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| The sawtooth-to-triangle converter consists of IC-5, IC-6, and IC-8.
IC-5 takes the zero to +5 ramp from IC-2, amplifies it by a factor of 4 and
level shifts it. The result is an inverted sawtooth from +10 to -10. IC-6
is an inverter which gives back the normal (rising) sawtooth from -10 to
+10. This is brought out as the sawtooth output, attenuated and impedance
adjusted by R28-R29 to a ramp from -5 to +5 with an output impedance of lk.
The diode arrangement of Dl and D2 selects the higher of the two waveforms
- the sawtooth or the inverted sawtooth. This is easily seen to be a triangle
from +10 to zero. IC-8 amplifies this by a factor of two and level shifts
for zero DC average. The output of IC-8 is thus a +10 to -10 triangle. The
output is obtained through R37 -R38 as a ±5 triangle. We have used a
"counterglitch" circuit here to remove (to a large degree) the switching
glitch caused by the diodes. This counterglitch is provided from the inverted
sawtooth through C6 and R26. Some minor adjustments of the value of C6 may
be desirable in some setups. R34 pulls down the diodes, resulting in a better
positive "point" on the triangle output, and C7 acts to further remove any
switching glitches.
Rectangular waveforms are provided using uncompensated 301 type op-amps (or 748 types can be used). The square is provided by IC-7, and a variable pulse is provided by IC-9, relative to a reference voltage level provided by IC-10. This is all very standard, but keep in mind that both IC-7 and IC-9 are left completely uncompensated so that they will go as fast as possible (no capacitor between pins 1 and 8), and the positive feedback provided by the 2.2M resistors relative to the 2.2k input provides mild hysteresis for additional "snap" and noise rejection. The outputs of IC-7 and IC-9 range from +15 to -15, so 3k-1.5k voltage dividers are used to scale these to ±5 volt levels. Finally, we use the FET type sinewave shaper as,driven by the triangle waveform. We chose this rather than the CA3080 shaper (used in later options) because it gives a slightly better looking waveform, and because we do have the ±10 volt triangle to drive it. It normally requires a 6 to 7 volt signal to reach the non-linear region. It is probably obvious that since we are using ±10 volt levels inside the circuit, it is easy to bring these out, For easy reference, the conversion is listed below:
At this point, we want to say something about the resistor R*, which is the resistor that provides high frequency compensation by Franco's method [See S. Franco, "Hardware Design of a Real-Time Musical System", Dept of Computer Science Report UIUCDCS-R-74-677, Univ. of Illinois, Urbana-Champaign]. The principle is basically as follows: There is a finite switching time which causes an oscillator to go flat on the high end. The higher frequencies correspond to higher charging currents. Thus, by inserting a resistor in series with the integrating capacitor, an additional voltage is impressed across the R-C combination, and this causes the oscillator to reach its peak voltage a little earlier. A full analysis (see reference above or chapter on VCO's in MEH) will show that this is an exact correction for a constant reset time, and that the R* x Cl product should be equal to the switching time, which we saw above was about 400 ns. This gives a value of R* of about 166 ohms. This is a good starting value. In addition, it turns out that the error due to the bulk base-emitter resistance of the exponential current stage transistors can be corrected by a term that is the same order as the delay time correction. Thus, by making R* larger than is necessary to correct for delay time, we can also do some correction for bulk resistance. Of course, all the analysis in the world is generally no substitute for an actual experiment, and we can easily find the value for R* by an experiment - basically as shown in Fig. 5.
The data from an actual experiment is shown in Fig. 7.
Here we have tabulated control voltage, approximate frequencies, and the ratio of frequencies that we actually observed for a one volt change of control voltage. Ideally, this should be 2.00 in all cases. By studying these figures, you can see that 680 ohms of Franco compensation pretty much solves the problem over the audio range. It is well not to use much more resistance than this as the method does result in some imperfections in the waveforms, and the oscillator may stall at low frequencies. Note however that the imperfections that result from the 680 ohm resistor are not too important as they only become appreciable at frequencies above 5 kHz or so, and the harmonic content in waveforms at such frequencies is of little importance because much of it is beyond the upper frequency limit of the ear. |
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It should not be too difficult to construct this circuit. A little care
should be used handling the MOS op-amps (CA3130 and CA3140), and of course
be careful with the expensive AD818 pair. All op-amps are powered between
+15 and -15 except for IC-2, the CA3130. Also, be sure to note the unusual
pin connections for the LM311 comparator, and be sure not to forget the pull-up
resistor R15. All the type 4859 FET's we have seen have the base diagram
shown in Fig. 8, as seen from the bottom view.
This includes the 2N4859, the KE4859, and the PN4859. Some may have three in-line wires at the very base, but will have the triangular diagram further out.
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