A 2.6 GS/s 8-Bit Time-Interleaved SAR ADC in 55 nm CMOS Technology

: This paper presents an eight-channel time-interleaved (TI) 2.6 GS/s 8-bit successive approximation register (SAR) analog-to-digital converter (ADC) prototype in a 55-nm complementary metal-oxide-semiconductor (CMOS) process. The channel-selection-embedded bootstrap switch is adopted to perform sampling times synchronization using the full-speed master clock to suppress the time skew between channels. Based on the segmented pre-quantization and bypass switching scheme, double alternate comparators clocked asynchronously with background offset calibration are utilized in sub-channel SAR ADC to achieve high speed and low power. Measurement results show that the signal-to-noise-and-distortion ratio (SNDR) of the ADC is above 38.2 dB up to 500 MHz input frequency and above 31.8 dB across the entire ﬁrst Nyquist zone. The differential non-linearity (DNL) and integral non-linearity (INL) are +0.93/ − 0.85 LSB and +0.71/ − 0.91 LSB, respectively. The ADC consumes 60 mW from a 1.2 V supply, occupies an area of 400 µ m × 550 µ m, and exhibits a ﬁgure-of-merit (FoM) of 348 fJ/conversion-step.


Introduction
High-speed analog-to-digital converters (ADCs) with a moderate resolution of 6-8 bits while maintaining excellent power efficiency for longer battery life are highly demanded for applications such as 802.11ad (WiGig) radio architectures and the next-generation mobile communication system (5G) [1].Compared with flash and pipeline ADC, successive approximation register (SAR) ADC has superior energy efficiency and is more suitable for the aggressive downscaling of technology because of its primarily digital nature [2][3][4].In order to overcome the speed limitation of a single ADC, time-interleaved (TI) architecture running multiple parallel ADCs is an attractive approach.In general, TI SAR ADC is the most feasible solution to realize both over GHz operation and medium resolution around 8-bit [5].However, the inter-channel non-ideal factors like offset, gain mismatch, and time skew, will deteriorate the overall performance [6], and can be compensated for by either circuit improvement in the analog domain or special digital calibration.As digital calibration is often complex, it is preferred to minimize these mismatches using on-chip design optimization to relax calibration requirements, especially when the number of interleaved channels is not large.
This paper demonstrates a 2.6 GS/s 8-bit SAR ADC prototype with an eight-channel direct sampling TI architecture.In the sampling front-end, in order to suppress the time skew error among different channels, the channel-selection-embedded bootstrap switch is used as the sampling switch to ensure the uniformity of sampling times by the master clock.In the sub-channel SAR ADC design, segmented pre-quantization and a bypass switching scheme is employed to avoid unnecessary large capacitors switching, reducing power consumption and non-linearity.Double comparators clocked asynchronously in alternate mode are used to improve the conversion rate, with the background offset calibration function integrated on-chip.This ADC exhibits lower calibration complexity and achieves an acceptable efficiency in terms of area and power consumption.

Proposed TI SAR ADC Architecture
TI structures can generally be categorized as hierarchical sampling and direct sampling.In a hierarchical sampling structure, there are at least two sampling switches in series in each sub-channel.In contrast, a direct sampling architecture, wherein all parallel channels have individual sample/hold circuits, provides the shortest signal transmission path from the input to the sampling capacitors, and is very efficient for a small number of parallel channels (usually ≤8) [7].
In this design, a direct sampling architecture is adopted to implement the 2.6 GS/s 8-bit TI ADC prototype, which mainly consists of multi-phase clock generator (MPCG), sampling switch, eight-channel 325 MS/s 8-bit SAR ADC, and multiplexer (MUX), as depicted in Figure 1.
Electronics 2019, 8, x FOR PEER REVIEW 2 of 12 to ensure the uniformity of sampling times by the master clock.In the sub-channel SAR ADC design, segmented pre-quantization and a bypass switching scheme is employed to avoid unnecessary large capacitors switching, reducing power consumption and non-linearity.Double comparators clocked asynchronously in alternate mode are used to improve the conversion rate, with the background offset calibration function integrated on-chip.This ADC exhibits lower calibration complexity and achieves an acceptable efficiency in terms of area and power consumption.

Proposed TI SAR ADC Architecture
TI structures can generally be categorized as hierarchical sampling and direct sampling.In a hierarchical sampling structure, there are at least two sampling switches in series in each sub-channel.In contrast, a direct sampling architecture, wherein all parallel channels have individual sample/hold circuits, provides the shortest signal transmission path from the input to the sampling capacitors, and is very efficient for a small number of parallel channels (usually ≤8) [7].
In this design, a direct sampling architecture is adopted to implement the 2.6 GS/s 8-bit TI ADC prototype, which mainly consists of multi-phase clock generator (MPCG), sampling switch, eightchannel 325 MS/s 8-bit SAR ADC, and multiplexer (MUX), as depicted in Figure 1.The current-mode logic (CML) sinusoidal input clock signal is buffered and then transformed to complementary metal-oxide-semiconductor (CMOS) level full-speed master clock CKmaster.The multiphase clock pulse signals CKch,1-CKch,8 are generated from CKmaster using the cascaded D flip-flop (DFF) chain [8][9][10] and combinational logic circuits using synchronous frequency division, as shown in Figure 2a.The DFF is constructed using two latches [11], as shown in Figure 2b.The internal signals q1, q2, q3 and q4 with a duty cycle of 50% are the divide-by-eight clocks of CKmaster such that a clock pulse signal CKdiv8 with a duty cycle of 12.5% is obtained through AND logic operation.Since the initial state of the shift registers is uncertain, the feedback logic is added to activate self-starting such that the MPCG can automatically return from the non-ideal state to normal.The shift operation of CKdiv8 is executed to get CKch,1-CKch,8, which have definite phase sequence relationships and the delay between each other is one period of CKmaster, as shown in Figure 2c.The non-overlapping sampling phases guarantee that only one sampling switch is turned on, thus reducing the channel load at the input.CKch,1-CKch,8 are not only used as the control signals for the sampling switches, but also initiate the conversion process of each channel.
As the input signal is sampled onto the capacitors array of respective sub-ADC sequentially for quantization, the sampling instants are controlled uniformly using CKmaster to mitigate the time skew between channels.Finally, the multi-path digital outputs from the sub-ADCs array are aggregated into a one-way data stream using MUX.The DFF is constructed using two latches [11], as shown in Figure 2b.The internal signals q1, q2, q3 and q4 with a duty cycle of 50% are the divide-by-eight clocks of CK master such that a clock pulse signal CK div8 with a duty cycle of 12.5% is obtained through AND logic operation.Since the initial state of the shift registers is uncertain, the feedback logic is added to activate self-starting such that the MPCG can automatically return from the non-ideal state to normal.The shift operation of CK div8 is executed to get CK ch,1 -CK ch,8 , which have definite phase sequence relationships and the delay between each other is one period of CK master , as shown in Figure 2c.The non-overlapping sampling phases guarantee that only one sampling switch is turned on, thus reducing the channel load at the input.CK ch,1 -CK ch,8 are not only used as the control signals for the sampling switches, but also initiate the conversion process of each channel.
As the input signal is sampled onto the capacitors array of respective sub-ADC sequentially for quantization, the sampling instants are controlled uniformly using CK master to mitigate the time skew between channels.Finally, the multi-path digital outputs from the sub-ADCs array are aggregated into a one-way data stream using MUX.

Channel-Selection-Embedded Bootstrap Switch
Time skew refers to the mismatch in the sampling instants among TI channels, which originated from the non-uniform sampling clock edges [12].Some timing-skew, calibration-free techniques have been proposed to suppress the time skew by circuit design and layout [13][14][15].We attempted to realize similar skew tolerance via circuit improvement in the analog domain for design simplicity rather than digital calibration with complex algorithms that will consume extra hardware and power.The channel-selection-embedded bootstrap switch [16] is utilized in the sampling front-end, so that the sampling instants of each channel are aligned to the master clock CK master , while the corresponding TI clock signals CK ch,i (i = 1-8) are used to perform the channel selection, as described in Figure 3.

Channel-Selection-Embedded Bootstrap Switch
Time skew refers to the mismatch in the sampling instants among TI channels, which originated from the non-uniform sampling clock edges [12].Some timing-skew, calibration-free techniques have been proposed to suppress the time skew by circuit design and layout [13][14][15].We attempted to realize similar skew tolerance via circuit improvement in the analog domain for design simplicity rather than digital calibration with complex algorithms that will consume extra hardware and power.The channel-selection-embedded bootstrap switch [16] is utilized in the sampling front-end, so that the sampling instants of each channel are aligned to the master clock CKmaster, while the corresponding TI clock signals CKch,i (i = 1-8) are used to perform the channel selection, as described in Figure 3.When CKch,i becomes high, the switching transistor M0 is turned on, and the channel begins to track the input signal.CKen,i is a delayed version of CKch,i, used to prepare for sampling synchronization.When CKen,i is high, once the rising edge of CKmaster comes, M1 and M2 are both turned on, and the gate voltage VG of M0 is released from Vin + VDD to the ground level, thus the sampling instants are determined by the rising edge of CKmaster.Then, the channel finishes the sampling process and enters the holding phase.As CKen,i goes low, the gate of M0 is in floating state and vulnerable to the interference of other signals.M3 from CKr,i provides a discharging path, and the VG is fixed to the ground level, therefore avoiding the floating node at the holding phase.The inter-channel sampling synchronization that is determined uniformly by CKmaster ensures the consistency of the sampling instants, and it is beneficial to suppress the time skew among channels.

Asynchronous Timing of Alternate Comparators
The sub-ADC is implemented with 325 MS/s 8-bit SAR ADC [17], including fundamental building blocks, such as capacitive digital-to-analog converter (CDAC), comparators and control logic, as illustrated in Figure 4a.When CK ch,i becomes high, the switching transistor M 0 is turned on, and the channel begins to track the input signal.CK en,i is a delayed version of CK ch,i , used to prepare for sampling synchronization.When CK en,i is high, once the rising edge of CK master comes, M 1 and M 2 are both turned on, and the gate voltage V G of M 0 is released from V in + V DD to the ground level, thus the sampling instants are determined by the rising edge of CK master .Then, the channel finishes the sampling process and enters the holding phase.As CK en,i goes low, the gate of M 0 is in floating state and vulnerable to the interference of other signals.M 3 from CK r,i provides a discharging path, and the V G is fixed to the ground level, therefore avoiding the floating node at the holding phase.The inter-channel sampling synchronization that is determined uniformly by CK master ensures the consistency of the sampling instants, and it is beneficial to suppress the time skew among channels.

Asynchronous Timing of Alternate Comparators
The sub-ADC is implemented with 325 MS/s 8-bit SAR ADC [17], including fundamental building blocks, such as capacitive digital-to-analog converter (CDAC), comparators and control logic, as illustrated in Figure 4a.If only one comparator is used in the SAR ADC, the comparator needs to be fully reset to avoid the residual effect from the previous conversion process, so the overall conversion speed is slowed down.Double dynamic comparators with cross-coupled latches are used [18], and the preamplifier has been designed for moderate gain to reduce its offset, and more importantly, to limit the kick-back noise from the latch [19].The two comparators are clocked asynchronously in alternate operation, as shown in Figure 4b.Under the control of CK1 and CK2, when one comparator is in a comparison state, another comparator is reset, reducing the impact of reset time on the critical path, and thus improving the conversion speed [20].Once the preceding comparison is over, a successful decision is detected as the trigger signal for the following comparison process.This asynchronous conversion process repeats like dominoes until all bits are resolved [21].
The pulse labeled "CC" corresponds to the operation for the compensation capacitor in the CDAC.At the end of the conversion, the inputs of the comparators are shorted together using CKreset for calibration purposes.With the pulse labeled "cal" the background offset calibration based on the charge pump principle in the analog domain for each comparator is carried out once every two cycles.

The Background Offset Calibration of Comparator
The diagram of comparator's background offset calibration is shown in Figure 5.An auxiliary differential pair is introduced to calibrate the offset voltage of the comparator.Only the generation circuit of Vcalp is presented.Another calibration voltage Vcaln can be generated in two ways, one is set to a constant voltage using a resistive voltage divider [20], and the other is similar to the generation of Vcalp, except that the corresponding control voltage is different.In this design, the latter method is adopted.Vcalp and Vcaln change in opposite directions and jointly cancel the impact of the offset.If only one comparator is used in the SAR ADC, the comparator needs to be fully reset to avoid the residual effect from the previous conversion process, so the overall conversion speed is slowed down.Double dynamic comparators with cross-coupled latches are used [18], and the preamplifier has been designed for moderate gain to reduce its offset, and more importantly, to limit the kick-back noise from the latch [19].The two comparators are clocked asynchronously in alternate operation, as shown in Figure 4b.Under the control of CK1 and CK2, when one comparator is in a comparison state, another comparator is reset, reducing the impact of reset time on the critical path, and thus improving the conversion speed [20].Once the preceding comparison is over, a successful decision is detected as the trigger signal for the following comparison process.This asynchronous conversion process repeats like dominoes until all bits are resolved [21].
The pulse labeled "C C " corresponds to the operation for the compensation capacitor in the CDAC.At the end of the conversion, the inputs of the comparators are shorted together using CK reset for calibration purposes.With the pulse labeled "cal" the background offset calibration based on the charge pump principle in the analog domain for each comparator is carried out once every two cycles.

The Background Offset Calibration of Comparator
The diagram of comparator's background offset calibration is shown in Figure 5.An auxiliary differential pair is introduced to calibrate the offset voltage of the comparator.Only the generation circuit of V calp is presented.Another calibration voltage V caln can be generated in two ways, one is set to a constant voltage using a resistive voltage divider [20], and the other is similar to the generation of V calp , except that the corresponding control voltage is different.In this design, the latter method is adopted.V calp and V caln change in opposite directions and jointly cancel the impact of the offset.
During the offset calibration phase of the comparator, the input signals V ip and V in of the main differential pair are shorted together.In the case of no offset, V ip = V in , then the output voltage of the preamplifier stage is equal, that is, V A = V B .Finally, the output signal of the comparator OUTP = OUTN = 0, and the corresponding complementary output signal OUTP = OUTN = 1.At this time, M5 and M8 are on, the upper capacitor C p is charged to the power supply, and the lower C p is discharged to the ground level.Both M6 and M7 are off, and the calibration voltage V calp remains unchanged.There is no calibration effect yet.If the offset exists, OUTP or OUTN will change.Usually, the output changes caused by offset can be equivalent to the input changes.Taking an offset output case as an example, if OUTP = 0 and OUTN = 1, this offset effect is the same as the situation when Vip < Vin.Note that VA > VB now.In the calibration voltage generation circuit, M6 is turned on, the voltage on Cp charges Ccal, and Vcalp is pumped up.Then Vcalp is fed back to the preamplifier input stage such that VA decreases to approximate VB.After a number of calibration cycles, once the decreasing VA is equal to VB, OUTP = OUTN, thereby realizing offset calibration.The calibration step size or accuracy is related to the capacitance values of Cp and Ccal.The parasitic capacitor can be used as Cp, which is usually small.The larger the calibration capacitor Ccal, the higher the calibration accuracy and the better the calibration effect.However, a large Ccal will affect the calibration settling time, and a trade-off between calibration accuracy and settling time is required to determine the value of Ccal.

Segmented Pre-Quantization and Bypass Switching Scheme
The control logic is used to generate internal asynchronous clocks, register the decision results of the comparators, and control the switching of the CDAC accordingly [20].Several typical powerefficient switching sequences for CDAC, such as monotonic [22], splitting monotonic [23], and bypass switching techniques, have been proposed to improve the power efficiency.According to the reference [24], it was observed that the bypass method yields better results with less switching activity [25][26][27] because of the basic idea to skip the conversion steps for several significant bits when the signal is within a predefined window.Moreover, the skip operation reduces the error accumulation to improve the static performance.In this design, the CDAC is built with a segmented pre-quantization and bypass switching scheme [28], and the actual differential structure is displayed as single-ended for clarity in Figure 6.If the offset exists, OUTP or OUTN will change.Usually, the output changes caused by offset can be equivalent to the input changes.Taking an offset output case as an example, if OUTP = 0 and OUTN = 1, this offset effect is the same as the situation when V ip < V in .Note that V A > V B now.In the calibration voltage generation circuit, M6 is turned on, the voltage on C p charges C cal , and V calp is pumped up.Then V calp is fed back to the preamplifier input stage such that V A decreases to approximate V B .After a number of calibration cycles, once the decreasing V A is equal to V B , OUTP = OUTN, thereby realizing offset calibration.The calibration step size or accuracy is related to the capacitance values of C p and C cal .The parasitic capacitor can be used as C p , which is usually small.The larger the calibration capacitor C cal , the higher the calibration accuracy and the better the calibration effect.However, a large C cal will affect the calibration settling time, and a trade-off between calibration accuracy and settling time is required to determine the value of C cal .

Segmented Pre-Quantization and Bypass Switching Scheme
The control logic is used to generate internal asynchronous clocks, register the decision results of the comparators, and control the switching of the CDAC accordingly [20].Several typical power-efficient switching sequences for CDAC, such as monotonic [22], splitting monotonic [23], and bypass switching techniques, have been proposed to improve the power efficiency.According to the reference [24], it was observed that the bypass method yields better results with less switching activity [25][26][27] because of the basic idea to skip the conversion steps for several significant bits when the signal is within a predefined window.Moreover, the skip operation reduces the error accumulation to improve the static performance.In this design, the CDAC is built with a segmented pre-quantization and bypass switching scheme [28], and the actual differential structure is displayed as single-ended for clarity in Figure 6.The capacitors array of CDAC is divided into two parts with high and low weight by the switch Smerge.To keep the comparator's input common-mode voltage constant, each capacitor is split into two identical small capacitors.The input signal is sampled onto the capacitors array via channelselection-embedded bootstrap switches.
After sampling, all the switches are turned off, and only the low-weight capacitors array is connected to the comparator, equivalent to a 4-bit ADC.The comparator directly performs the first comparison without switching any capacitors to obtain the first digital code D1 [22], which is fed back to switch the minimum capacitor 8C in the high-weight capacitors array, providing an initial voltage.The subsequent digital codes D2-D4 are compared with D1, as Figure 6a shows.If one of the codes is the same as D1, that means the previous output of the CDAC is not enough, so the associated large capacitor is switched, contributing a corresponding weight output to the CDAC.In case the code is different from D1, it indicates that the last output of the CDAC is excessive, and the relevant large capacitor is bypassed, just maintaining the original state without switching.The monotonic procedure is either upward or downward to avoid unnecessary opposite direction switching of highweight large capacitors, therefore reducing the power consumption and nonlinearity.
Once the high-weight capacitors are properly set, the switch Smerge is turned on, and the two arrays are merged.Meanwhile the low-weight capacitors array is reset to the initial condition.Then, the entire structure is changed back to 8-bit ADC, entering the residual quantization phase for the low 4-bit digital codes D5-D8, as shown in Figure 6b.In the whole conversion process, all quantization is done using the low-weight capacitors array, relaxing the settling constraints of the CDAC.
Ideally, the proportion of 4C in the low-weight capacitors array should be the same as that of 64C in the whole capacitors array, both being 1/2.However, the presence of parasitic capacitance changes the ratio.Since the total capacitance of high-weight capacitors array is much larger than that of low-weight capacitors array, even the same parasitic capacitance will occupy different proportions in different weight capacitor arrays, resulting in gain errors in CDAC output between high 4-bit coarse quantization and low 4-bit global quantization stages, so it is necessary to insert equilibrium The capacitors array of CDAC is divided into two parts with high and low weight by the switch S merge .To keep the comparator's input common-mode voltage constant, each capacitor is split into two identical small capacitors.The input signal is sampled onto the capacitors array via channel-selection-embedded bootstrap switches.
After sampling, all the switches are turned off, and only the low-weight capacitors array is connected to the comparator, equivalent to a 4-bit ADC.The comparator directly performs the first comparison without switching any capacitors to obtain the first digital code D1 [22], which is fed back to switch the minimum capacitor 8C in the high-weight capacitors array, providing an initial voltage.The subsequent digital codes D2-D4 are compared with D1, as Figure 6a shows.If one of the codes is the same as D1, that means the previous output of the CDAC is not enough, so the associated large capacitor is switched, contributing a corresponding weight output to the CDAC.In case the code is different from D1, it indicates that the last output of the CDAC is excessive, and the relevant large capacitor is bypassed, just maintaining the original state without switching.The monotonic procedure is either upward or downward to avoid unnecessary opposite direction switching of high-weight large capacitors, therefore reducing the power consumption and nonlinearity.
Once the high-weight capacitors are properly set, the switch S merge is turned on, and the two arrays are merged.Meanwhile the low-weight capacitors array is reset to the initial condition.Then, the entire structure is changed back to 8-bit ADC, entering the residual quantization phase for the low 4-bit digital codes D5-D8, as shown in Figure 6b.In the whole conversion process, all quantization is done using the low-weight capacitors array, relaxing the settling constraints of the CDAC.
Ideally, the proportion of 4C in the low-weight capacitors array should be the same as that of 64C in the whole capacitors array, both being 1/2.However, the presence of parasitic capacitance changes the ratio.Since the total capacitance of high-weight capacitors array is much larger than that of low-weight capacitors array, even the same parasitic capacitance will occupy different proportions in different weight capacitor arrays, resulting in gain errors in CDAC output between high 4-bit coarse quantization and low 4-bit global quantization stages, so it is necessary to insert equilibrium capacitor (denoted as C E ) to balance the parasitic differences between the two capacitor arrays, as shown below: C H and C L represent the total capacitance of high and low weight capacitors array, respectively; that is, C H = 64C + 32C + 16C + 8C = 120C, C L = 4C + 2C + C + C = 8C.C PH and C PL represent the parasitic capacitance respectively, which can be obtained from the layout parameters extraction.
In order to further solve the potential wrong conversion caused by inaccurate parameter extraction and manufacturing process variation, a compensation capacitor (denoted as C C ) with the weight of 4 is used to provide 1-bit redundancy (corresponding to digital code D C ), whose error correction range is up to 4/128 = 3.125%.
The gain error of TI SAR ADC mainly comes from the parasitic effect and capacitance mismatch of CDAC.When selecting a capacitor size, there are two main factors to consider: thermal noise (kT/C) and matching accuracy [9].A compact and reasonable CDAC layout is deliberately designed by using full-custom metal-oxide-metal (MOM) capacitors [29] with the unit capacitance of 1.5 fF.Benefiting from 1-bit redundancy, intrinsic capacitor matching, and careful layout routing, the gain error can be minimized to a tolerant level [30].

Measured Results
The ADC prototype was manufactured in a 55-nm one-poly nine-metal (1P9M) CMOS process with a core area of 400 µm × 550 µm, and a large number of decoupling capacitors were filled inside the chip to keep the power supply voltage clean and stable.The die micrograph is shown in Figure 7. capacitor (denoted as CE) to balance the parasitic differences between the two capacitor arrays, as shown below: CH and CL represent the total capacitance of high and low weight capacitors array, respectively; that is, CH = 64C + 32C + 16C + 8C = 120C, CL = 4C + 2C + C + C = 8C.CPH and CPL represent the parasitic capacitance respectively, which can be obtained from the layout parameters extraction.
In order to further solve the potential wrong conversion caused by inaccurate parameter extraction and manufacturing process variation, a compensation capacitor (denoted as CC) with the weight of 4 is used to provide 1-bit redundancy (corresponding to digital code DC), whose error correction range is up to 4/128 = 3.125%.
The gain error of TI SAR ADC mainly comes from the parasitic effect and capacitance mismatch of CDAC.When selecting a capacitor size, there are two main factors to consider: thermal noise (kT/C) and matching accuracy [9].A compact and reasonable CDAC layout is deliberately designed by using full-custom metal-oxide-metal (MOM) capacitors [29] with the unit capacitance of 1.5 fF.Benefiting from 1-bit redundancy, intrinsic capacitor matching, and careful layout routing, the gain error can be minimized to a tolerant level [30].

Measured Results
The ADC prototype was manufactured in a 55-nm one-poly nine-metal (1P9M) CMOS process with a core area of 400 μm × 550 μm, and a large number of decoupling capacitors were filled inside the chip to keep the power supply voltage clean and stable.The die micrograph is shown in    The output fast Fourier transform (FFT) spectrum is shown in Figure 9 at a 115 MHz input frequency and 2.6 GS/s, with an spurious-free dynamic range (SFDR) of 52.0 dB and signal-to-noiseand-distortion ratio (SNDR) of 41.52 dB. Figure 10 shows SNDR and SFDR versus input frequency at 2.6 GS/s.Within the input frequency range of 500 MHz, the SFDR was greater than 47.9 dB, the SNDR was greater than 38.2 dB, and the effective number of bits (ENOB) was greater than 6-bit.SFDR was above 40.3dB and SNDR was above 31.8dB in the first Nyquist zone.However, as the input frequency increased to the Nyquist frequency, the SNDR decreased by about 9 dB, which was much lower than the expected theoretical values.This result reveals that although the proposed method could suppress sample/hold circuit mismatch, the performance was not satisfactory in the highfrequency region due to other non-ideal factors, such as the master clock path mismatch, input signal path mismatch, and so on [5].output fast Fourier transform (FFT) spectrum is shown in Figure 9 at a 115 MHz input frequency and 2.6 GS/s, with an spurious-free dynamic range (SFDR) of 52.0 dB and signal-to-noise-and-distortion ratio (SNDR) of 41.52 dB. Figure 10 shows SNDR and SFDR versus input frequency at 2.6 GS/s.Within the input frequency range of 500 MHz, the SFDR was greater than 47.9 dB, the SNDR was greater than 38.2 dB, and the effective number of bits (ENOB) was greater than 6-bit.SFDR was above 40.3dB and SNDR was above 31.8dB in the first Nyquist zone.However, as the input frequency increased to the Nyquist frequency, the SNDR decreased by about 9 dB, which was much lower than the expected theoretical values.This result reveals that although the proposed method could suppress sample/hold circuit mismatch, the performance was not satisfactory in the high-frequency region due to other non-ideal factors, such as the master clock path mismatch, input signal path mismatch, and so on [5].The output fast Fourier transform (FFT) spectrum is shown in Figure 9 at a 115 MHz input frequency and 2.6 GS/s, with an spurious-free dynamic range (SFDR) of 52.0 dB and signal-to-noiseand-distortion ratio (SNDR) of 41.52 dB. Figure 10 shows SNDR and SFDR versus input frequency at 2.6 GS/s.Within the input frequency range of 500 MHz, the SFDR was greater than 47.9 dB, the SNDR was greater than 38.2 dB, and the effective number of bits (ENOB) was greater than 6-bit.SFDR was above 40.3dB and SNDR was above 31.8dB in the first Nyquist zone.However, as the input frequency increased to the Nyquist frequency, the SNDR decreased by about 9 dB, which was much lower than the expected theoretical values.This result reveals that although the proposed method could suppress sample/hold circuit mismatch, the performance was not satisfactory in the highfrequency region due to other non-ideal factors, such as the master clock path mismatch, input signal path mismatch, and so on [5].Based on the simulation results, the total power consumption of 60 mW at 1.2 V supply voltage was composed as follows: 12 mW for the clock generation module and 48 mW for the SAR ADCs array (that is, 6 mW/slice for every sub-ADC).The FoM calculated within the 500 MHz input frequency was 348 fJ/conversion-step.The performance summary is shown in Table 1.

Conclusions
A 2.6 GS/s 8-bit SAR ADC prototype with eight-channel direct sampling TI architecture has been presented.The SNDR was above 38.2dB up to 500 MHz input frequency and above 31.8dB up to the Nyquist frequency.The DNL and INL were +0.93/−0.85LSB and +0.71/−0.91LSB, respectively.The ADC consumed 60 mW, occupied an area of 400 μm × 550 μm, and realized a FoM of 348 fJ/conversion-step.In general, this design is a beneficial attempt of time-skew, calibration-free technology, which achieves acceptable results in low and medium frequency, and provides a reference for related research and design.If the calibration for time skew is used for future work, better performance can be promised.Based on the simulation results, the total power consumption of 60 mW at 1.2 V supply voltage was composed as follows: 12 mW for the clock generation module and 48 mW for the SAR ADCs array (that is, 6 mW/slice for every sub-ADC).The FoM calculated within the 500 MHz input frequency was 348 fJ/conversion-step.The performance summary is shown in Table 1.

Conclusions
A 2.6 GS/s 8-bit SAR ADC prototype with eight-channel direct sampling TI architecture has been presented.The SNDR was above 38.2dB up to 500 MHz input frequency and above 31.8dB up to the Nyquist frequency.The DNL and INL were +0.93/−0.85LSB and +0.71/−0.91LSB, respectively.The ADC consumed 60 mW, occupied an area of 400 µm × 550 µm, and realized a FoM of 348 fJ/conversion-step.In general, this design is a beneficial attempt of time-skew, calibration-free technology, which achieves acceptable results in low and medium frequency, and provides a reference for related research and design.If the calibration for time skew is used for future work, better performance can be promised.

Figure 1 .
Figure 1.Eight-channel time-interleaved (TI) successive approximation register (SAR) analog-to-digital converter (ADC) architecture.The current-mode logic (CML) sinusoidal input clock signal is buffered and then transformed to complementary metal-oxide-semiconductor (CMOS) level full-speed master clock CK master .The multi-phase clock pulse signals CK ch,1 -CK ch,8 are generated from CK master using the cascaded D flip-flop (DFF) chain[8][9][10] and combinational logic circuits using synchronous frequency division, as shown in Figure2a.

Figure 5 .
Figure 5.The diagram of comparator's background offset calibration.

Figure 5 .
Figure 5.The diagram of comparator's background offset calibration.

Figure 6 .
Figure 6.(a) Pre-quantization stage, and (b) global quantization stage in segmented pre-quantization and bypass switching scheme.

Figure 6 .
Figure 6.(a) Pre-quantization stage, and (b) global quantization stage in segmented pre-quantization and bypass switching scheme.

Figure 7 .
Figure 7. Die micrograph with layout view.Figure 7. Die micrograph with layout view.

Figure 7 .
Figure 7. Die micrograph with layout view.Figure 7. Die micrograph with layout view.