A pipelined analog-to-digital converter (ADC) architecture suitable for high-speed (150 MHz), Nyquist-rate A/D conversion is presented. At the input of the converter, two parallel track-and-hold circuits are used to separately drive the sub-ADC of a 2.8-b first pipeline stage and the input to two time-interleaved residue generation paths. Beyond the first pipeline stage, each residue path includes a cascade of two 1.5-b pipeline stages followed by a 4-b “backend” folding ADC. The full-scale residue range at the output of the pipeline stages is half that of the converter input range in order to conserve power in the operational amplifiers used in each residue path. An experimental prototype of the proposed ADC has been integrated in a 0.18- m CMOS technology and operates from a 1.8-V supply. At a sampling rate of 150 MSample/s, it achieves a peak SNDR of 45.4 dB for an input frequency of 80 MHz. The power dissipation is 71 mW.
Index Terms—Analog–digital (A/D) conversion, CMOS analog integrated circuits, comparators, folding A/D  converters, mixed analog–digital integrated circuits, operational amplifiers, pipeline processing, switched-capacitor circuits.

CMOS Nyquist-rate analog-to-digital converters (ADCs) in modern electronic systems tend to fall in two broad categories: those that operate at very high sampling rates, up to several gigahertz, with resolution in the range of 4–8 b, and those that perform conversions at rates of tens of megahertz while providing resolution in the range of 10–15 b. The very high-speed low-resolution converters find use primarily in applications such as instrumentation, wideband communications, and data retrieval from magnetic storage media. Power consumption is rarely a primary concern in these applications, and the principal challenge is to achieve a high sampling rate for resolutions that can be readily achieved within the matching limitations of CMOS technologies. The target applications for converters providing higher resolution at sampling rates of tens of megahertz include communication and medical systems, as well as image and video data acquisition. The challenge here is to achieve a high resolution in the presence of component mismatch, thermal noise, and circuit nonlinearity.
The ADC introduced in this work targets performance between the two categories noted above, namely, a sampling rate of 150 MSample/s and a resolution of 8 bits. These specifications are typically appropriate for high-speed wireline and wireless communications. For example, the 1000BASE-T Ethernet protocol requires a conversion rate of 125 MSample/s and a resolution of 7–9 bits, depending on the overall system architecture. Since four converters must be integrated in a single transceiver, power consumption becomes an important consideration. For the IEEE 802.11a/g wireless LAN protocol, ADCs with conversion rates of the order of 80 MSample/s are required, also with resolution in the range of 7–9 bits. Here, power consumption is of paramount importance when the target application is portable systems.
 The low-power ADC described in this paper utilizes a combination of architectural concepts and circuit techniques to achieve the target performance while dissipating only 71 mW of power from a 1.8-V supply. Chapter II provides a detailed overview of the converter architecture and reviews the choices made to minimize the power dissipation. Chapter III describes the design of the circuit blocks that have been used to accommodate low-voltage operation. Chapter IV presents measured results for the experimental prototype.
Fig. 2.1 offers a detailed view of the ADC architecture. The input track-and-hold network is actually “split” into two parallel track-and-hold circuits, TH1 and TH2, both of which are clocked at the full conversion rate (150 MHz) and sample the input at nominally identical instances in time. TH1 drives the analog residue generation paths, while TH2 drives the six comparators comprising the sub-ADC of the 2.8-b first stage of the pipeline. A 2.8-b first stage was chosen to minimize the power and area required for the overall converter. The track-and-hold function at the input of the converter is split so as to combat the coupling of kickback noise from the first-stage sub-ADC comparators into the sensitive residue generation paths, in a manner similar.  Since the six comparators comprising the sub-ADC in the first pipeline stage are compact, fast, low power latches without preamplification, their operation creates noise at the level of several tens of millivolts. With the proposed arrangement, noise from the operation of the comparators does not degrade the quality of the analog input signal used for residue generation since the outputs of TH1 and TH2 are isolated from each other during the hold mode.
As is also shown in Fig. 2.1, residue generation is split into two paths, A and B, in the first pipeline stage. Each path comprises a sampling network (not shown explicitly), a 2.8-b DAC, a subtractor and an interstage gain of 2. These functions are performed by a switched-capacitor network that is described in detail in Section III. The two residue generation paths operate at half the conversion rate (75 MHz) and in antiphase; that is, when path A samples the output of TH1, path B amplifies its held input. Time- interleaving the operation of two residue paths results in significant savings in power. Most of the power in each path is dissipated by the operational amplifiers used for residue generation, and the use of two paths operating at 75 MHz results in nearly a factor of two reduction in power consumption compared to a single path operating at the full conversion rate of 150 MHz. The first-stage sub-ADC operates at the full rate of the converter, and its decisions are routed to each of the two residue generation paths with the use of an appropriate digital switch.
The gain in each of the first-stage residue paths is 2, rather than a gain of 4 that would typically be used for a pipeline stage providing two bits of encoding. Thus, instead of maintaining a full-scale range for the residue output that is the same as that of the analog input to the stage, the output range is scaled by a factor of 2. Specifically, while the differential full-scale range of the input is 1.6Vpp, the differential range of the residue is 0.8Vpp. This “scaling” of the signal range facilitates a substantial reduction in the power dissipated by the operational amplifiers used for residue generation.
The ideal transfer characteristic of the 2.8-b pipeline stage, also known as a “3-b stage with digital error correction”, is shown in Fig. 2.2. The stage resolves 2 bits of the conversion using six, rather than three, comparators. This allows for the compensation of large comparator offsets, as shown in Fig. 2.2. For this design, comparator offsets as large as 100 mV can be tolerated in the first pipeline stage.
For each residue path emanating from the first stage, a cascade of two additional 1.5-b pipeline stages is used to encode the next two most significant bits. These stages employ two comparators each and an interstage gain of 2. Therefore, the differential full-scale range of the residue output of each pipeline stage is maintained at 0.8Vpp. For the described arrangement of interstage gains, the step size at the converter input corresponding to one LSB is 6.25 mV, while at the outputs of the first three pipeline stages it is 12.5, 25, and 50 mV, respectively.
After digital error correction, the first three stages of the converter pipeline provide the four most significant bits (MSBs) of the conversion. In each residue path a 4-b flash stage follows the three pipeline stages to encode the four least significant bits (LSBs), for a total of 8 bits. The “backend” 4-b stage uses a simple folding technique as described in Section III. All comparator outputs for this architecture are fed to a decoding and error-correction block that generates the final 8-b digital output. This digital-logic block can be easily realized in dedicated hardware or with a digital signal processor.

The two track-and-hold circuits at the input of the converter are implemented in a pseudodifferential fashion, while all of the remaining analog blocks are fully differential circuits. All of the circuits are powered from a 1.8-V supply.

 Fig. 3.1.1 shows a single-ended schematic of the circuit used to implement both of the track-and-hold networks. TH2 is a scaled version of TH1. The track-and-hold network comprises Fig. 3.1.1. Track-and-hold network. a sampling switch MSW with an associated bootstrapping network, a hold capacitor CH, and a source-follower buffer. Capacitor represents the sampling capacitance of the residue generation network for either path A or B, whichever is sampling the output of TH1 on a given cycle. For TH2, CL represents the sampling capacitance at the combined input of the six sub-ADC comparators.
 The bootstrapping network in Fig. 3.1.1 resembles the one described. During the tracking phase Φ1, switches M6 and M7 conduct, and the voltage on the bootstrap capacitor CB is applied between the gate and source of the sampling switch. Therefore, VGS for the sampling switch remains approximately constant for varying input voltages. This in turn gives rise to a constant resistance for the sampling switch during track mode, which improves the linearity of the sampling network. During the hold phase Φ, switches M6 and M7 are off and transistor conducts, turning off the sampling switch MSW. The sampled input voltage is thus held on CH. During the same phase, switches M8 and M9 conduct, charging the bootstrap capacitor CB to a bias voltage VB of about 1.3 V.
The principal difference between this implementation and that described is that the bias voltage VB is less than the supply voltage VDD. As a result, although during the tracking mode the voltage at the top plate of CB is allowed to go above VDD, it still remains low enough to avoid introducing long-term reliability concerns associated with voltage stress on the sampling switch during transients. As a further precaution, the connection for the inverter that drives M7 is made to the bottom plate of CB, the body of M7 is connected to its source, and transistor M5 is used as a cascode to M4.
Transistor M1 in Fig. 3.1.1 is a PMOS source follower with its body connected to its source. Therefore, the gain from its gate to the source is nearly unity. Transistor M2 serves as a current source to bias M1. The use of this simple source follower as a buffer is well suited to low-voltage operation with the full-scale voltage range of 0.8 Vpp at each of the differential inputs. As the input voltage changes, the variation in VDS for M1 and M2 causes a “compression” of the output voltage for large signal excursions, leading to third-order distortion in the differential output. Buffers such as this have been used extensively in converters requiring only 6-b linearity and recent results suggest that the topology may be suitable for achieving linearity as high as 10 bits. Simulations and the observed performance of the experimental prototype indicate that the linearity achieved with this sampling network is approximately 9 bits.
Switch MSW in the track-and-hold circuit should be as small as possible while still providing sufficient bandwidth to transfer the highest input frequencies of interest ( 70 MHz). Its small size guarantees minimal charge injection (fraction of an LSB) into CH. Clock jitter of approximately 4 ps can be tolerated in the sampling switches.
3.1.2 depicts the output of the track-and-hold networks before and after the sampling instance, which is denoted by t0. Owing to the time interleaving, during a given conversion cycle, either residue path A or B samples the output of TH1 at time , which also marks the end of the hold phase for the track and hold networks. The first-stage comparators begin resolving the output of TH2 at an intermediate time t1 between t0 and t2.
 As shown in Fig. 3.1.2, immediately after sampling, there is a transient at the track-and-hold output. The tail of this transient may result in a difference of as much as 30 mV between the voltage encoded by the first-stage sub-ADC and the voltage sampled by the residue paths. This transient is not the result of potentially nonlinear second-order effects during sampling, such as sampling switch charge injection, but is rather due solely to the linear behavior of the sampling network and the source follower buffers. The origin of the transient is explained in detail in the Appendix, where (A14) indicates that the maximum magnitude of the transient can be as large as 11% of the input full-scale range. The resulting difference in the voltage encoded by the sub-ADC and that used between the analog residue paths must be taken into account when budgeting the total offset for the comparators of the first stage.
 The simple track-and-hold circuits used here are linear enough to achieve the desired resolution while offering a significant power savings compared to those that are based on the use of an operational amplifier in a feedback network. The power in the track-and-hold networks is largely that consumed for biasing the source followers, and there are no power-demanding auxiliary circuits; the bootstrap network dissipates negligible power.

First-Stage Comparators
Fig. 3.2.1 shows a circuit diagram for the comparators used in the first-stage sub-ADC. Each of the six comparators comprises a regenerative core preceded by a switched-capacitor network that establishes its equivalent reference voltage. Input voltages Vin1 and Vin2 correspond to the two outputs of the pseudodifferential track-and-hold network TH2. The timing diagram in Fig. 3.2.2 shows the clock phases Φ1 and Φ2 used to control the operation of the comparators. The sampling clock and clock are used to control the timing in the analog residue paths.
During phase Φ1, reference voltages +Vref and –Vref (where Vref=0.4) are sampled onto capacitors CS1 and CS2, as shown in Fig. 3.2.1. During phase Φ1, the output of TH2 is applied on both capacitors.                                                  
Capacitor ratios (CS1/CS2) of 3/13, 5/11, 7/9and their inverses are used for the six comparators to establish the necessary equivalent differential references.
Also during phase Φ1, the PMOS switch Mbias in the regenerative core is activated and bias current flows through the latch. However, regeneration begins later, with the onset of phase Φ2, when switch Mreg is turned off. It can be shown analytically that establishing current flow in the latch well before initiating regeneration significantly reduces the latch’s dynamic input-referred offset.
The comparator dissipates approximately 0.5 mW of power when operating at 150 MHz and exhibits 3σ a static offset of about 36 mV. This offset value has been estimated with simulations using typical technology parameters for transistor mismatch. The six comparators are allowed to regenerate for about 0.75 ns, while φ2 is low. After regeneration is discontinued, the resulting outputs are amplified and stored in set-reset (SR) latches, not shown in Fig. 3.2.1.
 For the first-stage architecture shown in Fig. 1.1, Table 3.2.1 summarizes the main factors contributing to a difference between the equivalent voltage encoded by the first-stage sub-ADC and that sampled by a residue generation path. The approximate worst-case magnitudes of these contributions as referred to the input of the overall ADC are included in Table 3.2.1. These differences can be treated as added comparator offset for the firststage sub-ADC and are well tolerated, provided that all sources of mismatch remain within the correctable range of 100 mV mentioned in Section II. An explanation of the various contributions follows.
 In addition to static offsets in the comparators, there may exist a settling error with respect to the final values of the reference voltages sampled on CS1 and CS2 in Fig. 3.2.1. Also, since the comparators regenerate for a limited time, there may not be enough time for an input voltage that lies within 5 mV of the equivalent reference of one of the comparators to be resolved correctly. Other error contributions result from mismatch between the two track-and-hold networks. A static mismatch may exist between TH1 and TH2. Also, TH1 and TH2 may not sample at precisely the same instance due to sampling clock propagation delay. This time difference would translate to a sampled value offset for a time-varying input waveform. In the layout of the experimental prototype, the sampling switches for the two track-and-hold networks are placed next to each other to minimize any sampling time differences. Finally, there is the offset component due to the transients at the output of the track-and-hold networks, as described in Section III-A. In a worst-case scenario, all of these offset contributions add up to a total of about 85 mV, therefore leaving a healthy margin to the maximum correctable range of 100 mV.

Residue Generation Paths
Fig. 3.3.1 is a schematic of the switched-capacitor network used for each of the residue generation paths in the first pipeline stage. Although the residue paths are implemented as fully differential circuits, a single-ended version is shown in Fig. 3.3.1 for clarity. A total sampling capacitance CS1 is divided into eight equal capacitors. During phase φ3, for one of the two residue paths, the output of TH1, denoted as Vin1 in Fig. 3.31, is sampled onto all eight sampling capacitors. At the same time, the input and output of the op amp are held at the common-mode voltage VCM. During phase φ3, reference voltages +Vref and –Vref are applied on the two “outermost” sampling capacitors in Fig. 3.3.1, respectively. During this same phase, the decision of the six comparators of the first-stage sub-ADC controls whether +Vref or –Vref is applied to the remaining six sampling capacitors. The subtraction of the charge sampled on the sampling capacitors during φ3 from the charge that was sampled on them during φ3 corresponds to the subtraction of the DAC output from the output of TH1 depicted in Fig. 1.1. The feedback capacitance CF is half the total sampling capacitance CS, thus realizing a closed-loop gain of 2.
 For stages 2 and 3 in each residue path, the residue generation network is very similar to that shown in Fig. 3.3.1. However, in this case, the sampling capacitance is divided into only four equal capacitors, and the polarity of the references for two of them is controlled by the two comparators that form the sub-ADC in each 1.5-b stage. The comparators employ the same topology as those in the first stage, shown in Fig.3.2.1, and are driven by the output of the preceding stage through a simple preamplifier that reduces kickback noise.
 Sampling capacitor sizes for stages 1–3 were conservatively set to 1.6, 1.2, and 1 pF, respectively.

Operational Amplifier
A schematic of the operational amplifier topology used for residue generation in all stages of the pipeline is shown in Fig. 3.4.1. Capacitors marked CN in Fig. 3.4.1 are used to partially neutralize the gate-to-drain capacitance of input transistors M1 and M2, thereby increasing the circuit’s bandwidth. Common-mode feedback is provided by means of a switched-capacitor network.
 As noted in Section II, for the residue output of every pipeline stage, a full-scale differential range of only 0.8Vpp is used in order to conserve power. Given the 0.8-V differential full-scale range, the voltage range at each of the two amplifier outputs is 0.4Vpp. This small voltage range is acceptable since the signal-to-noise ratio (SNR) of this converter is limited by quantization rather than thermal noise. The differential output of the amplifier is reset to zero during the sampling phase by resetting the two outputs to the middle of their 0.4-Vpp range. Thus, during amplification, the maximum voltage excursion at either of the two outputs is 200 mV.
  At the beginning of the amplification phase, voltage “spikes” are induced at the inputs of the operational amplifier. As charge redistributes between the sampling and feedback capacitors, these voltage spikes decay exponentially to a value close to zero, while at the same time the op amp outputs settle to their final values. For a closed-loop gain of 2 in every stage, the maximum magnitude of the voltage spike at any of the op amp inputs is no more than 100 mV. An example of the voltage response at one of the inputs and one of the outputs of the op amp during the amplification phase is shown in the inset of Fig. 3.4.1. The magnitude of the initial spike at the input is within the linear range of the input differential pair and therefore too small to cause slewing at the op amp output or drive any of the op amp transistors, including current sources M0,M3,M4,M9 and M10, out of saturation. Thus, there are no long voltage transients due to slewing or to bias current recovery that affect the response of the op amp during the amplification phase. The absence of such transients obviates the need for large currents in transistors M7, M5, M3 and M8, M6, M4 the cascade branches of the amplifier. As a result, only 320 A of bias current is needed in these devices.
The low bias currents in the casocde branches are sufficient to drive the output capacitive load, and their small value has two beneficial effects. First, it reduces the power consumed by the op amp to only 5.11 mW. This is approximately 35% less than the typical case where the currents in the cascade branches are comparable to those flowing in the input devices, M1 and M2. Second, the small current through M7, M5, M3 and M8, M6, M4 results in a large output resistance for the cascode transistors, corresponding to a high op amp gain. The amplifier provides an open-loop gain of 80 dB over the entire differential output range.
 The only drawback of the low currents in the cascade branches is a relatively low value of gm for cascode transistors M7 and M8, which translates to a low nondominant pole for the amplifier. This is reflected in the unity-gain bandwidth of the op amp, which is only 400 MHz. During the amplification phase, the feedback factor for the closed-loop configuration is at most 14 dB, and the phase margin for that feedback factor is about 60.
 Since the settling requirements are more relaxed in the second and third stages, the op amps for those stages are biased at a lower current.

“Backend” 4-B ADC
A schematic of the 4-b backend ADC used in each path is shown in Fig. 3.5.1. A coarse sign comparator makes an early decision as to the polarity of its differential input voltage while the input is still settling. After the input has settled, its magnitude is encoded by a 3-b flash ADC. The threshold voltages for the 3-b flash ADC are provided by a differential reference ladder, with their polarity (positive or negative) determined by the result of the coarse sign comparison, as shown in Fig. 3.5.1. For positive input voltages, the polarity of the reference voltages that set the thresholds in the 3-b flash ADC is positive, while the opposite is true for negative inputs, as indicated by the stage’s transfer characteristic in Fig. 3.5.2.

Also included in the backend ADC is a “fine” sign comparator, as shown in Fig. 3.5.1. After the input voltage has settled, this comparator makes an accurate determination of the sign of the input, which is important for the case when the input voltage lies within ±1LSB of the threshold in the middle of the input range. With this configuration, it is possible that the decisions of the coarse and fine sign comparators are not identical.A typical such situation is depicted in Fig. 3.5.3. The input voltage to the stage experiences a small initial “peak” caused by transients in the settling of the switched-capacitor network of the preceding pipeline stage during the amplification phase. Moreover, the coarse comparator may also exhibit an offset. As shown in the figure, the decisions of the coarse and fine comparators can thus be different. If the input settles to a final value with a magnitude of less than 50 mV (corresponding to the LSB step size for this stage), the discrepancy is of no consequence since none of the thresholds of the 3-b flash ADC are ever be reached by an input of such small magnitude, regardless of whether it is positive or negative. For an input to the stage with a final value of magnitude larger than 50 mV, the input, as it settles, quickly moves away from the center region of the input range. Provided that the offset of the coarse sign comparator is no more than 50 mV, the decisions of the two sign comparators will then match. The realization of this last scenario was extensively examined via simulations. If there is concern that the two sign comparators may still make different decisions for an input more than ±1LSB from the center, additional comparators need to be used.
Each of the comparators comprising the flash ADC in Fig. 3.5.1, as well as the fine sign comparator, includes two preamplifiers with an intermediate input-output offset cancellation network. These comparators in the final stage are responsible for the LSB transitions of the overall converter. They are preceded by a total gain of only 8 (three pipeline stages, each with an interstage gain of 2. Therefore, offset cancellation for the comparators is necessary to ensure that the target DNL performance can be achieved.
With the architecture shown in Fig. 3.5.1, the backend ADC can encode the 4 LSBs using only nine comparators, instead of the usual 15 required for a 4-b flash ADC.

CMOS Switches
The CMOS switches used in the switched-capacitor networks are shown in Fig. 12. When such a switch is conducting, the body of the PMOS device is connected to its source. Because of the absence of body effect, the resistance of the switch is lowered, especially near the middle of the voltage range, where the switch resistance is highest. When the switch is off, the body of the PMOS device is connected to the highest voltage present (VDD) to ensure that the drain-to-bulk and source-to-bulk diodes for this device are always reverse biased for any voltage levels between ground and VDD on either side of the switch. This arrangement lowers the peak resistance of the switch during conduction by about 50% compared to the case where the body of the PMOS transistor is permanently connected to VDD. The reduction in resistance in turn allows a reduction in the size of the switches and their associated parasitic loading on the switched-capacitor network that employs them. Since the capacitance of the n-well of the main PMOS transistor in the switch to the substrate is small, the devices used to switch the body of the main PMOS transistor are approximately 16 times smaller than the PMOS transistor itself.

A 150-MSample/s, 8-b, low-power ADC based on a pipeline architecture has been described. Two open-loop track-and-hold circuits are used to isolate the sensitive residue path from the noisy inputs to the comparators of the first pipeline stage. The use of two time-interleaved residue paths in the first and subsequent stages saves power relative to a single path operating at the full conversion rate. Since both residue paths are driven from the same track-and-hold circuit, no distortion is introduced by timing mismatch between the time-interleaved paths. Signal scaling is used to facilitate the use of a low-power, high-speed, high-gain op amp. A simple folding technique is used in the final 4-b stage to reduce the number of comparators needed.
The experimental prototype chip dissipates 71 mW, which represents the lowest power consumption reported to date for a CMOS, full-Nyquist, 150-MSample/s, 8-b converter that does not require calibration.

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