This work proposes two versions of a 12 b 100 MS/s successive-approximation register
(SAR) ADC based on a non-binary C-R hybrid DAC. The proposed DAC applies a non-binary
weighted capacitor array to the 7 MSBs to meet the settling requirement of the DAC
output and determines the remaining 5 LSBs using the reference voltages generated
from a simple resistor string to reduce the DAC area significantly. The Version 1
ADC in a 28 nm CMOS adopts a synchronous SAR logic and a comparator with a tail capacitor
and a reset switch to minimize power consumption. The Version 2 ADC in a 0.18 μm CMOS
employs an asynchronous SAR logic with simple meta-stability correction logic to achieve
high-speed operation. The Version 1 ADC which has an active die area of 0.042 mm^{2} shows a maximum signal-to-noise-and-distortion ratio (SNDR) and spurious-free dynamic
range (SFDR) of 62.3 and 77.3 dB, respectively, consuming 1.3 mW with a 1.0 V supply
voltage. The Version 2 ADC is based on a similar analog circuit topology, showing
a maximum SNDR and SFDR of 60.1 and 73.5 dB, respectively, with an active die area
of 0.30 mm^{2}, operating at a 1.8 V supply voltage.

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## I. INTRODUCTION

With the expansion of new mobile communication systems such as 5G networks and wearable
devices, there has been an increase in demand for mobile devices based on such systems
^{(1-}^{3)}. These mobile devices require analog-to-digital converters (ADCs) that can achieve
a resolution of over 10 b at a sampling rate exceeding 100 MS/s while maintaining
high power efficiency and small chip area when the speed is adjusted as needed. To
meet these stringent requirements for the ADCs, much research has been conducted on
the development of low-power, small-area successive-approximation register (SAR) ADCs.
However, SAR ADCs are typically limited in their application due to the difficulty
in achieving the required digital-to-analog converter (DAC) output settling time at
high-speed operation ^{(4-}^{6)}. To overcome this limitation in SAR ADCs, research is being conducted on time-interleaving
and 2b/cycle techniques. However, these techniques require the use of additional circuit
blocks, thereby reducing efficiency with respect to power consumption and chip area.
While some correction schemes can relax the DAC settling requirement for high-speed
operation, commonly employed methods include non-binary search algorithm and binary-scaled
error compensation. Compared to the binary-scaled error compensation scheme, the non-binary
search algorithm could correct a relatively higher number of bit error decisions with
the same number of unit capacitors ^{(7)}. This work thus proposes 12 b 100 MS/s SAR ADCs based on a non-binary weighted DAC
to shorten the required DAC output settling time.

The proposed SAR ADC architecture in this work is shown in Section II. Detailed circuits are described in Section III, while the measurement results are discussed in Sections IV and V.

## II. PROPOSED SAR ADC TOPOLOGY

The overall structure of the proposed ADC is illustrated in Fig. 1. The proposed ADC consists of a non-binary weighted C-R hybrid DAC, a comparator, a SAR logic block, and an encoder that converts a 14 b non-binary digital code into a 12 b binary digital code.

The C-R hybrid DAC shown in Fig. 1 is again composed of a 9 b non-binary weighted capacitor-array (C-array) and a 5
b C-array, where CU represents a unit capacitor of 21 fF. The 9 b C-array is used
to decide the 7 most significant bits (MSBs). In this structure, 30 CU's are employed,
compared to the typical nominal binary weighted 32 CU's, with 2 CU's as redundant
capacitors to alleviate the settling requirement of the DAC output with error correction
^{(8-}^{10)}. The remaining 5 least significant bits (LSBs) are decided by five unit capacitors
in the 5 b array, combined with 10 reference voltages obtained from a simple resistor
string ^{(11)}. Since the proposed DAC employs a total of only 68 capacitors rather than the 4096
required for a full binary weighted 12 b resolution, the required die area for the
SAR ADC is significantly reduced, even when taking into account the extra area occupied
by the noncritical simple resistor string. The proposed ADCs are implemented in two
versions with different processes. The Version 1 ADC in a 28 nm CMOS employs a synchronous
SAR logic circuit with a low power dynamic comparator to minimize power consumption.
Meanwhile, The Version 2 ADC in a 0.18 μm CMOS employs an asynchronous SAR logic circuit
for the same 100 MS/s target operation for a relatively long channel. The Version
2 ADC also proposes a simple meta-stability correction logic circuit to remove the
meta-stable state of the comparator.

## III. CIRCUIT DESCRIPTION

### 1. Non-binary Weighted DAC

An example of the SAR operations based on both the binary and non-binary weighted
DACs used to determine a 4 b digital output is illustrated in Fig. 2. The decision range of the binary weighted DAC is not overlapped, while that of the
non-binary weighted DAC is overlapped by the redundancy generated from the two separate
redundant capacitors, 3 CU and 1 CU ^{(8-}^{10)}.

The signal settling range of the non-binary weighted DAC can be considerably increased in proportion to the overlapped range, as shown in the waveform of Fig. 3, while the output voltage of the binary weighted DAC needs to be settled within a maximum 1/2 LSB of the ideal settling level. The required settling times of the DAC output can be calculated by the equations in boxes of Fig. 3, where ‘ts,b’ and ‘ts,nb’ represent the output settling time in the full-binary and non-binary DAC, respectively.

The elements ‘τ’, ‘Weight’, and ‘Redundancy’ are the time constant, the weighted value of the CDAC capacitor, and the overlapped decision range of the non-binary weighted DAC, respectively. In the conventional DAC, the maximum ‘Weight’ is 2048 LSB for the MSB capacitor and the estimated maximum ts,b is 8.32 τ. However, the proposed DAC has a ‘Redundancy’ of 128 LSB, generated by the 2 CUs, and the ‘Weight’ of the MSB capacitor is 1920 LSB. The estimated ts,nb of the proposed DAC is 2.71 τ, with a reduction factor of 67 %, while the maximum output settling time does not occur in the first conversion cycle. Instead, the maximum output settling time in the proposed DAC is 4.85 τ, which occurs in the eighth conversion cycle, where the ‘Weight’ is 64 LSB and there is no more ‘Redundancy’. As a result, the estimated total sum of the output settling time in the conventional DAC is 54.07 τ, compared to 29.74 τ in the proposed DAC. Therefore, the maximum settling time and the total sum of the settling time of the DAC output voltage are dramatically reduced by 42% and 45%, respectively, in the proposed non-binary weighted DAC.

### 2. Low Power Dynamic Comparator

To achieve low power consumption, a dynamic comparator with a tail capacitor, CT,
and a reset switch, MR, is employed in the Version 1 ADC ^{(12,}^{13)}. As shown in Fig. 4, the charged voltages of the LN, LP, and VS nodes in the conventional comparator
are completely discharged to 0 V. However, the charged voltages of the same three
nodes in the comparator are discharged to approximately 65% of the initial values.
The comparator thus significantly improves the power efficiency and operating speed
of the ADC.

### 3. Asynchronous SAR Logic

The Version 2 ADC in a 0.18 μm CMOS adopts an asynchronous SAR logic to eliminate
the idle periods between conversion steps for the same 100 MS/s high conversion target
as the Version 1 ADC which is applied in a 28 nm CMOS ^{(14)}. In addition, since the conversion speed of the SAR ADC tends to be limited by the
SAR loop delay time, the delay time-reduced SAR logic adopted in the Version 2 ADC
is able to directly control the CDAC switch from the REG output without any extra
DAC switching logic. The asynchronous SAR logic with its specific timing diagram is
illustrated in Fig. 5.
As soon as the logic status of the sampling clock ‘FSB’ and the reset clock ‘RST’
changes, the comparator is ready to compare two ‘CDAC’ outputs with the ready clock
‘RDY’ set to ‘high’, starting a bit conversion. In succession, the register-enable
clock ‘EN<0>’ is set to ‘high’ and selects ‘REG0’ to store the corresponding comparator
output. Immediately after the bit conversion is completed, the compared output ‘LP,
LN’ resets the ‘RDY’ clock to turn off the comparator, and accordingly, ‘LP, LN’ is
also reset to ‘high’. The proposed SAR logic operates asynchronously during the total
14 b conversion cycles ^{(15)}. After the last 14th bit conversion, the ‘EOC’ clock is set to ‘low’ indicating that
the overall 14 b conversion is completed.

### 4. Proposed Meta-stability Correction Logic

With the significantly reduced SAR conversion time due to the asynchronous operation, a simple meta-stability correction logic is also proposed in the Version 2 ADC. The proposed meta-stability correction logic forces all the lower bits from the possible meta-stable bit to be set to ‘100...’ as illustrated in the example of Fig. 6.

When the comparator operates without any meta-stable state in all conversion cycles, the digital code ‘D<0:13>’ is generated by the register outputs ‘T<0:13>’. However, if a meta-stable state occurs in the comparator, the corresponding meta-stable bit is considered as ‘1’, and the remaining bits are considered as ‘0’. As a result, all bits including the meta-stable bit are considered as ‘100...0’. For example, as shown in Fig. 6, if the first bit ‘D<0>’ is ‘1’ and the meta-stable state occurs in the second conversion cycle, the corresponding register output ‘T<1>’ and the register enable clock ‘EN<1>’ are set to ‘low’ and ‘high’, respectively. Therefore, the digital code ‘D<1>’ is determined as ‘1’ through the NAND gate that receives ‘T<1>’ and ‘EN<1>’ as inputs. Meanwhile, all the lower bits from ‘D<2>’ are set to ‘00...0’ based on the remaining NAND gates and the register enable clock. As a result, the 12-bit digital code is considered as ‘110000000000’.

## IV. MEASUREMENT RESULTS

The proposed non-binary DAC-based 12 b 100 MS/s ADCs are implemented in two versions
with 28 nm and 0.18 μm CMOS processes. The active die area of the two prototype ADCs
is 0.042 mm^{2} and 0.30 mm^{2}, as shown in Fig. 7, respectively. The Version 1 ADC consumes 1.3 mW with a 1.0-V supply voltage while
the Version 2 ADC consumes 11.3 mW with a 1.8-V and 1.7-V for analog and digital supply
voltage, respectively. The power breakdown is detailed in Fig. 8.

The measured differential non-linearity (DNL) and integral non-linearity (INL) of the prototype ADCs are shown in Fig. 9. The DNL and INL of the Version 1 ADC are within 0.67 LSB and 1.55 LSB, while the DNL and INL of the Version 2 ADC are 0.66 LSB and 1.65 LSB, respectively.

The measured signal-to-noise-and-distortion ratio (SNDR) and spurious-free dynamic range (SFDR) of the prototype ADCs are plotted in Fig. 10and 11. The Version 1 ADC shows maximum SNDR and SFDR of 62.3 dB and 77.3 dB, while the Version 2 ADC shows maximum SNDR and SFDR of 60.1 dB and 73.5 dB, respectively, at an operating speed of 100 MS/s and an input frequency of 1 MHz. When the input frequency is increased to the Nyquist frequency at 100 MS/s, the SNDR and SFDR of the Version 1 ADC are maintained above 61.5 dB and 76.3 dB, while the SNDR and SFDR of the Version 2 ADC are maintained above 58.4 dB and 72.1 dB, respectively.

The performance of the Version 1 ADC is summarized and compared with previously reported ADCs in Table 1.

Table 1. Performance comparison of the Version 1 ADC

## V. CONCLUSIONS

This work proposes 12 b 100 MS/s SAR ADCs based on a non-binary C-R hybrid DAC for high-speed residue settling. The proposed ADCs are implemented in two versions based on different processes. The Version 1 ADC employs a synchronous SAR logic and a low power dynamic comparator to minimize power consumption. The Version 2 ADC employs an asynchronous SAR logic with simple meta-stability correction logic to achieve high-speed operation. Although the power and the die area of the Version 2 ADC are much larger than the Version 1 ADC, primarily, due to two substantially different CMOS processes of 28 nm and 0.18 μm, the Version 2 ADC properly operates at a high-speed of 100 MS/s even in a 0.18 μm CMOS process. Based on the benefits of scaled-down process, the Version 1 ADC with a 28 nm CMOS process achieves a competitive figure-of-merit (FoM) of 12.2 fJ/conversion-step.

### ACKNOWLEDGMENTS

This work was supported by Samsung Electronics Co., Ltd (IO201210-08008-01), the IDEC of KAIST, and the MSIT under the ITRC program (IITP-2021-2018-0-01421) supervised by the IITP.

### REFERENCES

## Author

Jae-Geun Lim received the B.S. degree in electronic engineering from Sogang University, Seoul, Korea, in 2019, where he is currently pursuing the Ph.D. degree.

His current research interests include low-power and high-speed analog-to-digital converter.

Je-Min Jeon received the B.S. and M.S. degrees in electronic engi-neering from Sogang University, Seoul, Korea, in 2019 and 2021, respectively.

He has been with the Samsung Electronics Co., Ltd.

His current interests are in the design of high-resolution CMOS data converters, and very high-speed mixed-mode integrated systems.

Jun-Ho Boo received the B.S. degree in electronic engineering from Sogang University, Seoul, Korea, in 2017, where he is currently pursuing the Ph.D. degree.

His current research interests include analog and mixed-signal circuits, data converters, and sensor interfaces.

Yoon-Bin Im received the B.S. in electronic engineering from Sogang University, Seoul, Korea, in 2020 where she is currently pursuing M.S. degree.

Ms. Im is a recipient of a scholarship sponsored by Samsung electronics.

Her research interests include high-speed analog-to-digital converters design.

Jae-Hyuk Lee received the B.S. degree in electronic engineering from Sogang University, Seoul, Korea, in 2020, where he is currently pursuing the M.S degree.

His current interests are in the design of high-speed, high-resolution CMOS data converters, and very high-speed mixed-mode integrated systems.

Sung-Han Do received the B.S. and M.S. degrees from Sungkyunkwan University, Suwon, Korea, in 2014 and 2016, respectively.

He joined Samsung Electronics, Hwaseong, South Korea, in 2016.

Currently, he is an engineer in Samsung Foundry, where he is researching the high-speed CMOS data converters.

Young-Jae Cho received the master’s and Ph.D. degrees from Sogang University, Seoul, South Korea, in 2003 and 2007, respectively.

He joined Samsung Electronics, Hwaseong, South Korea, in 2010.

Currently, he is a principle engineer in Samsung Foundry, leading data converter development.

His major fields are high-speed data converters and application specific analog front-ends for various applications such as digital TV, 5G network, touch controller, CIS and automotive wired/wireless communications.

Michael Choi received the master’s and Ph.D. degrees from the University of California, Los Angeles, CA, USA, in 1998 and 2002, respectively.

He joined Samsung Electronics, Hwaseong, South Korea, in 2006.

Currently, he is a Master in Samsung Foundry, leading analog IP development.

His expertise includes high-speed data converters and various analog front-ends for UHD digital TV, WiFi & 5G connectivity, automotive V2X, touch controller, and CMOS image sensor.

Gil-Cho Ahn received the B.S. and M.S. degrees in electronic engineering from Sogang University, Seoul, Korea, in 1994 and 1996, respectively, and the Ph.D. degree in electrical engineering from Oregon State University, Corvallis, in 2005.

From 1996 to 2001, he was a Design Engineer at Samsung Electronics, Kiheung, Korea, working on mixed analog-digital integrated circuits.

From 2005 to 2008, he was with Broadcom Corporation, Irvine, CA, working on AFE for digital TV. Currently, he is a Professor in the Department of Electronic Engineering, Sogang University.

His research interests include high-speed, high-resolution data converters and low-voltage, low-power mixed-signal circuits design.

Seung-Hoon Lee received the B.S. and M.S. degrees in electronic engineering from Seoul National University, Korea, in 1984 and 1986, respectively, and the Ph.D. degree in electrical and computer engineering from the University of Illinois, Urbana-Champaign, in 1991.

He was with Analog Devices Semiconductor, Wilmington, MA, from 1990 to 1993, as a Senior Design Engineer.

Since 1993, he has been with the Department of Electronic Engineering, Sogang University, Seoul, where he is currently a Professor.

His current research interests include design and testing of high-resolution high-speed CMOS data converters, CMOS communication circuits, integrated sensors, and mixed-mode integrated systems.