![SA ADC block diagram](https://upload.wikimedia.org/wikipedia/commons/6/61/SA_ADC_block_diagram.png)
A successive-approximation ADC is a type of
analog-to-digital converter
In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a digital signal. An ADC may also provide ...
that converts a continuous
analog waveform
An analog signal or analogue signal (see spelling differences) is any continuous signal representing some other quantity, i.e., ''analogous'' to another quantity. For example, in an analog audio signal, the instantaneous signal voltage varies ...
into a discrete
digital representation using a
binary search
In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search algorithm that finds the position of a target value within a sorted array. Binary search compares the target value to the ...
through all possible
quantization levels before finally converging upon a digital output for each conversion.
Algorithm
The successive-approximation
analog-to-digital converter
In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a digital signal. An ADC may also provide ...
circuit typically consists of four chief subcircuits:
# A
sample-and-hold
In electronics, a sample and hold (also known as sample and follow) circuit is an analog device that samples (captures, takes) the voltage of a continuously varying analog signal and holds (locks, freezes) its value at a constant level for a ...
circuit to acquire the input
voltage
Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to ...
.
# An analog voltage comparator that compares to the output of the internal
DAC and outputs the result of the comparison to the successive-approximation
register
Register or registration may refer to:
Arts entertainment, and media Music
* Register (music), the relative "height" or range of a note, melody, part, instrument, etc.
* ''Register'', a 2017 album by Travis Miller
* Registration (organ), th ...
(SAR).
# A successive-approximation register subcircuit designed to supply an approximate digital code of to the internal DAC.
# An internal reference DAC that, for comparison with , supplies the
comparator
In electronics, a comparator is a device that compares two voltages or currents and outputs a digital signal indicating which is larger. It has two analog input terminals V_+ and V_- and one binary digital output V_\text. The output is ideally
: ...
with an analog voltage equal to the digital code output of the .
![4-bit Successive Approximation DAC](https://upload.wikimedia.org/wikipedia/commons/b/b2/4-bit_Successive_Approximation_DAC.gif)
The successive approximation register is initialized so that the
most significant bit
In computing, bit numbering is the convention used to identify the bit positions in a binary number.
Bit significance and indexing
In computing, the least significant bit (LSB) is the bit position in a binary integer representing the binar ...
(MSB) is equal to a
digital 1. This code is fed into the DAC, which then supplies the analog equivalent of this digital code into the comparator circuit for comparison with the sampled input voltage. If this analog voltage exceeds , then the comparator causes the SAR to reset this bit; otherwise, the bit is left as 1. Then the next bit is set to 1 and the same test is done, continuing this
binary search
In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search algorithm that finds the position of a target value within a sorted array. Binary search compares the target value to the ...
until every bit in the SAR has been tested. The resulting code is the digital approximation of the sampled input voltage and is finally output by the SAR at the end of the conversion (EOC).
Mathematically, let , so in is the normalized input voltage. The objective is to approximately digitize to an accuracy of . The algorithm proceeds as follows:
# Initial approximation .
# approximation , where, is the
signum function
In mathematics, the sign function or signum function (from '' signum'', Latin for "sign") is an odd mathematical function that extracts the sign of a real number. In mathematical expressions the sign function is often represented as . To avo ...
( for , for ). It follows using mathematical induction that .
As shown in the above algorithm, a SAR ADC requires:
# An input voltage source .
# A reference voltage source to normalize the input.
# A DAC to convert the approximation to a voltage.
# A comparator to perform the function by comparing the DAC's voltage with the input voltage.
# A register to store the output of the comparator and apply .
![ADC animation 20](https://upload.wikimedia.org/wikipedia/commons/5/54/ADC_animation_20.gif)
Example: The ten steps to converting an analog input to 10 bit digital, using successive approximation, are shown here for all voltages from 5 V to 0 V in 0.1 V iterations. Since the reference voltage is 5 V, when the input voltage is also 5 V, all bits are set. As the voltage is decreased to 4.9 V, only some of the least significant bits are cleared. The MSB will remain set until the input is one half the reference voltage, 2.5 V.
The binary weights assigned to each bit, starting with the MSB, are 2.5, 1.25, 0.625, 0.3125, 0.15625, 0.078125, 0.0390625, 0.01953125, 0.009765625, 0.0048828125. All of these add up to 4.9951171875, meaning binary 1111111111, or one LSB less than 5.
When the analog input is being compared to the internal DAC output, it effectively is being compared to each of these binary weights, starting with the 2.5 V and either keeping it or clearing it as a result. Then by adding the next weight to the previous result, comparing again, and repeating until all the bits and their weights have been compared to the input, the end result, a binary number representing the analog input, is found.
Variants
* Counter type ADC: The D to A converter can be easily turned around to provide the inverse function A to D conversion. The principle is to adjust the DAC's input code until the DAC's output comes within LSB to the analog input which is to be converted to binary digital form.
* Servo tracking ADC: It is an improved version of a counting ADC. The circuit consists of an up-down counter with the comparator controlling the direction of the count. The analog output of the DAC is compared with the analog input. If the input is greater than the DAC output signal, the output of the comparator goes high and the counter is caused to count up. The tracking ADC has the advantage of being simple. The disadvantage, however, is the time needed to stabilize as a new conversion value is directly proportional to the rate at which the analog signal changes.
Charge-redistribution successive-approximation ADC
![ChargeScalingDAC](https://upload.wikimedia.org/wikipedia/commons/1/1d/ChargeScalingDAC.png)
One of the most common implementations of the successive-approximation ADC, the ''charge-redistribution'' successive-approximation ADC, uses a charge-scaling
DAC. The charge-scaling DAC simply consists of an array of individually switched binary-weighted capacitors. The amount of charge upon each capacitor in the array is used to perform the aforementioned binary search in conjunction with a comparator internal to the DAC and the successive-approximation register.
![CAPadc](https://upload.wikimedia.org/wikipedia/commons/1/1a/CAPadc.png)
# The capacitor array is completely discharged to the offset voltage of the comparator, . This step provides automatic offset cancellation (i.e. the offset voltage represents nothing but dead charge, which can't be juggled by the capacitors).
# All of the capacitors within the array are switched to the input signal . The capacitors now have a charge equal to their respective capacitance times the input voltage minus the offset voltage upon each of them.
# The capacitors are then switched so that this charge is applied across the comparator input, creating a comparator input voltage equal to .
# The actual conversion process proceeds. First, the MSB capacitor is switched to , which corresponds to the full-scale range of the ADC. Due to the binary-weighting of the array, the MSB capacitor forms a 1:1 charge divider with the rest of the array. Thus, the input voltage to the comparator is now . Subsequently, if is greater than , then the comparator outputs a digital 1 as the MSB, otherwise it outputs a digital 0 as the MSB. Each capacitor is tested in the same manner until the comparator input voltage converges to the offset voltage, or at least as close as possible given the resolution of the DAC.
Use with non-ideal analog circuits
When implemented as an analog circuit – where the value of each successive bit is not perfectly (e.g. 1.1, 2.12, 4.05, 8.01, etc.) – a successive-approximation approach might not output the ideal value because the binary search algorithm incorrectly removes what it believes to be half of the values the unknown input cannot be. Depending on the difference between actual and ideal performance, the maximal error can easily exceed several LSBs, especially as the error between the actual and ideal becomes large for one or more bits. Since the actual input is unknown, it is therefore very important that accuracy of the analog circuit used to implement a SAR ADC be very close to the ideal values; otherwise, it cannot guarantee a best match search.
See also
*
Quantization noise
Quantization, in mathematics and digital signal processing, is the process of mapping input values from a large set (often a continuous set) to output values in a (countable) smaller set, often with a finite number of elements. Rounding and t ...
*
Digital-to-analog converter
In electronics, a digital-to-analog converter (DAC, D/A, D2A, or D-to-A) is a system that converts a digital signal into an analog signal. An analog-to-digital converter (ADC) performs the reverse function.
There are several DAC archit ...
References
Further reading
* ''CMOS Circuit Design, Layout, and Simulation, 3rd Edition''; R. J. Baker; Wiley-IEEE; 1208 pages; 2010;
* ''Data Conversion Handbook''; Analog Devices; Newnes; 976 pages; 2004;
External links
Understanding SAR ADCs: Their Architecture and Comparison with Other ADCs- Maxim
Choose the right A/D converter for your application- TI
{{DEFAULTSORT:Successive Approximation Adc
Electronic circuits
Digital signal processing
Analog circuits
Approximations