0.1 VCO

Function :The voltage controlled oscillator (VCO) is the core of a synthesizer. It is the unit that

produces the raw sound that is modified by the rest of the modules, and it outputs waveformswith a frequency range of about 10 Hz to 20 kHz without significant distortion. It includesexponential control voltage inputs (since musical notes are perceived exponentially, whereevery note is twice the frequency of the same note an octave below it); linear AC controlvoltage inputs (for use with the LFO for frequency modulation, or vibrato); and adjustablesaw, triangle, square, and sine wave outputs.

Schematic :

Figure 1: VCO Full Schematic

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Theory of Operation :The voltage controlled oscillator is an exponential current source feeding into a current

controlled oscillator to produce a ramp wave. This then feeds into a triangle waveshaper,which is then fed into both the square and the sine waveshaper. This design was inspiredby several circuits, including the ASM VCO-1 by Gene Stopp and Thomas Henry’s VCO-1,both of which are heavily influenced by Electronotes designs. Pieces from all the designswere combined with other circuits to form a sort of “franken-circuit.” Different pieces arethrown together with some heavy modification, creating a stable and full-featured VCO withseveral output waveform choices.

Exponential Current Source :

Figure 2: Exponential Current Source Schematic

This is a differential pair current source. Since the collector current is exponentiallyrelated to the base-emitter voltage, and linearly related to the voltage at the collector, it hasboth exponential and linear controls. A differential pair reduces Is dependence.

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IC1 =15

RC

− vlinear

Rlin

IC = ISeVBEVT

⇒ VBE = ln(ICIS

)vin = VBE1 − VBE2

vin = VT ln

(IC1

IC2

)

IC1 = e−qvin

kT

⇒ IC2 =(

15

RC

− vlinear

Rlin

)e−vinVT

Therefore, there is a linear dependence on vlinear and an exponential dependence on vin,as was required. With no input voltage, IC2 = 15

RC= 15

150kΩ= 0.1mA.

Sawtooth oscillator :This is an integrator with a reset switch attached. The output of the integrator is fed

into a comparator. When this output goes above 5V , the comparator will pull its outputdown to -15V, which turns on the JFET. The capacitor then discharges through the Rds(on)of the JFET, which is 250Ω for this particular transistor, resetting the waveform. Thisdischarge must be maintained for long enough to drop the wave back to 0V . Thus, aftera time constant determined by the 47 pF capacitor and the 15kΩ resistor, the JFET turnsoff. This means that the output waveform is a slow ramp up (the integration of the steadycurrent), followed by a quick drop (the discharge through the JFET). This is a sawtoothwave. This is expressed mathematically below.

Vcapacitor =1

C4

∫Iindt

Since this goes up to 5V before resetting, and since Iin is a constant DC current,

5V =1

C4

Iin ∗ tperiod

tperiod =5V ∗ C4

Iin

frequency =Iin

5V ∗ 2.2nF

With no input voltage (CV is at ground), Iin = 0.1mA.

fo =0.1mA

5V ∗ 2.2nF= 9090Hz

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Figure 3: Sawtooth Oscillator

The time constant at the comparator is set to be about 14

of the reset time through theJFET.

treset = C4 ∗RDS = 2.2nF ∗ 250Ω = 0.55µs

tcomparator = R38 ∗ C5 = 47pF ∗ 3.3kΩ = 0.14µs

Triangle waveshaper :This piece is a simple absolute value circuit, or a full-wave rectifier. A rectified sawtooth

is a triangle wave with an offset. The resistor values have to be exact for a perfect glitch-freewaveform, so trimming pots were included. This waveform is then passed through a capacitorto remove the DC bias. This wave is then passed into a buffer to isolate the load-sensitiverectifier, then an inverting amplifier so that the amplitude can be easily controlled.

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Figure 4: Triangle Waveshaper

Figure 5: Triangle Waveshaper Method

As shown above, the rectifier circuit first inverts and rectifies part of the waveform,resulting in a positive wave where the original waveform was negative. The rectified input isscaled by two, then added to the original input by the second op-amp, which is a summingamplifier. The scaled rectified pieces add to the original negative pieces to result in anunscaled positive piece. Thus, the original waveform has been rectified completely, resultingin a triangle wave with an offset.

Square waveshaper :

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Figure 6: Square Waveshaper

The square waveshaper is extremely straightforward. It passes the output of the trianglewave buffer into a comparator. When the triangle wave is above zero, the square wave ishigh, and it is low when the triangle wave is negative. This wave is then passed into aninverting amplifier, so the amplitude can be easily controlled. Q1 and Q2 are a matchedpair.

Sine waveshaper :

Figure 7: Sine Waveshaper

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The idea for this circuit came from an IEEE paper regarding triangle to sine waveshap-ing. It reports an ideal total harmonic distortion of 0.2%, which is remarkably good. Thiswaveshaper does not really produce a pure sine wave. It uses a cheat, instead, to producea wave that approximates a sine wave remarkably well. A single input differential amplifierattempts to amplify an input triangle wave. However, at the extremes of the triangle, itdrops out of the forward active region into saturation. Thus, this amplifier has non-lineargain. Near zero, it follows the triangle wave (slope of 1) as a sine wave does. At higherlevels, it smooths out, and flattens the top of the triangle wave. As the oscilloscope outputshows, the resultant waveform looks quite like a sine wave. Two potentiometers adjust thelook of the final waveform. P1 determines how the amplitude of the input waveform, andtherefore how overdriven the differential pair is. At one extreme, the input levels keep thedifferential pair in its active region, so the output is still a triangle wave. At the other, thetransistor is extremely overdriven, and begins to resemble a square wave. The second potadjusts the symmetry of the waveform by controlling the current through each transistor.Moving the pot in one direction rounds out the top more than the bottom, and the otherdirection rounds out the bottom more.

The potentiometer and R41 are idealised as two current sources as shown in the schematicbelow.

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Figure 8: Sine Waveshaper Schematic for Analysis

Kirchoff Loop:vin = VBE1 + iR3 − VBE2

Q1 and Q2 are a matched pair, so IS is the same for both transistors:

VBE1 = VT ln(IC1

IS

)and

VBE2 = VT ln(IC2

IS

)So,

vin = iR + VT ln

(IC1

IC2

)Let I1 = (I + 1) and I2 = (I − 1).

vin

VT

=i

I

(IR

VT

)+ ln

(1 + i

I

1− iI

)

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Expanding this out by use of a power series (as explained in the IEEE paper): 1IRVT

+ 2

vin

VT

=i

I+

2

3

1IRVT

+ 2

( iI

)3

+2

5

1IRVT

+ 2

( iI

)5

+ ...

This is of the form i = Ki sin(K2vin), where K1 = 1, and K2 =(

1IRVT

+2

)1

VT.

Results :Some captured waveforms:

Saw :

Figure 9: Sawtooth Wave

Triangle :

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Figure 10: Triangle Wave

Square :

Figure 11: Square Wave

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Sine :

Figure 12: Sine Wave

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Figure 13: VCO Control Voltage vs. Frequency

The numerical results are on the next page.

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Voltage In (V) Frequency Voltage In (V) Frequency-7 10.9 0.2 1300

-6.5 15.3 0.4 1475-6 21.3 0.6 1672

-5.5 29.9 0.8 1890-5 42 1 2135

-4.5 58.3 1.2 2405-4 81.6 1.4 2700

-3.5 113.9 1.6 3050-3 159.7 1.8 3400

-2.8 182 2 3800-2.6 208 2.2 4250-2.4 237.5 2.4 4730-2.2 271 2.6 5250-2 309 2.8 5800

-1.8 354 3 6400-1.6 404 3.5 8100-1.4 462 4 10000-1.2 526 4.5 12340-1 599 5 15170

-0.8 680 5.5 18700-0.6 780 6 22790-0.4 883 6.5 27100-0.2 1000 7 309900 1144

Error Analysis/Discussion The triangle wave has an inaudible glitch in it, due to theprocess of rectification. This glitch is carried over to both the square and the sine waves,since they both are derived from the triangle wave.

As seen above, the frequency tracks the voltage exponentially well at lower frequencies.However, at higher frequencies, the error becomes larger. This is because the capacitorhas a finite discharge time. Since this particular JFET has a fairly high RDS of 250Ω (forcontrast, the JFET usually used for synthersizers, a 2N4856, has an RDS of 25Ω), the resettime through the JFET is comparable to the period of the waveform itself. This is partiallycompensated for by the resistor placed in series with the capacitor in the sawtooth oscillator,since it sets the voltage just before integration at a value of Isource ∗R36. This is intended toaccount for the lost time of integration when the JFET is resetting. To improve the tracking,a 1kΩ potentiometer can be placed instead of the current 680Ω resistor, and this pot can betrimmed to improve the voltage tracking of the VCO.

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Bibliography

Meyer, R.G.; Sansen, W.M.C.; Peeters, S.; , ”The differential pair as a triangle-sine waveconverter,” Solid-State Circuits, IEEE Journal of , vol.11, no.3, pp. 418- 420, Jun 1976doi: 10.1109/JSSC.1976.1050748URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1050748&isnumber=22548

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