Generate Sine Waves with PSLab Device

Sine wave is type of a waveform with much of a use in frequency related studies in laboratories as well as power electronics to control the level of input to devices. PSLab device  is capable of generating sine waves with a very high accuracy using PSLab-firmware and a set of filters implemented in the PSLab-hardware.

How Sine Wave is generated in PSLab Device

PSLab device uses a PIC micro-controller as its main processor. It has several pins which can generate square pulses at different duty cycles. These are known as PWM pins. PWM waves are a type of a waveform with the shape resembling a set of square pulses. They have an attributed called ‘Duty Cycle’ which varies between 0% to 100%. A PWM wave with 0% duty cycle means simply a zero amplitude block of square pulses repeating at every period. When duty cycle is set to 100%, it is a set of square pulses with the highest amplitude throughout the period repeating in every period. The following figure illustrates how the PWM wave changes according to its duty cycle. Image is extracted from http://static.righto.com/images/pwm1.gif PSLab device is capable of generating this type of pulses with arbitrary duty cycles as per user requirements.

In this context where sine waves are generated, these PWM pins are used to generate a Sinusoidal Pulse Width Modulated (SPWM) waveform as the first step to output a sine wave with high frequency accuracy. The name SPWM is derived from the fact that the duty cycle of the waveform follows an alternatively increasing and decreasing pattern as illustrated in the figure below.

Deriving a set of duty cycles which follows a sinusoidal pattern is a redundant task. Without deriving them mathematically, PSLab firmware has four hard-coded sine_tables which stores different duty cycle values related to a SPWM waveform. These sine_tables in the firmware related to different resolutions set by the PSLab device user. The following code block is extracted from PSLab firmware related to one of the sine_tables. It is used to generate the SPWM wave with 512 data points. Each data point represents a square pulse with a different pulse width. The duty ratio is calculated from dividing an entry by the value 512 and converting it to a percentage.

sineTable1[] = {256, 252, 249, 246, 243, 240, 237, 234, 230, 227, 224, 221, 218, 215, 212, 209, 206, 203, 200, 196, 193, 190, 187, 184, 181, 178, 175, 172, 169, 166, 164, 161, 158, 155, 152, 149, 146, 143, 141, 138, 135, 132, 130, 127, 124, 121, 119, 116, 114, 111, 108, 106, 103, 101, 98, 96, 93, 91, 89, 86, 84, 82, 79, 77, 75, 73, 70, 68, 66, 64, 62, 60, 58, 56, 54, 52, 50, 48, 47, 45, 43, 41, 40, 38, 36, 35, 33, 32, 30, 29, 27, 26, 25, 23, 22, 21, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 8, 7, 6, 6, 5, 4, 4, 3, 3, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 25, 26, 27, 29, 30, 32, 33, 35, 36, 38, 40, 41, 43, 45, 47, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 73, 75, 77, 79, 82, 84, 86, 89, 91, 93, 96, 98, 101, 103, 106, 108, 111, 114, 116, 119, 121, 124, 127, 130, 132, 135, 138, 141, 143, 146, 149, 152, 155, 158, 161, 164, 166, 169, 172, 175, 178, 181, 184, 187, 190, 193, 196, 200, 203, 206, 209, 212, 215, 218, 221, 224, 227, 230, 234, 237, 240, 243, 246, 249, 252, 256, 259, 262, 265, 268, 271, 274, 277, 281, 284, 287, 290, 293, 296, 299, 302, 305, 308, 311, 315, 318, 321, 324, 327, 330, 333, 336, 339, 342, 345, 347, 350, 353, 356, 359, 362, 365, 368, 370, 373, 376, 379, 381, 384, 387, 390, 392, 395, 397, 400, 403, 405, 408, 410, 413, 415, 418, 420, 422, 425, 427, 429, 432, 434, 436, 438, 441, 443, 445, 447, 449, 451, 453, 455, 457, 459, 461, 463, 464, 466, 468, 470, 471, 473, 475, 476, 478, 479, 481, 482, 484, 485, 486, 488, 489, 490, 492, 493, 494, 495, 496, 497, 498, 499, 500, 501, 502, 503, 503, 504, 505, 505, 506, 507, 507, 508, 508, 509, 509, 509, 510, 510, 510, 511, 511, 511, 511, 511, 511, 511, 511, 511, 511, 511, 510, 510, 510, 509, 509, 509, 508, 508, 507, 507, 506, 505, 505, 504, 503, 503, 502, 501, 500, 499, 498, 497, 496, 495, 494, 493, 492, 490, 489, 488, 486, 485, 484, 482, 481, 479, 478, 476, 475, 473, 471, 470, 468, 466, 464, 463, 461, 459, 457, 455, 453, 451, 449, 447, 445, 443, 441, 438, 436, 434, 432, 429, 427, 425, 422, 420, 418, 415, 413, 410, 408, 405, 403, 400, 397, 395, 392, 390, 387, 384, 381, 379, 376, 373, 370, 368, 365, 362, 359, 356, 353, 350, 347, 345, 342, 339, 336, 333, 330, 327, 324, 321, 318, 315, 311, 308, 305, 302, 299, 296, 293, 290, 287, 284, 281, 277, 274, 271, 268, 265, 262, 259};

 

The frequency of the sine wave is achieved using interrupts generated at different time intervals depending on the frequency set by the user. The accuracy of the frequency depends on the number of elements in the sine table array which is known as resolution. As the number of points in the table increases, the accuracy will be increased or resolution will be high. PSLab uses Timer3 and Timer4 counters available in the PIC micro-controller to generate the interrupt time intervals. If the required frequency is f, the interrupt time interval can be derived as

Interrupt time = f/512

The derived SPWM waveform will be then passed through a cascaded setup of Op Amp and RC filter as in Figure 1 to cut off the high frequency components and combine the square pulses in such a manner that a smoother waveform is derived resembling a sine wave.

Filter Circuit in PSLab

Figure 1

This is an inverting filter circuit designed using Op Amps available in PSLab-hardware. The SPWM waveform will be connected to the circuit through R1 resistor. It uses C1 capacitor which creates a short circuit path to high frequency components to ground which will let only the low frequency components to pass through. This will smoothen the square waves reducing the sharp edges forming a simple RC filter circuit.

The C2 capacitor plays an important role in generating the sine wave. It will compensate any voltage drops and absorb excess voltage levels that might occur during transition to let the output waveform follow a path which is similar to a smooth sine wave.

The output waveform can be observed from the SINE1 pin of the PSLab device. As in this schematic, it is the ‘Sine Wave’ pin to the right starting from the Op Amp output.

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