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基于
ROM
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温度计
解码器
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基于ROM结构的温度计码解码器设计说明书,基于,ROM,结构,温度计,解码器,设计,说明书
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Thermometer-to-Binary Decoders for Flash Analog-to-Digital ConvertersAbstract: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 ConvertersI. INTRODUCTIONApplications 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 with a single stage of parallel comparators, where N is the number of bits in 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 larger 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-binarydecoders 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. DECODERSFour 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. ROMA 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.Figure 1Another 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 thermometer 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.,.B. Ones-CounterThe 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 2In 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 using 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 TreeFigure 3In 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-BasedThe 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 multiplexers used in this work are based on transmission gates. An inverter is used as a buffer in each transmission gate multiplexer.Figure 4III. B EHAVIORAL LEVEL SIMULATIONThe effect of the chosen decoder topology on the ADC performance was evaluated by behavioral level simulations for the four different architectures. The timing difference t between the clock signal and the input signal to each comparator was modeled by a Gaussian distribution, according to 。The timing difference is of concern if no sample-and-hold circuit is used, which is acceptable for converters with a resolution less than 6 bits 12. The timing difference mismatch between the comparators introduces bubble errors. The bubble errors have significant effect on the ADC performance, e.g., in terms of effective number of bits (ENOB). The performance of the decoders can thereby be compared by plotting the ENOB as a function of the standard deviation .A MATLAB model was developed to enable the performance comparison. In the behavioral level simulations a single tone sinusoid input were assumed according to.Figure 5where VFS is the full-scale voltage. An approximation of the maximum time derivative of the input is The effect of the timing difference is therefore an uncertainty in the sampled input voltage, . Using (3), the maximum uncertainty in the sampled input voltage has a Gaussian distribution according to .The uncertainty is added to the input in the simulations. The sampling time uncertainty is therefore modeled as an offset voltage on the input of the comparators, given by (4). This model was used in the MATLAB simulations of a flash ADC with the four different decoders, i.e., the ROM decoder with 3-input NAND gates for bubble error correction, the ones-counter decoder, the MUX-based decoder, and the 4-level folded Wallace tree decoder. The results of the simulations are shown in Fig. 6. In Fig. 6 the average ENOB of a 6-bit ADC is plotted as a function of the standard deviation of the timing difference between he clock lines and the signal lines, i.e., . As seen in the figure the performance of the MUX-based decoder is about the same as for the ROM decoder with 3-input NAND gates used for the bubble error correction. Note that the MUX-based decoder has no special bubble error correction circuits. It is also seen that the ones-counter decoder has better performance than both the ROM decoder and the MUXbased decoder. Finally, the 4-level folded Wallace tree decoder has a slightly lower average ENOB than the ones-counter. The reason for this is that the folded Wallace tree topology is more sensitive to bubble errors at the thermometer input levels that are connected to the 3-input OR gates shown in Fig. 4, since these levels control the MUX seen in the same figure.Figure 6IV. MEASUREMENT RESULTSFrom the behavioral simulation we saw that the ones-counter decoder was the most insensitive to bubble errors. Of the other decoders, the MUX-based stands out as having the lowest hardware cost, but a somewhat higher sensitivity to bubble errors. We choose these two decoders for hardware
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