# Successive Approximation ADC – Analog to Digital Converter

In this tutorial, we will talk about successive approximation ADC. This type of ADC converts an analog signal into a digital signal using a binary search through all possible quantization levels. Firstly, we will discuss what is ADC? After that we will discuss the introduction, working, example circuits, advantages, and disadvantages of successive approximation ADC.

ADCs are the bridge between the real world and the digital world. All the information whether it be temperature, audio or pressure e.t.c is in the form of continuous analog signals. But to process and manipulate these signals we need to interface them with microcontrollers and processors and translate them to their digital representation. This is where Analog to digital converters come in handy. These are the essential blocks that convert real analog signals from the sensors to binary set values.

The ADC is a device to convert the analog sine waves to binary digitals for data acquisition. The precision of an ADC is determined through two key elements i.e, sampling rate that is based on the Nyquist theorem and Bit resolution that shows how accurate the output signal is.

### Sampling Rate

The input signal is sampled at the Nyquist rate which says that the sampling frequency should be twice the interested signal’s frequency. This avoids the aliasing or overlapping of the signals to retain all the information and avoid data distortion or loss. The samples are then assigned finite levels by a process called quantization and followed by the encoding of the signal into binary format.

### Quantization Error

It is the difference between the assigned value and the closest available digital value at each sampling point. The formula for the quantization error is

` Quantization Error = Vref/2N`

For example, let say the reference voltage is 16 volts and the number of bits is 4 then quantization error is

``` Quantization Error = 16/2^4
Quantization Error = 1 Volt```

It depicts that any input voltage less than 1 volt will be considered as zero. Any voltage greater than 1 volt will change the ADC output voltage. This introduces an error and known as quantization error.

### Bit Resolution

The resolution of an ADC is based on the number of bits which tell us about the number of levels an ADC can produce and quantize the input analog signal. The general formula is

` Resolution=2N`

Where N represents the number of bits. The higher the resolution, the more accurate are the resultant signals. For a 4-bit ADC, the resolution will be 16.

Though ADC is implemented using various techniques these days, this article will focus on the Successive Approximation method.

It is the most frequently used ADC technique for general applications. The ADC comprises a comparator, digital to analog converter, register, and a control circuit. The schematic is shown below:

At the point when the new conversion begins, the sample and hold circuit samples the input voltage and then this sampled signal is compared with the output signal of the digital to analog converter.

## 4-bit Successive Approximation ADC Example

To grasp the concept, consider a 4-bit ADC with a sampling rate i.e Vin to be 11.2 Volts. We take the comparator reference voltage as16 Volts. Whenever the new transformation begins, the successive approximation register sets the most significant bit to 1 and all others to zero. As the register is followed by the DAC, the input to the DAC is 1000. So the output voltage of the DAC corresponding to the stated digital code and reference voltage of 16 turns out to be

```Vout = – Vref { B0 (1/16) + B1 (1 /8) + B2 (1/4) + B3(1/2) }
Vout = 8 Volts```

This is the threshold voltage to which the input voltage will be compared. Thus, the output voltage of the comparator will change the output value of the successive register.

This sets two conditions:

### When Vdac < Vin

If the output voltage of DAC is lesser than the input voltage then the most significant bit remains intact and the next bit will be changed to 1 for new comparison.

### When Vdac > Vin

On the other hand, if the output DAC voltage is greater than the input voltage then the MSB is transformed to zero but the next bit is pulled high for the new comparison.

## Working of Successive Approximation ADC

As we have calculated, the output voltage of DAC is 8 Volts and Vin is 11.2 volts. So, the condition Vin>Vdac is satisfied which results in unchanged most significant bit and successive bit is set to 1. Now, the code has become 1100. So, the output of DAC corresponding to this binary code is 12 Volts measured using the same output voltage formula. This is the new DAC voltage set to be compared with.

Once more, the input voltage is compared with the DAC voltage. If again, the latter is lesser, then the second bit remains the same while the third bit is made 1 for the new comparison. But if vice versa happens then the second bit is changed to zero and the third bit to 1 for the next comparison. It means that the current input code for the DAC is 1010. We will deduce the output voltage which is updated to 10 Volts. Repeat the same process again.

If Vin is less than 10 Volts then the third bit is kept as it is and the least significant bit is made high. For vice versa, the third bit is turned to 0 and LSB alters to 1 to compare with the input voltage. The input is for sure greater than the Vdac so, the next input code is 1011. The corresponding output voltage becomes 11 Volts. It is again compared and the final code is 1011.

Below is the tree hierarchy that depicts all the possibilities that occur during the iterations. Hence, based on the comparison, only one code is selected in the end.

## Time Domain Representation

The four-cycle time domain representation of the sequence for the visual is shown below:

## Conversion Time

It is the time needed by analog to digital converter to completely convert continuous signals to digital signals. The conversion time is based on the number of bits because the N number of bits takes N number of clock cycles. Each bit iteration takes one cycle. So, the general conversion time formula is

`Tc = N x Tclk`

We can see that the conversion time is independent of the input voltage which is not the case in the majority of the other ADCs.

## Conversion Speed

The speed with which the conversion of the signal takes place is called conversion speed. Successive Approximation ADC typical conversion speed is between 2-10 Mega Samples Per Second. (MSPS).

Talking about the resolution, it is the number of bits utilized by the analog to digital converter to discrete the analog inputs. The typical resolution of the successive approximation analog to digital converter is in a wide range starting from 8-bits to 16-bits. Still, some exceptions can resolve up to 20-bits.

## SA DAC Latency

Data latency is the time taken by the converter to make the data available for the download. It is measured in either time or conversion cycles. If the data is available after a single conversion cycle then it is called a Zero latency ADC. The successive approximation is a zero-latency ADC. So, it is used in applications where data is required immediately.

• They output the binary representation serially.
• They are highly accurate due to their high-resolution power.
• Successive Approximation ADCs are reliable and power effective.