope's X and Y inputs. This article describes an Optical Synthesizer that uses Lissajous principles to create seemingly three-dimensional figures of extraordinary beauty and intricacy. Front panel controls are provided that vary these figures and permit the user to create an enormous variety of effects.

 

Waveform Table. Click image to enlarge.

About the circuit

The secret lies in summing together one low-frequency and one high-frequency Lissajous figure. The low-frequency Lissajous figure comprises a fundamental frequency f and its harmonic mf,while the high-frequency figure is defined by frequency components nf and pf. Here m, n and p are integers, with n and p both much larger than m. Imagine that the low-frequency Lissajous figure is a large circle and that the high-frequency figure is a small square. When the two are summed, as the electron beam rapidly traces small squares, it also slowly describes a large circle, resulting in a "doughnut" shape with a square cross section. The low-frequency Lissajous pattern determines the overall shape, while the high-frequency figure defines the cross section.

Agreat variety of complex figures can be generated by changing the waveforms used and their phase relationships. Furthermore, if the high-frequency pattern is amplitude-modulated by a frequency qf, in which q is some small integer, the cross-sectional area can be made to vary through space. To sumthe two Lissajous patterns, the two X components and the two Y components must be summed independently. These two composite signals are then applied to the scope's X (horizontal) and Y (vertical) inputs, respectively.

How It Works

Figure 1. Schematic diagram. Click image to enlarge.

The schematic diagram of the Optical Synthesizer is shown in Fig. 1. The CD4011N forms a astable clock generator and associated components comprising of IC4A, IC4B, IC4C, R2,R3, R4. (R1 is not used). Capacitor C1 which is a Mylar or Polyester film type, do not use disc! IC4D is not used (N.C.). The output of the clock which drives IC1, a CD4024BE chip binary ripple divder. There are seven synchronized, harmonically related squarewaves that appear at IC1's output pins 3,4,5,6,9,11,and 12. Pin 12 has the highest frequency signal (3840Hz), and pin 3 has the lowest frequency signal (60 Hz). From pin 12 down to pin 3, signal frequencys are successively divided by two. This provides a set of even harmonics from which to construct the Lissajous patterns. Odd harmonics can also be used, although trying to obtain a more complete harmonic spectrum is more costly. Besides, there are sufficient harmonics to make an excellent Optical Synthesizer.

The squarewaves from IC1 must be shaped into waveforms that can be used to create Lissajous patterns. Six synthesized waveforms are shown at points A through F in fig. 1. Traingular waves, formed by integrating the squarewaves, are available at points B, D and E. At points A and C the triangular waves have been clipped, but fig. 2 shows that these waveforms are not only clipped but also phase-shifted. Finally there is a digitally synthesized staircase waveform at point F.

The low-frequency Lissajous patterns discussed earlier will have waveforms A, B, C and D as the X and Y components. For example, if waveform A is used as the X component and waveform B is used as the Y component, plotting the result on a piece of paper would show the Lissajous figure to be a parallelogram. Other combinations of A, B, C, and D yield more complex and unusual images.

Only one high-frequency Lissajous figure is used in the synthesizer. This figure is generated by amplitude-modulating the 3840-Hz squarewave (IC1 pin 12). This squarewave signal is fed via R24, R25 and R26 to input pin 2 of IC3, which is a LM13700N operational amplifier. The gain of IC3 is a function of the current passing through R30 into pin 1; this current is, in turn, a function of the voltage at output pin 6 of IC2, which is connected as a noninverting feedback amplifier. Operational amplifier IC2 is an LM308 chosen because of its lowsupply current drain. The modulating signals, routed to the input of IC2, consist of triangular waveform B, D and E; staircase waveform F; and fixed DC potential 1.

An amplitude-modulated squarewave appears at output pin 3 of IC3. When switch S4 selects the DC voltage from point 1, IC3's output will be a squarewave of constant amplitude, i.e., unmodulated. Resistors R28 and R29 cancel IC3's input offset voltage. Capacitor C11, connected across R31, lengthens the transition times of the modulated squarewave in order to improve the display. In addition to being part of IC3's load resistor R31 supplies bias current to emitter follower this is used to reduce the very high output impedance, and is a "Darlington configuration (compound amplifier)", which is also part of IC3. The load for the Darlington consists of R32, R33, R34 and C12. An amplitude modulated, slightly rounded squarewave is available at point G, and at point H there is an amplitude-modulated triangular waveform. If modulation is constant and if points G and H are connected to the X and Y inputs of an oscilloscope. a rectangle with two rounded corners appears.

Now all that remains is the summation of the low-frequency and high-frequency Lissajous patterns. The Y components of the two figures are mixed in R35, while the X components are summed in R36. Capacitors C13 and C14 block the DC supply so that only AC signals are mixed. Switch S2, the SHAPE selector, chooses various low-frequency waveform combinations, and switch S3 reverses the high-frequency signal connections. Output jacks J1 and J2 must feed high-impedance loads (1 megohm or greater) for proper mixing action, and although J1 connects to the vertical scope channel and J2 connects to the horizontal scope channel, the connections to the scope can be reversed. When the mixers are terminated with a high-impedance load, each output is the weighted average of the two input signals. All such input signals (waveforms A through G) have the same nominal 1.2-volt peak-to-peak magnitude. Therefore, the peak-to-peak output of each mixer remains a constant 1.2 volts as each potentiometer is rotated. This means that the area occupied by the display on the oscilloscope screen also remains constant, regardless of mixer settings.

Figure 3. Top foil pattern. Click image to enlarge

Two 9-volt transistor batteries power the circuit. Diodes D5 and D6 protect against incorrect battery installation and, at the same time, slightly reduce the supply voltage since fresh 9- volt batteries may actually supply 10 volts. The diodes insure that the maximum supply voltage limit of IC1 is never excceded, even with fresh batteries. Capacitors C15 and C16 provide a low-frequency supply bypass, and capacitors C17 and C18 provide high-frequency bypassing.

 

Figure 4. Foil pattern for bottom. Click image to enlarge.

Construction

It is relatively easy to build the Optical Synthesizer, but you must be careful because any errors will be visible on the display. The safest procedure is to use a printed circuit board. The foil pattern is shown in fig. 3 for the top side and fig. 4 for for the bottom side of the foil. And the component placement diagram is shown in fig. 5. If you don't use a printed circuit board, it is important that you follow the layout shown in fig. 5 as closely as possible.

A socket should be installled for IC1 and IC4 which since it is a CMOS units, should be installed only after all soldering is completed. Furthermore, be sure to use a CD4024BE for IC1; devices with an "AE" sulffx cannot supply enough output current install capacitor C10 as close as possible to IC2. Although most components mount on the PC board,capacitors C13 and C14 are wired point -to-point.

Pay attention to polarities for all IC's and diodes as well as electrolytic capacitors C15 and C16. In addition do not confuse IC2 with IC3; the former is an LM308, and the other is a LM13700. For best results use 5% tolerance resistors and 5% polystyrene capacitors where specified.

Figure 5. Component placement. Click image to enlarge.

The front panel layout is not critical. Switch S2 in the prototype was a pushbutten unit that happened to be around at the time of construction. You can just as well use a rotary switch that will probably be more readily available and less expensive. Output jacks J1 and J2 should match the oscilloscope connectors. Generally, these connectors will be either BNC or binding-post types.

Make a battery holder for BATT1 and BATT2 with a 16-gauge aluminum strap, bent to fit the battery dimensions. Use two fresh high quality batteries. If the battery voltages are unequal, triangular waveforms B, D and E will not be symmetrical with respect to ground, and some signal clipping will result. While this sort of clipping may produce some interesting visual effects, battery voltages should be as equal as possible when the initial adjustments are made on the synthesizer.

Note how switch S2 is wired. One position of the switch may send waveform signal A to the vertical mixer and waveform signal B to the horizontal mixer, but the next switch position will reverse these connections. Such a connection reversal results in an image reversal on the screen. This doubles the number of possible displays. By means of switch S3, the high-frequency mixer inputs can also be reversed. Interchanging the high-frequency components produces interesting and sometimes dramatic changes in the display, depending upon the settings of the mixers and of switch S2.

When wiring mixer potentiometers R35 and R36, connect them so that their actions are similar. Wire them so that when each wiper advances fully counterclockwise, it directly contacts a low-frequency input. Advancing both controls together in a clockwise direction then causes the simultaneous increase in high-frequency coutent of both outputs. Of course, the controls will usually be manipulated independently, but they are easier to correlate if the actions have a similar effect.

Calibration

After construction is complete, install IC4 and apply power. Connect a frequency counter to pin 1 of IC1, and adjust the clock trimmer which is a 50K potentiometer R4 so it reads 4830-Hz on the frequency counter. Next install IC1 and use your oscilloscope to verify the waveform signals A through F, which should all have a peak-to-peak amplitude of about 1.2 volts Now adjust S4 so that the 60-Hz triangle waveform B is applied to IC2. Attach a probe to IC2 output pin 6 and adjust trimmer R21 for the largest possible unclipped triangular waveform, which will have an amplitude of around 15 volts peak-to-peak.

Now leaving S4 where it is, ground IC3 pin 4 usinga short jumper lead. Attach your scope probe to IC3 output pin 5 and adjust trimmer R29 to eliminate the 60-Hz triangular waveform. You will probably be picking up some low-level, high-frequency signals at the same time. This pickup is unavoidable and should be ignored. After the 60-Hz triangular wave has been cancelled, disconnect the probe and remove the ground lead from IC3 pin 4. Reconnect the scope probe to point G in the circuit. Set S4 so that the DC potential at point I is applied to IC2. Adjust trimmer R25 so that the peak-to-peak voltage of the 3840-Hz squarewave at point G is 1.2 volts. Since the potential at point G is always more negative than ground, set the vertical amplifier for a DCinput signal. When a 1.2-volt peak-to-peak signal has been obtained at point G, check point H, where you should observe a triangular wave of the same magnitude. Now dial in the various modulating waveforms via S4 and verify that modulation occurs at points G and H. This compleres the calibration procedure and the synthesizer is ready for use.

Using the Synthesizer

The Optical Synthesizer is easy to use. First connect the outputs to the X and Y oscilloscope inputs. After the scope has warmed up, center the dot on the screen. If you wish remove the scope's graticule, as it can be distracting.

Set modulation selectorswitch S4 so that the IC2 input connects to point I. Turn both mixing potentiometers fully counterclockwise so that their wipers directly contact the low-frequency inputs A, BB, C or D. Now apply power to the synthesizer, and adjust the oscilloscope's X and Y input sensitivity controls so that the image just fills the scope's screen.

Use the focus and astigmatism controls on the scope to obtain a sharp display over the entire screen. Use all eight positions of shape-selector switch S2 to obtain the four low-frequency Lissajous patterns plus their four reversed counterparts.

Set S2 so that there is a parallelogram on the screen, and rotate the scope's intensity control to maximum. Advance both mixers, stoping when you have some degree of three-dimensionality in the display. Next, dial in the various modulating waveforms via switch S4 to notice the effects. You can now experiment with the rest of the controls to note their effect on the display.

The mixers are the most important controls on the synthesizer, and careful mixing will yield many fascinatingdisplays. The visual effects include a change in the size relationships between various parts of an image plus apperent rotations about two axes. As a display rotates, certain lines may coincide, causing the display to take on a whole new character.

As more of the high-frequency signal is mixed with the low-frequency signal, various sections of an image overlap. Consequently, the distinction between the overall shape of the image and the shape of the cross section is lost as a new pattern emerges.

When you have become familiar with the mixing procedure, you can create dynamic displays that twirl and change shape on the screen as the two mixers are slowly rotated. Experiment with the controls until you become familiar with their effects.

PARTS LIST for the OPTICAL SYNTHESIZER

ALL RESISTORS ARE 1/4 WATT @ 5% TOLERANCE UNLESS OTHERWISE NOTED
R1-not used
R2, R28-1 meg.
R3, R6, R7, R9, R10-68.000 ohms
R4-50.000 ohms trimmer potentiometer
R5, R8-36.000 ohms
R11-51.000
R12, R24-91.000 ohms
R13-180.000 ohms
R14-390.000 ohms
R15-820.000 ohms
R16-1.5meg.
R17-3.3meg.
R18-3300 ohms
R19-30.000 ohms
R20-470.000 ohms
R21-5000 ohms trimmer potentiometer
R22-6800 ohms
R23-100.000 ohms
R25-2000 ohms trimmer potentiometer
R26-220 ohms
R27-470 ohms
R29-200.000 ohms trimmer potentiometer
R30-150.000 ohms
R31, R34-39.000 ohms
R32-27.000 ohms
R33-5600 ohms
R35, R36-250.000 linear taper potentiometer front panel mount
R37-15.000 ohms

ALL CAPACITORS ARE 5% UNLESS OTHERWISE NOTED
C1-0.001 uF polystyrene
C2, C3, C17, C18-0.1 uF disc
C4, C5-1.0 uF paper or mylar
C6, C7-0.47 uF paper or mylar
C8, C13, C14-0.33 uF paper or mylar
C9-0.005 uF paper or mylar or use a 0.0047uF and a 300pF mica in paralel
C10-5 pF polystyrene
C11-100 pF polystyrene
C12-0.01 uF polystyrene
C15, C16-220 uF 16 volt electrolytic

D1-D6-1N914 or 1N4148 small signal diodes
IC1-CD4024BE -7 stage ripple divider counter
IC2-LM308 op-amp percision
IC3-LM13700 dual op-amp transconductance
IC4-CD4011N quad NAND gate
J1, J2- BNC or binding-post output jacks
S1-DPST toggle switch
S2-DPDT toggle switch
S3-SP5Pos. rot. switch or pushbutton
S4-DP8pos. rot. switch or pushbutton
BAT-1 and BAT-2- 9volt transistor batterys