Introduction to ADC and DAC

Hey friends, welcome to the YouTube channel ALL ABOUT ELECTRONICS. So in this video, we will briefly learn about the ADC and the DAC. So this ADC stands for the Analog to Digital Converter. And as its name suggests, it converts the analog signal into the digital signal. Similarly, this DAC stands for the digital to analog converter and it converts the digital input into the analog signal. And knowingly or unknowingly, we all are using this ADC and DAC in our day to day life. For example, whenever we are streaming the music on our smartphone, then this digital bit stream is converted into the electrical signal and through the smartphone speaker, we are able to hear this music. And here. This DAC inside the smartphone converts the digital bit stream into the analog signal. Similarly, while talking on the phone, the microphone converts our voice into the electrical signal and using this ADC, this signal is digitized and it is transmitted in the form of radio waves. Similarly, at the receiver side. Using the DAC, this received digital data is converted into the analog signal and through the speaker, we are able to hear the voice of the other person. So in short, in our day to day life, by some or other way, we are using this ADC and the DAC. But then the question arises, why we are using this ADC and the DAC? And what is the need of converting the signals back and forth in this analog and digital domain? So, let's find out the answer. Now, most of the signals which we find around us are analog in nature. For example, the temperature, pressure, sound or velocity, all signals are analog in nature. And using the transducer, this analog signal is converted into the electrical signal. But still, these signals remain analog in nature. Now, these analog signals are very susceptible to the noise, particularly whenever they are used in the communication. Apart from that, it is very difficult to process and store these analog signals. On the other hand, the digital signals are less susceptible to the noise and they are easy to process and store in the digital domain. And that is why the analog signals are converted into the digital signal so that they can be easily processed and stored. And whenever it is required, then using the DAC, it is possible to retrieve these signals. But these conversions are not lossless. That means during the conversion, some information of the analog signal will be lost. Because if you see the analog signal, then it is continuous in time as well as in the amplitude. So, if this analog signal is varying in a certain range, then it can take any value in this given range. For example, let's say if this analog signal is varying from 0 to 5 volt. then it can take any value between 0 to 5V. Therefore, theoretically we can say that the analog signal has an infinite resolution. But whenever this signal is converted into the digital signal, then it is discrete in time as well as discrete in amplitude. So, to understand that, let's see the steps which are involved in the analog to digital conversion. So, first of all, the analog signal is sampled at a particular rate. And after the sampling, this signal is quantized in the finite levels. And after the quantization, this signal is encoded in the binary format. So one by one, let's understand it in detail. And first of all, let's talk about the quantization. So in this quantization process, a sampled signal is assigned a particular value from the discrete set of values. So as you can see here. A signal is quantized in the 16 different levels. And a sample signal is assigned a nearest value from these 16 levels. And the resolution of the ADC decides how the assigned value or the quantized value is close to the actual value. So usually, this resolution is defined in the number of bits. And here, this bit refers to the number of bits in which the quantized signal is going to get encoded. So, basically this resolution defines the minimum change in the input signal which can be detected by the ADC. So, for a given ADC, if the resolution is n bits, then in a binary number system, the total number of discrete levels which can be defined is equal to 2 to the power n. That means the input signal will get quantized into 2 to the power n levels. So, for example, for a 1 ADC, if the resolution is 3 bits, then the input signal will get quantized into 8 levels. And in terms of the voltage, this resolution can be defined as the full-scale range of the ADC divided by the 2 to the power total number of bits. Where this full-scale range is the maximum voltage range which can be converted by the ADC. And sometimes, It is also defined as the V reference divided by 2n. So, let's say for a 3-bit ADC, the full scale range is 10V, then the resolution of the ADC is equal to 10 divided by 2 to the power 3. That is equal to 1.25V. That means the minimum change in the input which can be detected by the ADC is equal to 1.25V. So, if the change in the input signal is less than 1.25V, then it won't get detected by this given ADC. On the other hand, if the full scale range of the ADC is 1V, in that case, the resolution of the ADC will be equal to 1V divided by 2 to the power 3. That is equal to 125 mV. So now, the minimum change which can be detected by the ADC is equal to 125 mV. So in this way, by changing the reference voltage, the minimum detectable voltage can be increased. But at the same time, the conversion range of the ADC will also reduce. So, in a way, we can say that there is a trade-off for changing the reference voltage of the given ADC. But keeping the same reference voltage, by increasing the number of bits, we can increase the resolution. For example, the resolution of 8-bit ADC with 10V of reference voltage is equal to 10V divided by 2 to the power 8, which is roughly around 39 mV. So, this 8-bit ADC will now be able to detect the change of even 39 mV. So, in short, by increasing the number of bits, we can increase the resolution. So, this graph shows the transfer function of the 3-bit ADC with a full scale range of 1V. And as you can see, this transfer function looks like a staircase. And this blue line shows the ideal transfer function of the ADC. That means if the resolution of the ADC is infinite, in that case, the transfer function would look like a straight line. So, for this 3 bit ADC, the minimum detectable voltage or the resolution will be equal to 1V divided by 2 to the power 3. That is equal to 0.125V. That means whenever the input voltage is between 0 to 0.125V, in that case it will be considered as zero. And the output of the ADC will change only when the input goes above this 0.125V. So, due to this quantization process, the error will be introduced in the output of the ADC. And this error is known as the quantization error. So, for a 3-bit ADC with a 1V voltage range, the quantization error is equal to 0.125V. Or in general, irrespective of the number of bits and the reference voltage, it can be defined in the terms of Lsb. So we can say that the quantization error is equal to 1 Lsb. Because here if you see in the transfer function, each step corresponds to 1 Lsb. So of course, this quantization error can be reduced by increasing the number of bits. But just by shifting the transfer function to the left, we can reduce this quantization error from 1 LSP to 0.5 LSP. And to explain that, let me simplify this horizontal axis. So now if you see, whenever the input is between 0 to 0.5V, then the output of the EDC is equal to 000. And it will change whenever the input goes above this 0.5V. So, now the maximum possible error in the output is equal to plus minus 0.5V. Or we can say that the maximum possible error in the output is now plus or minus 0.5 LSB. Alright, so this is all about the quantization. Now let's talk about the sampling. Now as I said, the first step in the conversion process is the sampling. That means the analog signal is sampled at the particular rate. And as you can see, the more samples we take, the more accurately we can represent the analog signal. Now, according to the Nyquist sampling theorem, the sampling rate should be at least 2 times the maximum frequency of the input signal. So that after the sampling, the signal can be reconstructed. So for a sine wave with a maximum frequency of fmax, the minimum sampling rate should be equal to 2 times fmax. And if the sampling rate is less than this, then the aliasing effect will be seen in the reconstructed waveform. That means the frequency of the constructed signal will be less than the original signal. So, to avoid this Eliasson effect, the sampling rate should be at least 2 times the maximum frequency. Alright, so now let's see what happens when the input is square wave. So, let's say we have square wave with a frequency of f0. And we are sampling this square wave with a sampling rate which is more than the 2f0. So, according to the theorem, we should be able to deconstruct this square wave. But if you are aware, apart from the fundamental frequency, the square wave also contains the harmonics. And due to that, no matter what is the sampling rate, the aliasing effect will occur in the constructed signal. And to avoid that, the anti-aliasing filter is always used with the ADC. So, before sampling, the signal is passed through this anti-aliasing filter which is basically a low-pass filter. So, for the given ADC, if the maximum sampling frequency is let's say fs, then the cutoff frequency of this low-pass filter should be equal to fs by 2. So, using this anti-aliasing filter, we can remove the high frequency components and we can reduce the effect of aliasing. So, in this way, this sampling is also a very important parameter for the ADC. Now, so far we have assumed that during the conversion, just after the sampling, immediately the signal is quantized and encoded. But in reality, the ADC will take some time for this quantization as well as in the encoding. So, during that time, the signal should remain constant. And for that, the sample and hold circuit is always used with the ADC. So, this sample and hold circuit samples the signal and holds the output to the same value until the next sample is taken. So, if you see the oral block diagram of the ADC, then it can be represented like this. That means first, using the sample and hold circuit, the signal is sampled and then it is quantized and encoded. So, these are the basic steps for the analog to digital conversion. And similarly, let's briefly discuss about the DAC. So, in case of the DAC, according to the digital bitstream, the analog signal is generated. And here, how accurately the signal is reconstructed, that depends on the resolution of the DAC. For example, a 12-bit DAC can reconstruct the signal more accurately than the 3-bit DAC. And by improving the resolution, we can improve the accuracy of the output waveform. So, the important parameters for the DAC are resolution, reference voltage and the settling time. So, basically here this settling time decides the maximum frequency which can be reconstructed by this DAC. And apart from these parameters, here is the list of other important parameters for the ADC and the DAC. Which includes the gain and the offset error, non-linearity and the total harmonic distortion. So, in the upcoming videos of this ADC and DAC, we will learn more about all these parameters. Now this ADC and DAC can be designed in different ways. And each design has some advantages over the other design. For example, some ADCs provide a better resolution while the other ADCs have a faster conversion time. So, here is the list of different types of ADCs and the DACs which are commonly used in the electronics. So, one by one, we will see all these types of ADCs and DSCs in the upcoming videos. But first of all, we will start with the DSCs. So, I hope in this brief discussion, you understood what is ADC and DSC and why they are used in the electronics. And what are the important parameters for this ADC and the DSC. So, if you have any question or suggestion, do let me know here in the comment section below. If you like this video, hit the like button and subscribe to this channel for more such videos.

Similarly, this DAC stands for the digital to analog converter and it converts the digital input into the analog signal. And knowingly or unknowingly, we all are using this ADC and DAC in our day to day life. For example, whenever we are streaming the music on our smartphone, then this digital bit stream is converted into the electrical signal and through the smartphone speaker, we are able to hear this music. And here.

This DAC inside the smartphone converts the digital bit stream into the analog signal. Similarly, while talking on the phone, the microphone converts our voice into the electrical signal and using this ADC, this signal is digitized and it is transmitted in the form of radio waves. Similarly, at the receiver side.

Using the DAC, this received digital data is converted into the analog signal and through the speaker, we are able to hear the voice of the other person. So in short, in our day to day life, by some or other way, we are using this ADC and the DAC. But then the question arises, why we are using this ADC and the DAC?

And what is the need of converting the signals back and forth in this analog and digital domain? So, let's find out the answer. Now, most of the signals which we find around us are analog in nature.

For example, the temperature, pressure, sound or velocity, all signals are analog in nature. And using the transducer, this analog signal is converted into the electrical signal. But still, these signals remain analog in nature. Now, these analog signals are very susceptible to the noise, particularly whenever they are used in the communication.

Apart from that, it is very difficult to process and store these analog signals. On the other hand, the digital signals are less susceptible to the noise and they are easy to process and store in the digital domain. And that is why the analog signals are converted into the digital signal so that they can be easily processed and stored.

And whenever it is required, then using the DAC, it is possible to retrieve these signals. But these conversions are not lossless. That means during the conversion, some information of the analog signal will be lost.

Because if you see the analog signal, then it is continuous in time as well as in the amplitude. So, if this analog signal is varying in a certain range, then it can take any value in this given range. For example, let's say if this analog signal is varying from 0 to 5 volt. then it can take any value between 0 to 5V.

Therefore, theoretically we can say that the analog signal has an infinite resolution. But whenever this signal is converted into the digital signal, then it is discrete in time as well as discrete in amplitude. So, to understand that, let's see the steps which are involved in the analog to digital conversion.

So, first of all, the analog signal is sampled at a particular rate. And after the sampling, this signal is quantized in the finite levels. And after the quantization, this signal is encoded in the binary format. So one by one, let's understand it in detail.

And first of all, let's talk about the quantization. So in this quantization process, a sampled signal is assigned a particular value from the discrete set of values. So as you can see here. A signal is quantized in the 16 different levels.

And a sample signal is assigned a nearest value from these 16 levels. And the resolution of the ADC decides how the assigned value or the quantized value is close to the actual value. So usually, this resolution is defined in the number of bits.

And here, this bit refers to the number of bits in which the quantized signal is going to get encoded. So, basically this resolution defines the minimum change in the input signal which can be detected by the ADC. So, for a given ADC, if the resolution is n bits, then in a binary number system, the total number of discrete levels which can be defined is equal to 2 to the power n. That means the input signal will get quantized into 2 to the power n levels. So, for example, for a 1 ADC, if the resolution is 3 bits, then the input signal will get quantized into 8 levels.

And in terms of the voltage, this resolution can be defined as the full-scale range of the ADC divided by the 2 to the power total number of bits. Where this full-scale range is the maximum voltage range which can be converted by the ADC. And sometimes, It is also defined as the V reference divided by 2n. So, let's say for a 3-bit ADC, the full scale range is 10V, then the resolution of the ADC is equal to 10 divided by 2 to the power 3. That is equal to 1.25V.

That means the minimum change in the input which can be detected by the ADC is equal to 1.25V. So, if the change in the input signal is less than 1.25V, then it won't get detected by this given ADC. On the other hand, if the full scale range of the ADC is 1V, in that case, the resolution of the ADC will be equal to 1V divided by 2 to the power 3. That is equal to 125 mV.

So now, the minimum change which can be detected by the ADC is equal to 125 mV. So in this way, by changing the reference voltage, the minimum detectable voltage can be increased. But at the same time, the conversion range of the ADC will also reduce. So, in a way, we can say that there is a trade-off for changing the reference voltage of the given ADC.

But keeping the same reference voltage, by increasing the number of bits, we can increase the resolution. For example, the resolution of 8-bit ADC with 10V of reference voltage is equal to 10V divided by 2 to the power 8, which is roughly around 39 mV. So, this 8-bit ADC will now be able to detect the change of even 39 mV. So, in short, by increasing the number of bits, we can increase the resolution.

So, this graph shows the transfer function of the 3-bit ADC with a full scale range of 1V. And as you can see, this transfer function looks like a staircase. And this blue line shows the ideal transfer function of the ADC. That means if the resolution of the ADC is infinite, in that case, the transfer function would look like a straight line.

So, for this 3 bit ADC, the minimum detectable voltage or the resolution will be equal to 1V divided by 2 to the power 3. That is equal to 0.125V. That means whenever the input voltage is between 0 to 0.125V, in that case it will be considered as zero. And the output of the ADC will change only when the input goes above this 0.125V. So, due to this quantization process, the error will be introduced in the output of the ADC. And this error is known as the quantization error.

So, for a 3-bit ADC with a 1V voltage range, the quantization error is equal to 0.125V. Or in general, irrespective of the number of bits and the reference voltage, it can be defined in the terms of Lsb. So we can say that the quantization error is equal to 1 Lsb. Because here if you see in the transfer function, each step corresponds to 1 Lsb. So of course, this quantization error can be reduced by increasing the number of bits.

But just by shifting the transfer function to the left, we can reduce this quantization error from 1 LSP to 0.5 LSP. And to explain that, let me simplify this horizontal axis. So now if you see, whenever the input is between 0 to 0.5V, then the output of the EDC is equal to 000. And it will change whenever the input goes above this 0.5V.

So, now the maximum possible error in the output is equal to plus minus 0.5V. Or we can say that the maximum possible error in the output is now plus or minus 0.5 LSB. Alright, so this is all about the quantization.

Now let's talk about the sampling. Now as I said, the first step in the conversion process is the sampling. That means the analog signal is sampled at the particular rate.

And as you can see, the more samples we take, the more accurately we can represent the analog signal. Now, according to the Nyquist sampling theorem, the sampling rate should be at least 2 times the maximum frequency of the input signal. So that after the sampling, the signal can be reconstructed.

So for a sine wave with a maximum frequency of fmax, the minimum sampling rate should be equal to 2 times fmax. And if the sampling rate is less than this, then the aliasing effect will be seen in the reconstructed waveform. That means the frequency of the constructed signal will be less than the original signal.

So, to avoid this Eliasson effect, the sampling rate should be at least 2 times the maximum frequency. Alright, so now let's see what happens when the input is square wave. So, let's say we have square wave with a frequency of f0. And we are sampling this square wave with a sampling rate which is more than the 2f0. So, according to the theorem, we should be able to deconstruct this square wave.

But if you are aware, apart from the fundamental frequency, the square wave also contains the harmonics. And due to that, no matter what is the sampling rate, the aliasing effect will occur in the constructed signal. And to avoid that, the anti-aliasing filter is always used with the ADC.

So, before sampling, the signal is passed through this anti-aliasing filter which is basically a low-pass filter. So, for the given ADC, if the maximum sampling frequency is let's say fs, then the cutoff frequency of this low-pass filter should be equal to fs by 2. So, using this anti-aliasing filter, we can remove the high frequency components and we can reduce the effect of aliasing. So, in this way, this sampling is also a very important parameter for the ADC. Now, so far we have assumed that during the conversion, just after the sampling, immediately the signal is quantized and encoded. But in reality, the ADC will take some time for this quantization as well as in the encoding.

So, during that time, the signal should remain constant. And for that, the sample and hold circuit is always used with the ADC. So, this sample and hold circuit samples the signal and holds the output to the same value until the next sample is taken. So, if you see the oral block diagram of the ADC, then it can be represented like this.

That means first, using the sample and hold circuit, the signal is sampled and then it is quantized and encoded. So, these are the basic steps for the analog to digital conversion. And similarly, let's briefly discuss about the DAC. So, in case of the DAC, according to the digital bitstream, the analog signal is generated. And here, how accurately the signal is reconstructed, that depends on the resolution of the DAC.

For example, a 12-bit DAC can reconstruct the signal more accurately than the 3-bit DAC. And by improving the resolution, we can improve the accuracy of the output waveform. So, the important parameters for the DAC are resolution, reference voltage and the settling time. So, basically here this settling time decides the maximum frequency which can be reconstructed by this DAC. And apart from these parameters, here is the list of other important parameters for the ADC and the DAC.

Which includes the gain and the offset error, non-linearity and the total harmonic distortion. So, in the upcoming videos of this ADC and DAC, we will learn more about all these parameters. Now this ADC and DAC can be designed in different ways.

And each design has some advantages over the other design. For example, some ADCs provide a better resolution while the other ADCs have a faster conversion time. So, here is the list of different types of ADCs and the DACs which are commonly used in the electronics. So, one by one, we will see all these types of ADCs and DSCs in the upcoming videos. But first of all, we will start with the DSCs.

So, I hope in this brief discussion, you understood what is ADC and DSC and why they are used in the electronics. And what are the important parameters for this ADC and the DSC. So, if you have any question or suggestion, do let me know here in the comment section below.

If you like this video, hit the like button and subscribe to this channel for more such videos.

Transcript for:Introduction to ADC and DAC

Transcript for:
Introduction to ADC and DAC