Design Problem 2: Pulse Width Modulator
[email protected] Electrical and Electronics Engineering Engineering Institute University of the Philippines Diliman Abstract This design problem is for the partial fulfilment of — This Electronic Circuits Circuits Laboratory II which w ill focus on applying the knowledge learned about clamper, Schmitt trigger and ramp generator circuits using operational amplifiers. The objective is to design and implement pulse width modulator according to given specifications.
I. I NTRODUCTION NTRODUCTION Pulse width modulation or pulse duration modulation (PWM or PDM) is a pulse modulation technique used for information transmission, motor controls, and other application [1]. As the name implies, this technique varies the pulse width or duration according to the instantaneous amplitude of the input. For this design problem, pulse width modulation is to be done using a voltage comparator. Given an input wave, it will be offset to a specified DC voltage level that will match the peak-to-peak of a generated ramp wave. The comparator will then output a pulse with a duration the sa me as the time the ramp voltage is greater than the instantaneous amplitude of the input wave. This is shown in the figure below.
II. CIRCUIT DESIGN The three circuits: clamper, Schmitt trigger, and bootstrap ramp generator will be created according to a given specification: V max V min max = 10 V min = 5V f max = 6000 Hz f max min min = 3000 Hz V DC,source = -12 V to 12V All of the circuit blocks will use LF356 operational amplifier. A. Clamper Circuit
From the given maximum and minimum requirement, the input sinusoid with
voltage will
= + − be offset to a DC voltage level, = . To achieve this, a diode clamper circuit will be used, as shown in Figure 3.
Fig. 3. Diode clamper circuit with a desired voltage bias
Capacitor C1 and resistor R1 are selected such that the resistor will not discharge the capacitor during the negative or positive portion of the input sinusoid. For this, Fig. 1. Pulse modulated modulated wave from a sinusoid and ramp inputs
Now, to produce the pulse width modulator circuit, three blocks will will be needed: a clamper, clamper, a free-running ramp generator generator composed of bootstrap ramp generator and a Schmitt trigger, and a voltage comparator. The block diagram is shown in Figure 2 below.
= 10 100 ,
= 6.8 Ω Ω
On the other hand, the desire voltage bias is produced using a voltage divider from the supply voltage, V CC CC =12 V . To achieve the desired DC voltage level, a network of t wo resistors will be used where one will be varied accordingly. From the simulation, R2 = 180 k Ω and R3 = 100 k Ω.
Fig. 4. Voltage divider network for desired voltage bias
B. Bootstrap Ramp Generator
Fig. 2. Block diagram for the PWM circuit
In the circuit shown in Figure 5, the ramp is generated across capacitor C 1, which is charged via resistor R1. The charging current must be held constant so that the voltage across C 1 will appear linear. Furthermore, capacitor C 2 must be much larger
Fig. 7. Constructed PWM circuit
than C 1 that it will hold the voltage across R1 constant, and thus, a constant current is produced. On the other hand, the transistor acts as switch that will instantaneously discharge capacitor C 2 as the Schmitt trigger circuit drives the bootstrap ramp circuit; this will then produce the sawtooth or ramp waveform.
− , = 37 Ω @ = −@ ∗ = 50 µ @ = − , = 222 Ω @ = −@
For base resistor R B, it was set to 10 transistor, while R L was set to 1kΩ.
kΩ to
bias the PNP
C. Schmitt Trigger
For the Schmitt trigger, the upper and lower trigger points must be the maximum and minimum voltage, respectively. In this way, it will trigger pulses only when the bootstrap ramp circuit produces voltage same as the trigger points. The circuit is shown in the figure below. Fig. 5. Bootstrap ramp circuit
The capacitor and resistor values according to the ramp time are calculated as follows:
= 3µ =100∗ = 300 µ 1% 1 = 167 µ, = 1 = 1 = ∗ = = 10 ∗ = 417 470 . = 0.01∗
To achieve the maximum and minimum frequency, resistor R1 must be varied. In doing this, the charging current will be varied which controls the ramp time.
@ =
Fig. 6. Schmitt trigger circuit with adjusted LTP
Since the given specification for the trigger points are both positive, the Schmitt trigger must have an adjusted LTP. The resistor values are calculated as follows:
= = 10 Ω , = 10.5
=10=(, ) = 200 Ω KCL at V node, −, − − − = = 2.9 Ω 3 Ω . +
To test the bootstrap ramp block, it must output a ramp from a step input with a slope equal to the required t max and t min, measure from the minimum to maximum voltage level. The output waveforms from the bootstrap ramp are shown in Figure 9.
D. Voltage Comparator and PWM circuit
To have a well-defined pulse width modulated signal, the comparator must have a high slew rate, such that it switch from high to low almost instantaneously. The operational amplifier used was LF356, having a slew rate of 13 V/µs — which is enough for the circuit. For the free-running ramp generator that will produce the sawtooth or ramp waveform, the Schmitt trigger and bootstrap ramp generator circuits are connected in loop. In looping the circuits, the Schmitt trigger will only allow a ramp that goes from the minimum voltage to the maximum voltage.
(c)
Ramp at t min, or f min = 1 kHz.
(d)
Ramp at t max, or f max = 6 kHz
III. SIMULATION, ACTUAL IMPLEMENTATION , AND R ESULTS After simulating and implementing the circuit in actual, there were slight deviations from the resistor values, which are not that significant and within +/-10% of the original calculated values.
Fig. 9. Ramp output from a step input
(a)
Clamped input sinusoid at 1 kHz
Fig. 10. Schmitt trigger output, 50% duty cycle
(b)
Clamped input sinusoid at 6 kHz .
Fig. 8. Input and output waveforms of the diode clamper circuit
Fig. 11. The pulse modulated waveform
IV. CONCLUSION In designing and constructing this project, which is focused on operational amplifiers, RC and diode circuits, it was essential to take into consideration the currents and voltages significant for the creation of pulse width modulated signal. From the results, it was evident that the specifications were not precisely achieved, but the outputs were still close. It may have not achieved the required numerical values, the circuit still has accomplished the main function which was to modulate the duty cycle of a pulse waveform. R EFERENCES Fig. 10. Free-running ramp waveform with V min = 5V and V max = 10 V
[1] D. A. Bell, Solid State Pulse Circuits , Reston Publishing Company, Inc. A Prentice-Hall Company, Reston, Virginia, 1976
