Thermometer-to-Binary Decoders for Flash
80年代文学Analog-to-Digital Converters
Abstract:Decoders for low power, high-speed flash ADCs are investigated. The sensitivity to bubble errors of the ROM decoder with error correction, ones-counter, 4-level folded Wallace-tree, and multiplexer-based decoder are simulated. The ones-counter and multiplexer-based decoder,corresponding to the error insensitive and hardware efficient cases, are implemented in a 130 nm CMOS SOI technology. Measurements yield an ENOB of about 4.1 bit for both, and energy consumption of 80 pJ and 60 pJ, for the respective decoders. Hence we conclude that the MUX-based decoder seems to be a good choice with respect to area, efficiency, and speed.
Key words: Thermometer-to-Binary flash ADCs Converters
I. INTRODUCTION
Applications like ultra-wideband radio and the read channel in hard disk drives generally require high-speed analog-to-digital conversion with resolution four to six bits. These requirements are commonly satisfied by the flash analog-to-digital converter (ADC) architecture [1] that converts the analog input to a binary output
N parallel comparators, where N is the number of bits in with a single stage of 1
2
the output, followed by a digital decoder. The comparators compare the input with the quantization levels from a set of reference voltages generated by a resistive ladder and produce a logical output depending on the outcome of the comparison. The output pattern from this stage corresponds to thermometer code and is subsequently translated to binary code by the digital decoder, i.e. the thermometer-to-binary decoder. For a low speed converter the input to the decoder is indeed a perfect thermometer code, but for high speed there may be some erroneous bits in the thermometer code, so called bubbles [2]. The bubbles are due to a number of sources [3], e.g., metastability, offset, crosstalk, and bandwidth limitations of the comparators, uncertainty in the effective sampling instant, etc. Hence the decoder must be able to perform well even in the presence of the bubble errors in a high-speed converter.
Including requirements on power consumption and throughput, we see that the decoder must be paid significant consideration and trade-off in the design of a high-speed converter. In this work we focus on the design of decoders for low-power, high-speed six-bit ADCs. The work is a part of a larg
er project where the overall aim is to develop design techniques for implementation of high-performance analog circuits in CMOS silicon-on-insulator technology. We have investigated four types of thermometer-to-binary
decoders presented in Sec. II, through behavioral level simulations of the sensitivity to bubble errors presented in Sec. III, from which we have chosen two decoders that have been implemented in a 130 nm CMOS SOI technology. The measurement results are presented in Sec. IV and the conclusions are given in Sec. V.
II. DECODERS电子光学
Four different types of thermometer-to-binary decoders are presented. Two of them, the ROM and folded Wallace tree decoder,are only studied on behavioral level. The ones-counter decoder and the MUX-based decoder have also been implemented in two flash ADCs in a CMOS silicon-on-insulator technology. The corresponding results are thereby based on transistor level simulation results and measurements.
A. ROM
A common and straightforward approach to encode the thermometer code is to use a gray or binary-encoded ROM. The appropriate row m in the gray encoded ROM is selected by using a row decoder that has the output of comparator m and the inverse of comparator m + 1 as inputs. The output m of the row decoder, connected to memory row m, is high if the output of comparator m is high and the output of comparator m + 1 is low. The row decoder can be realized by, e.g., a number of 2-input NAND gates, where one input to each NAND gate is inverted. This type of row decoder selects multiple rows if a bubble error occurs, which introduces large errors in the output of the decoder [3], [4]. Considering single bubble errors only, these errors can be corrected by using 3-input NAND gates, as shown in Fig. 1. The 3-input NAND gates remove all bubble errors if they are separated by at least three bits in the thermometer scale. The main advantage of the ROM decoder approach is
its regular structure that is straightforward to design. A disadvantage is that more bubble errors are introduced as the conversion speed increases and a more advanced bubble error correction scheme is required. As the complexity of the bubble error correction circuit increases, its propagation delay does in general also increase. The longer propagation delay reduces the maximum sampling rate of the overall decoder if not pipelining is applied. The increased complexity of the circuit consumes more chip area and will likely consume more power [5], [6].
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Another bubble error suppression technique is the butterfly sorting technique presented in [7]. Applying this technique the bubbles are propagated upwards in the thermometer scale until the thermometer code is free from bubbles. Then the ROM decoder is used to encode the bubble-free th路网密度
ermometer code to binary code. In [7] the butterfly sorter only has eight levels. Bubbles further away from the transition level than eight positions cannot be removed. To guarantee that no bubbles will be present in the thermometer output code the depth of the butterfly sorter must be equal to the number of comparators, i.e.,12 N .
B. Ones-Counter
The output of a thermometer-to-binary decoder is the number of ones on the input represented in, e.g., gray or binary code. Hence a circuit counting the number of ones in the thermometer code, i.e., a ones-counter, can be used as the decoder [8].
The use of a ones-counter gives global bubble error suppression [3], [6], [8]. Another benefit of the approach is that a suitable ones-counter topology may be selected by trading speed for power. From this tradeoff the Wallace tree topology [9], illustrated in Fig. 2, is a good candidate as a decoder for high-speed converters [3], [6], [10].
Figure 2
In this work we use a tree of full adders (FAs) that reduce the 63 inputs to 10 outputs, as illustrated by Fig. 3. The different signal paths through the decoder are matched, i.e., each signal passes through the same number of full adders, where each input has approximately the same propagation delay to the output. The propagation delay of the signals through the decoder should thereby be approximately the same for all signals. The decoding of the 10 outputs to the binary value is done us
ing MATLAB. The depth of the tree is thereby limited to six levels in the hardware implementation presented in the next section, which enables the ADC to operate at higher speed. In an improved design the complete decoding to a binary output can be accomplished
onchip by introducing pipelining in the decoder. Further optimization of the sizing of each FA can also improve the performance to some degree.
C. Folded Wallace Tree
In a folded flash ADC, the idea is to reduce the amount of hardware by using the same comparator for different reference voltages [11]. This is the idea of the folded Wallace tree decoder shown in Fig. 4 [6]. The size of the Wallace tree and the delay depend on the number of bits that are added, i.e. the width of the base of the tree. The idea is to split the output of the comparators into different intervals. They are multiplexed to a reduced Wallace tree decoder, which is smaller compared with the full one [3]. A full adder may be realized from three 2:1 multiplexers with two multiplexers in the critical path.
D. MUX-Based
The multiplexer-based decoder consists entirely of multiplexers, as illustrated in Fig. 5, where N = 4 bit. It requires less hardware and has a shorter critical path than a ones-counter decoder [3], [5]. In addition it gives bubble error suppression, although the suppression is slightly lower than for a ones-counter decoder [5]. Another advantage of the multiplexer-based decoder is the more regular structure than, e.g., the ones-counter decoder. This is a major benefit in the layout of the circuit. The
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