High-Speed Analog to Digital Converters Ann Kotkat Barbara Georgy Mahmoud Tantawi Ayman Sakr Heidi El-Feky Nourane Gamal 1
Outline Introduction. Process of ADC. ADC Specifications. Flash ADC. Pipelined ADC. References. 2
Flash ADC Architectural details Comparator Resistive ladder Thermometer code Problems and Solutions Bubbles T\H Metastability Grey encoding Pros and cons 3
Architectural Details One Bit ADC 4
Architectural Details circuit employs 2 N -1 comparators. A resistive-divider with 2 N resistors provides the reference voltage. The reference voltage for each comparator is one least significant bit (LSB) greater than the reference voltage for the comparator immediately below it. Each comparator produces a 1 when its analog input voltage is higher than the reference voltage applied to it. Otherwise, the comparator output is 0. Thus, if the analog input is between V X4 and V X5, comparators X 1 through X 4 produce 1s and the remaining comparators produce 0s. The point where the code changes from ones to zeros is the point at which the input signal becomes smaller than the respective comparator reference-voltage levels. 5
Tracing example 6
Problems Bubbles: Normally, output of the comparator is thermometer code, such as 00111111. Errors may cause an output like 0011011. The spurious "0" in the result sequence is called a sparkle or a bubble. The bubble can be due to comparator timing mismatch. The magnitude of the error can be quite large and can be avoided by employing an input track-and-hold in front of the ADC along with an encoding technique that suppresses sparkle codes 7
Problems Measuring spurious-free dynamic range (SFDR) is a good way to observe converter performance. The "effective bits" achieved by the ADC is a function of input frequency; it can be improved by adding a track-and-hold (T/H) circuit in front of the ADC. The T/H circuit allows dramatic improvement, especially when input frequencies approach the Nyquist frequency, as shown in the next Figure. 8
Problems Meta-Stability: A severe limitation in very high-speed converters is meta-stability. It increases rapidly at high sampling frequencies. Meta-stability is caused by the finite gain in the comparators. Certain input signals generate output signals that can not be detected by the digital circuit Gray-code encoding can be used to improve metastability. (How?!) 9
Problems (cont.) 10
Problems (cont.) The encoder is composed of two parts, the one out of N (1-of-N) circuit and Gray ROM. The 1-of-N circuit is used to detect the 1 to 0 transition occurred in the Thermometer code which indicates the input voltage level, by an array of two input NAND logic gate with one input inverted ROM is actually a truth table in hardware form.next Figure shows an example of 3 bit Gray ROM based Thermometer to Gray encoder. Every input Thermometer code combination corresponds to an address, which is read to produce 3-bit Gray code. When the input in the non-inverted port is 1 and the inverted port 0 then only the output will be equal to 0. For the other input patterns the output will be equal to 1. In general if no bubble errors occurred there will only one 1 to 0 transition detected in the Thermometer code. So there will be only one 0 appearing at the output of 1-of-N circuit. This 0 signal used to enable the corresponding row in the Gray ROM. 11
Dec Thermometer code Grey Code Binary D T[7] T[6] T[5] T[4] T[3] T[2] T[1] G[2] G[1] G[0] B[2] B[1] B[0] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 2 0 0 0 0 0 1 1 0 1 1 0 1 0 3 0 0 0 0 1 1 1 0 1 0 0 1 1 4 0 0 0 1 1 1 1 1 1 0 1 0 0 5 0 0 1 1 1 1 1 1 1 1 1 0 1 6 0 1 1 1 1 1 1 1 0 1 1 1 0 7 1 1 1 1 1 1 1 1 0 0 1 1 1 12
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Problems (cont.) Now to understand how the Grey code encoding solves the problem of Metastability let s assume the case where the input voltage is almost equal the reference voltage of the 4th comparator hence T[4] is Metastable. thus we get a Thermometer code like this : 000X111 where X is undefined. Let s assume further that this X is interpreted as 1 and 0 by the 4th and 5th NAND gates respectively. Now both the 4th and 5th NAND gates will produce zero selecting the corresponding value stored in the ROM. In case of the Binary ROM: 4th NAND will enable B[2].But the 5th NAND will enable B[1] and B[2]. then the value obtained is 111 while either 011 or 100 was expected. In case of Gray ROM: 4th NAND will enable G[2] and G[1].But the 5th NAND will enable G[1]. And the value obtained will be 110 which is true. Gray-code encoding allows only one bit in the output to change at a time. The comparator outputs are first converted to gray-code encoding and then later decoded to binary. 15
Advantages and Disadvantages Advantages Very large Bandwidth A special nonlinear behaviour can be approached by varying the values of the resistors in the ladder, which could be used in some applications. Disadvantages Area (2 N -1 comparators) Power and Cost limited resolution (Max 8 or 10 bits) 16
Semi-Flash ADC For a trial to decrease the area and the number of comparators used. 2 flash ADCs are used, each will output half the number of bits; coarse ADC to output the most significant bits & fine ADC to output the least significant bits. The number of comparators are reduced drastically : Example: An 8-bit flash ADC has : (2^N - 1) ; N= 8 ; 255 comparators. An 8-bit semi-flash is realized by having two 4-bit flash ADCs (2^Nc -1) + ( 2^Nf -1) ; Nc = 4, Nf = 4 ; = 15 + 15 = 30 comparators. 17
Semi-Flash ADC The Semi-Flash has 2 extra blocks : DAC & subtractor Thus the latency of this ADC would be more than 2 times of the Flash latency, because the coarse ADC waits for the output of the fine ADC. - An amplifier of G = 2^Nc would be added after subtractor -to avoid the small residue signals that are sensitive to noise. -to make the signal swing equal for both ADCs - to simplify the design, Both ADCs use same Ladder. 18
Pipelined ADC... Binary search.. 19
Pipelined ADC... Basic Architecture 20
Pipelined ADC... To check in the binary tree: check polarity of Vin - α Vref. where α= ½, ¼ or ¾, ⅛ or ⅜ or ⅝ or ⅞,...so on α changes every stage!! But we need a recursive function.. Assume we have the function f=vres f(vin, Vref) = 2 Vin - Vref if Vin > 1/2 Vref = 2 Vin if Vin < 1/2 Vref 21
Pipelined ADC... For the 1st stage: if (Vin > ½ Vref ) then f(vin, Vref) = 2 Vin - Vref = 2*(Vin - ½ Vref) First check # else f(vin, Vref) = 2 Vin.Second check # end if; next stage it must be (Vin - ¾ Vref) for first check and (Vin - ¼ Vref) for second check.. 22
Pipelined ADC... For the 2nd stage: First check f(2 Vin - Vref, Vref) = 4 Vin - 2 Vref - Vref = 4*(Vin - ¾ Vref) Second Check f(2 Vin, Vref) = 4 Vin - Vref = 4*(Vin - ¼ Vref) *You can go on and check all the following steps to make sure you get the binary search right. 23
Pipelined ADC... MDAC Implementation.. 24
Pipelined ADC... Adding comparators to the design.. 25
Pipelined ADC... Fully differential from -Vref to Vref 1 Bit/stage ADC Over range problems due to: 1. gain/slope: (a result of capacitors mismatch). 2. Comparator offset: (ex, if -1mV input was read as 2 mv). 26
Pipelined ADC... 1.5 bit/stage ADC: f(vin, Vref) = 2 Vin - Vref if Vin > ¼Vref = 2 Vin if -¼Vref < Vin < ¼Vref = 2 Vin + Vref if Vin < -¼Vref 27
Summary of an MDAC stage O/P Figure. MDAC structure
Summary of an MDAC stage Fig. Sampling and Conversion Configurations for an MDAC
Latency vs Throughput! Fig. Pipelined behavior of the ADC
- Stages operate on the input like a shift register. - New output data EVERY clock cycle, but each stage introduces at least one half clock Latency.
Digital Correction - The DCL is actually a simple circuit of Half & Full adders to add the LSB of the higher stage ( the error bit) to the MSB (certain bit) of the next stage.. The Last stage LSB is TRUNCATED! - As long as the individual thresholds deviate no more than V r /4 from an ideal value, then the error can be corrected by adding shifted digital outputs of each of the stages.
High Speed Problems - OpAmp Finite gain Sol? Use a high gain Cascode amplifier designed to give a 20dB gain around the sampling frequency. - Capacitances Mismatching & the appearance of parasitic capacitances Sol? Design the feedback gain of the OpAmp including Cp in the calculations Accurate capacitance matching between Cs and Cf.
High Speed Problems Fig. Cascode Structure Amplifier For High Gain
References http://www.ti.com/lit/an/slaa510/slaa510.pdf http://www.te.kmutnb.ac.th/msn/223361report512.pdf SAR, Pipelined Versus. "A Tale of Two ADCs." IEEE SOLID-STATE CIRCUITS 39 (2015). http://www.ece.umn.edu/~harjani/courses/8331/adc-pipeline_lecture.pdf http://www.allaboutcircuits.com/textbook/digital/chpt-13/flash-adc/ https://www.maximintegrated.com/en/app-notes/index.mvp/id/810 https://www.researchgate.net/publication/274713910_thermometer_to_gray_encoders http://www.analog.com/media/en/training-seminars/tutorials/mt-003.pdf http://www.analog.com/media/en/training-seminars/tutorials/mt-004.pdf https://www.maximintegrated.com/en/app-notes/index.mvp/id/748 Walt Kester, Analog-Digital Conversion, Analog Devices, 2004, ISBN 0-916550-27-3. 37