Essay: Waveform generators

3.6 Waveform generators
3.6.1 Triangular wave generator
A triangular wave generator can be formed by simply connecting an integrator to a square wave generator. The resultant circuit is shown in Figure. This circuit requires dual op-amp, two capacitors, and at least five resistors.
Triangular wave generator
The frequencies of the square wave and triangular wave are the same. For fixed R1, R2and C values, the frequency of the square wave as well as the triangular wave depends on the resistance R.
As R is increased or decreased, the frequency of the triangular wave will decrease or increase respectively.
Although the amplitude of the square wave is constant at ±Vsat, the amplitude of the triangular wave will decrease as the frequency increases. This is because the reactance of the capacitor C in the feedback circuit decreases at high frequencies.
A resistance R4 is connected across C2, to avoid the saturation problem at low frequencies as in the case of practical integrator.
Output waveform
Another, triangular wave generator using lesser number of components is shown in Figure.
Triangular wave generator using lesser components
Output Waveforms
The triangular wave generator consists of a two level comparator and an integrator A2. The output of comparator A1 is a square wave and is applied to the (-) input terminal of the integrator A2 producing a triangular wave. This triangular wave is fed back as input to the comparator A1 through a voltage divider .
Initially, let us consider that the output of comparator A1 is +Vsat. The output of the integrator A2 will be a negative going ramp shown in Figure. Thus, one end of the voltage divider R2 R3 is at a voltage + Vsat and the other at the negative going ramp of A2.
At a time t = t1 when the negative going ramp attains a value of -V, the voltage at point P becomes slightly less than 0V. This switches the output of A1 from positive saturation to negative saturation level – Vsat.
During the time when the output of A1 is at -Vsat, the output of A2 increases in the positive direction. And at the instant t = t2 the voltage at point P becomes just above 0V, thereby switching the output of A1 from –Vsat +Vsat.
The cycle repeats and generates a triangular waveform. It can be seen that the frequency of the square wave and triangular wave will be same. However, the amplitude of the triangular wave depends upon the RC value of the integrator A2 and the output voltage level of A1.
The output voltage can be set to desired level by using appropriate zener diodes. The frequency of the triangular waveform can be calculate as follows.
The effective voltage at the point P during the time when output of A1 is at +Vsat level is given by
At t = t1, the voltage at point P becomes equal to zero. Therefore, from the above equation
Similarly, at t = t2 when the output of A1 switches from –Vsat to
Therefore, peak to peak amplitude of the triangular wave is
The output switches from – Vramp to + Vramp in half the time period T/2. Putting the values in the basic integrator equation,
Putting the value of V0(pp) from equation (4) we get,
Hence, the frequency of oscillation fO is
3.6.2 Sawtooth wave generators
Sawtooth wave refers to a wave form with its rise time being many times longer than corresponding fall time or fall time very longer as compared to the rise time.
Sawtooth waveform can be also generated by an asymmetrical astable multivibrator followed by an integrator. The sawtooth wave generators have wide application in time-base generators and pulse width modulation circuits.
The difference between the triangular wave and sawtooth waveform is that the rise time of triangular wave is always equal to its fall of time while in generator, rise time may be much higher than its fall of time.
Sawtooth Wave Generator :
The difference between the triangular and sawtooth waveforms is that the rise time of the triangular wave is always equal to fall time. That is, the same amount of time is required for the triangular wave to swing from -Vramp to + Vramp as from + Vramp to -Vramp .
On the other hand, sawtooth waveform has unequal rise time and fall time. The triangular waveform generator can be converted into sawtooth wave form generator by injecting a variable dc voltage into the non-inverting terminal of the integrator. This can be accomplished by using the potentiometer (pot) and connecting it to +VCC and -VEE as shown in the figure.
Depending on the pot setting ,a certain dc level is inserted in the output of the integrator. The duty cycle of the square-wave will be determined by the polarity and amplitude of this dc level.
A duty cycle less than 50% will then cause the output of integrator to be a sawtooth. With the wiper at the center of the pot , the output of integrator is a triangular wave.
For any other position of Pot , the output is a sawtooth waveform. Specifically as the pot variable is moved towards -VEE , the rise time of the sawtooth wave becomes longer than the fall time. On the other hand, as the pot is moved towards +VCC , the fall time becomes longer than the rise time.
Sawtooth wave generator