Saturday, October 30, 2010

Pulse Width Modulator

Table of Contents

1.0 Abstract …………………………………………… 2
2.0 Introduction …………………………………………3
3.0 Circuit Components …………………………………4
3.1 Triangle Wave Generator ……………………………4
3.2 Pulse Width Modulator ………………………………6
3.3 Tone control filters …………………………………8
3.4 Volume and balance control filters …………………10
3.5 H-Bridge amplification stage ………………………11
3.6 Demodulation filter ………………………….……12
4.0 Conclusion ………………………………………14

1.0 Abstract

This project consisted of the design and construction of a two channel, 10Watt class D audio amplifier with a carrier frequency of 44kHz, along with volume, balance, and tone controls. The main reason for the use of class D amplifiers is there extreme power efficiency. Class D amplifiers are composed of a few essential components. First the audio signal is converted into a pulse train using a pulse width modulator. That signal is then sent through a switched mode power gain stage and then the signal is demodulated with a low pass filter. The results of the project showed that the sound quality was relatively good for the carrier frequency specified above. However the tone controls were not as successful as we had hoped for especially the treble (high frequency) control.
2.0 Introduction
Class D amplifiers use pulse width modulation techniques to achieve a very power efficient amplifier. Class D amplifiers use transistors that are either on or off, and almost never in-between, so they waste the least amount of power. Class B amplifiers use linear regulating transistors to modulate output current and voltage and they can never be more efficient than 71%. Obviously, then, class D amplifiers are more efficient than class A, class AB, or class B. Some class D amplifiers have greater than 80% efficiency at full power. Class D amplifiers can also have low distortion, although not as good as class AB or class A. Because of the high power efficiency, they are ideal to use in small or portable electronics because they do not require large heat sinks to cool the transistors. The general components that make up the class D amplifier are a pulse width modulator, a switched mode power gain stage, and a demodulation filter.
Class D amplifiers have been around since the 60’s but were never very successful for audio applications because they had such high distortion. With the invention of the power MOS transistor, class D amplifiers suddenly became useful because the MOS transistor allowed for a very fast switching frequency with little distortion. Even with the Power MOS transistor the distortion level for high frequency signal can still be substantial. Today they are best used for subwoofers or low frequency signals in audio applications.
3.0 Circuit Components
The amplifier was composed of only a few components shown in the block diagram below.
All of the components up until the PWM will be referred to as the pre-amp in later sections. Over the course of the descriptions and explanations to come please refer to the complete attached schematics of the entire circuit.
3.1 Triangle Wave Generator
A triangle wave was needed to convert the audio signal into a pulse width modulated signal using a comparator. The triangle wave generator that we made consisted of an integrator and a hysteresis comparator. From an intuitive perspective, all the circuit did was integrate a square wave that was created by the hysteresis comparator. The biasing for the input and the positive feedback resistors of the hysteresis comparator were chosen such that the output would switch to the opposite rail when the input was at +/- 10 volts. This was done by setting the feed back resistor (R18) to 1k ohm, and analyzing the voltage divider network between the nodes A and B. The voltage at node B is limited by
the diodes to +/- 0.9 volts. By setting the voltage at the positive input to the op-amp to
zero(the point of witching) the value of R16 needed to switch the comparator at an input voltage of +/- 10 volts was found to be 8.5k ohms. When the comparator flips to the opposite rail, that signal then feeds around to the integrator, and the integrator begins to integrate the same function but of opposite sign from before. Thus a triangle wave comes out of the output of the op-amp at node A. If you refer to the calculations section(5.0), greater input resistance results in a smaller slope of the output waveform and a smaller input resistance results in a greater slope. Therefore adjusting the pot(R14) changes the frequency of the triangle wave by dictating how fast the output of the integrator climbs until it hits the voltage at which the comparator switches.
3.2 Pulse Width Modulator:
The pulse width modulator took the audio signal and converted it into a pulse signal with varying duty cycle that was proportional to the input signal at each sampled point. This was accomplished by sending the triangle wave and the audio signal from the pre-amp filters through a comparator. The results are shown below. As can be seen from the
oscilloscope plot of the waveforms, the triangle wave samples the input audio signal at every point that the two curves cross and converts it into a series of pulse signals of various lengths. A pull-up resistor was needed on the output of the comparator because it had an open collector output. Without the pull-up resistor the output square wave had a peak voltage of 500mv, but with the resistor the peak voltage was 16v. Converting the audio to a PWM signal is desirable because it is better to use a square wave to drive the power gain stage because there is far less power dissipated when the transistors are turned on and off by a square wave rather than turning them on slowly. In an effort to reduce some of the noise and oscillations in our amplifier, we put bypass capacitors around the positive and negative supply pins on the comparator. It helped somewhat in reducing the noise in the circuit.
One problem that was important to avoid, and one of which we learned the hard way was over modulation in the PWM. This occurred when the amplitude of the input signal exceeded the amplitude of the triangle wave. When this occurred the output signal became very distorted because there are point where the triangle wave goes through a whole cycle without intersecting the audio signal.
3.3 Tone Controls
A schematic of the tone controls is shown below. The filter on the left is the filter for the low frequencies and the filter on the right is the filter for the high frequencies. The low
frequency filter is an inverting op-amp configuration with a pot that changes the feedback and input resistance. When the pot is turned all the way to the right the input resistance is large and the gain is small and when it is turned all the way to the left the feedback resistance is large and the gain is large. The capacitors are there to nullify the affect of the pot at the frequency at which they act as a short. When that frequency is reached the position of the pot is irrelevant and the feedback and input resistances are the same, which yields a gain of one for all frequencies above the desired frequency. The frequency chosen was 1kHz and can be seen in the bode plot above. So by adjusting the pot the gain is varied between +/- 20dB for all frequencies up to 1kHz. So in reality this acted as the bass control for the audio signal.
The high frequency filter operated in a similar but inverted fashion. Unlike the low frequency filter where the gain was unity for all frequencies past 1kHz, the gain for the high frequency filter is unity for all frequencies up to 1kHz. When low frequency signals enter the filter the capacitors are open and therefore the setting on the pot has no affect on either the feedback or input resistances. This results in a gain of one because the feedback and input resistances are equivalent. When signals of frequencies greater than 1kHz enter the filter the pot adjust the gain of those signals by changing the ratio of feedback resistance to input resistance. This high frequency filter was the treble control for the audio signal. It was important to make the filters such that they did not over lap in frequency because the two filters were connected in series. When two things are
connected in series the overall gain is the product of the gain from each individual stage. So any signal that got amplified from one filter had a gain of unity in the other filter, so that no signal would be amplified twice. The overall range of the two filters in series can be seen in the bode plot above. The calculations for the component values can be found in section 5.0.
3.4 Volume and Balance
I will not elaborate much on the volume and balance controls for the amplifier because they were quite simple.
Both channels of the audio signal (left and right speakers) went through identical volume controls. The value of the input resistance for the volume control was chosen such that with the pot turned to 100% the volume of the music was at the desired maximum level.
The balance control was very similar. For this we wanted a gain of unity when the pot was turned to 100%. To make the two channels work opposite to each other we used a tandem pot with the feed back loop for the second channel connected to the opposite end of the pot from the first channel. So when the pot was at 100% one channel had unity gain while the other channel had a gain of zero. When the pot was at 50% the gain for both of the channels was equivalent.
3.5 H-Bridge
An H-bridge was used for the power amplification of the PWM signal. Shown in the schematic below, an H-bridge is a rectangular arrangement of transistors with a load
across the center. The idea is to drive the H-Bridge with a square wave on each side of bridge, with the driving signal on one side one half cycle out of phase from the other side. In our circuit we used two p-channel MOSFET’s for the two top transistors and three n-channel MOSFET’s, two for the bottom and one to invert the driving signal for the other side of the bridge. We chose to use two p-channel MOSFET’s for the top portion of the bridge because we did not want to use a separate IC or have a big messy thing of circuitry to drive a bridge made of all n-channels. P-channels turn on in exactly the opposite manner than that of an n-channel so it made sense to drive both the gates by the same signal. In order to make the H-Bridge work, we needed to turn on the MOSFET’s in diagonal pairs. This allowed a path of current to flow from +Vcc to ground across the load but twice as much voltage swing because the current is in the opposite direction across the load when the other diagonal pair turns on. By inverting the driving signal on
the right side and using that to drive the left side of the bridge, the bridge began to function properly. The simulations showed a fairly clean amplified signal across the load resistor with amplitude of about 8.5volts and an output power of about 12 watts. The output power for the H-Bridge is directly proportional to the variation in duty cycle in the PWM signal. As it was discussed earlier, when the triangle wave is much greater than the audio signal that it is sampling the variation of the duty cycle in the PWM signal is
very small, therefor the average power dissipated across the load in the H-Bridge is very small. When the amplitude of the input audio nears the amplitude of the triangle wave the output power becomes much louder because the variation in the duty cycle is much greater.
3.6 Demodulation Filter
The demodulation filter that we attempted to use was a double pole roll off LC filter. We used this to filter the PWM signal after it has gone through the H-Bridge. The pole was

placed at 20 kHz because that is the only portion of the signal that we really care about because the human ear can only hear up to that frequency. We chose an LC filter because it has a roll off that is twice as fast as would a first order low pass RC filter. In our actual project, we were unable to find inductor sufficient enough to meet our needs so the Filters were omitted due to time constraints.
4.0 Conclusion
Overall the project was a success. This project provided a sound medium in which I could enhance my knowledge and experience in electronics. Prior to embarking on this project I knew nothing about class D amps, pulse width modulation, active filters, and H-Bridges. Having spent this quarter researching and studying these things I feel I have learned a lot and have broadened my interests and made available new subjects of interest that I was previously unaware of. Perhaps one the most important skills that I really developed over the quarter was trouble shooting. It is very easy to get frustrated when things don’t work out like they should, especially when it comes to soldering the final product. Fortunately the four errors that we made in soldering up the circuit were ones that we discover and fixed in a relatively short amount of time.
One aspect that still has me somewhat puzzled was the fact that we were never able to get a really clean signal from our output. We tried putting bypass capacitors around the +/- Vcc to the comparator so that it would switch with the least amount of noise in the output wave and that seemed to give some improvement but it was not substantial. All in all I think that this project has bettered my understanding of electrical engineering knowledge and also time management skills.

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