Review Article  Open Access
Rida Assaad, Jose SilvaMartinez, "Recent Advances on the Design of HighGain Wideband Operational Transconductance Amplifiers", VLSI Design, vol. 2009, Article ID 323595, 11 pages, 2009. https://doi.org/10.1155/2009/323595
Recent Advances on the Design of HighGain Wideband Operational Transconductance Amplifiers
Abstract
Feedforward techniques are explored for the design of highfrequency Operational Transconductance Amplifiers (OTAs). For singlestage amplifiers, a recycling foldedcascode OTA presents twice the GBW (197.2โMHz versus 106.3โMHz) and more than twice the slew rate (231.1โV/s versus 99.3โV/s) as a conventional folded cascode OTA for the same load, power consumption, and transistor dimensions. It is demonstrated that the efficiency of the recycling foldedcascode is equivalent to that of a telescopic OTA. As for multistage amplifiers, a NoCapacitor FeedForward (NCFF) compensation scheme which uses a highfrequency polezero doublet to obtain greater than 90โdB DC gain, GBW of 325โMHz and better than phase margin is discussed. The settlingtime of the NCFF topology can be faster than that of OTAs with Miller compensation. Experimental results for the recycling foldedcascode OTA fabricated in TSMC 0.18โm CMOS, and results of the NCFF demonstrate the efficiency and feasibility of the feedforward schemes.
1. Introduction
The growing demand for highspeed and highprecision analog ICs dictates stringent design specifications for the amplifiers which are the basic building blocks for numerous applications; IF switchedcapacitor (SC) filters and highresolution data converters with sampling frequencies above 100โMHz require very fast OTAs with settling times less than 4 nanosecods for good performance [1โ24]. Highgain amplifiers use cascode structures or multistage designs with long channel length transistors biased at low current levels while highbandwidth amplifiers use singlestage designs with short channel length transistors biased at high current levels.
For singlestage amplifiers, the foldedcascode (FC) OTA has a higher signal swing than a telescopic OTA while still presenting a single parasitic pole and relatively large DC gain, and hence it is commonly used for highfrequency applications [5, 7โ18]. For such applications the typical FC structure presents some limitations. PMOS drivers are predominately used for their lower flicker noise and higher frequency parasitic pole, but the bandwidth is limited because of the lower carrier mobility in PMOS devices. If NMOS drivers are used, the settling behavior suffers because of the lowerfrequency parasitic pole, and in order to extend the bandwidth, several phase compensation schemes have been reported in literature [8โ12]. Another limitation of the FC, regardless of driver type, is that the maximum slewing current is roughly half the total OTA current unlike the telescopic OTA which utilizes the total current. It is shown that the recycling foldedcascode (RFC) OTA can alleviate many of the conventional FC limitations; it can settle faster and more accurately, boost slew rate, and improve overall efficiency.
In multistage amplifiers, cascading of individual gain stages increases the overall amplifier gain, but each stage introduces a low frequency pole, which produces a negative phase shift and degrades the phase margin. Many phase compensation schemes for multistage amplifiers have been reported in literature [6, 7, 19โ24]. Most of these are variations of the basic Miller compensation scheme for a twostage amplifier. The NCFF compensation scheme employs a feedforward path to create LHP zeros but does not use any Miller capacitor [25]. This topology results in a highergainbandwidth product (GBW) with a fast step response.
The theoretical aspects of feedforward techniques are discussed in Section 2. Section 3 deals with feedforward techniques associated with the FC OTA and introduces the RFC. A design case study in Section 4 compares several OTA aspects of the FC and RFC. Highgain twostage amplifiers without Miller compensation are considered in Section 5. Section 6 describes the circuit simulation and experimental results, and the conclusions are drawn in Section 7.
2. SettlingTime in the Presence of a PoleZero Pair
A macromodel of the capacitive amplifier used in switchedcapacitor circuits is shown in Figure 1(a). By using conventional circuit analysis techniques, the small signal transfer function can be calculated and is given by
(a)
(b)
where and are the amplifier openloop DC gain and the feedback factor, respectively. A typical open and closed loop magnitude response is depicted in Figure 1(b). The location of the pole is given by
where is the effective loading capacitor. The typical step response of the critically/overdamped capacitive amplifier is shown in Figure 2. It consists of two phases: the first is limited by the slew rate and the second by the closed loop bandwidth. The error in the final value is determined by the factor as can be seen in (1).
Singlestage OTA slew rate (SR) is determined by the amount of current that can be delivered to or extracted from the output and the effective load capacitor . The bandwidth limited phase is determined by both the effective poleโs frequency and phase margin, and in many practical lowvoltage cases dominates the overall settling time. If the slew rate and the RHP zero effects are ignored, the closedloop pulse response of the amplifier is given by (3), where is the ideal amplifierโs gain:
A highperformance amplifier should have a high for fast settling and a high DC gain for final value precision. The analysis of the amplifier impulse response in the presence of a polezero doublet is more complex; in [26โ28] it was shown that the presence of lowfrequency polezero pairs may generate slow components that reduces significantly the amplifier's speed. This is not the case if highfrequency polezero doublets are present. In order to consider the effects of highfrequency polezero pairs, the overall openloop transconductance of the amplifier can be simplified as
If the righthand side zero is ignored, using (1) and (4), the closedloop transfer function is obtained as
whereโโโdenotes and is defined by (2). According to (5), the closedloop poles are located at For real poles, both poles are located above and below . If the poles are complex conjugate, the magnitude of the real part is above . Notice that the zero reduces the imaginary part of the poles. Figure 3 shows the typical root locus of a 2pole and 1zero system. In both cases, the lowestfrequency pole is close to the frequency of the zero if enough feedback is used. A common case for the feedforward amplifiers to be discussed in the following sections is shown in Figure 4, which corresponds to the rootlocus shown in Figure 3(a). Both openloop and closedloop gains are depicted. Notice in this figure that the closedloop polezero doublet appears close to the openloop zeroโs frequency if enough feedback factor is present. The closedloop amplifierโs impulse response (assuming that ) is given by Slow output components caused by polezero spacing are avoided if both closedloop poles and are placed at high frequencies to guarantee small time constants; this is possible if and only if the zero is located at high frequencies, which directly impacts the location of and as seen in (6). An important observation here is that if the closedloop dominant pole is close to the location of the zero, its coefficient (proportional to ) is reduced thereby reducing the effect of possible slow components.
(a)
(b)
3. FeedForward Techniques for FoldedCascode OTAs
The typical FC OTA is shown in Figure 5 [7]. Its smallsignal transconductance gain is approximately given by (8), where is the smallsignal transconductance of , and is the capacitance associated with the source of :
The transconductance of the cascode transistors and the equivalent parasitic capacitor at that node determine the openloop poleโs frequency. For wide band applications, a large unity gain frequency is needed, and therefore the frequency of the parasitic pole must be as high as possible. PMOS drivers are preferred for FC amplifiers since the parasitic pole of the folding node is then associated with NMOS cascode devices and is located at a higher frequency. When reducing the widths of the cascode transistors, the benefit of increasing the frequency of the parasitic pole might be limited because the saturation voltage must be maintained within the limits dictated by the supply voltages and signal swing. Mobility degradation due to vertical electrical field becomes more critical in that case as well. Reducing the length of the cascode transistors reduces and increases ; the drawback is the reduction of the OTA DC gain. Increasing the bias current also increases the frequency of the parasitic poles, but the DC gain reduces, and the power consumption increases. Moreover, the choice of PMOS drivers is on the expense of a larger input capacitance for the same if NMOS drivers were used. Ideally, an OTA should use NMOS transistors for both differential pair and cascode devices, such that both the small signal transconductance and phase margin are increased. This is the major advantage of the telescopic structure [13, 14], but its output swing is limited, especially for lowvoltage applications and if low transistors are not available.
To overcome some of these tradeoffs, a number of feedforward compensation techniques have been reported [5, 8โ12]. The technique proposed in [9] uses RC networks connected to the gate of the cascode transistors; hence a zero is introduced such that the parasitic pole is partially compensated. In the technique proposed in [10], the lowfrequency signal flows throughout the PMOS cascode transistors, and, by using RC networks, the highfrequency signal flows throughout the NMOS cascode transistors. Due to the higher mobility of the NMOS devices, better performances can theoretically be achieved. The additional networks, however, increase silicon area and the capacitance of the parasitic nodes, thus reducing the frequency of the poles; a mediumfrequency polezero pair may increase amplifierโs settling time. In [11], the gate of the cascode transistor is directly connected to the input signals. By using that feedforward scheme, further improvements in the OTA phase margin are obtained due to the presence of a highfrequency zero. A major drawback of this technique, however, is that the gatedrain capacitors of the cascode transistors affect the precision of the system, especially for SC circuits. This drawback has been partially solved by using crosscoupled capacitors [12].
Complementary differential pairs have been used for a long time in the design of railtorail amplifiers [16]. They can also be used for fast amplifiers [17], where all cascode transistors can be exploited as shown in Figure 6. It can be shown that the smallsignal transconductance of the complementary OTA is given by
where denotes and and are the parasitic capacitors lumped to the source of transistors and , respectively. According to this result, if the poles at the source of and are placed at the same frequency, the overall small signal transconductance becomes with a single pole located at . In general, two signal paths generate poles located at different frequencies, leading to the socalled โphantom zeroโ; this term is used because there is not a physical element generating the zero, but this is a result of the addition of signal components with slightly phase difference.
The overall current consumption is , same as the FC OTA previously discussed. For same overall current and same input capacitance, its small signal transconductance is around more compared to the FC OTA. A downside is the introduction of the parasitic pole associated with the PMOS cascode transistor. Moreover, the addition of the signal paths generates a zero at a lower frequency than the pole associated with the NMOS cascode devices. Also, the input common mode range where the transconductance is maximized is limited. The slew rate, on the other hand, is higher because the sourced/sunk current can be as high as .
The currentmirror cascode OTA shown in Figure 7 has a non dominant pole at gate of in addition to the pole of the cascode transistor . The overall small signal transconductance is given by (10), where is the transconductance of transistor , is the capacitance associated with the gate of , is the capacitance associated with the source of the cascode device, and .
The currentmirror cascode OTA suffers from a similar limitation as the FC OTA; during negative slewing, only half of the drain current of is employed in discharging the load capacitance because the DC current provided by cancels the other half. However, a larger fraction of the overall current used can be transferred to the load if . With a current gain greater than 1 in the current mirror, the size of the input transistors can be reduced for same GBW as the FC OTA. Although this decreases the input capacitance, the parasitic capacitance at the gate of increases, which pushes the non dominant pole to lower frequencies. Also, for the same power consumption, increases the current levels at the output stage thereby lowering the OTAโs DC gain. Nonetheless, if the currentmirror OTA is designed with sufficient phase margin, it may settle faster than the FC OTA because of its enhanced slew rate and smaller input capacitance.
A recycling foldedcascode (RFC) OTA built by the combination of the conventional FC and the currentmirror OTAs is depicted in Figure 8 [18]. This architecture shares all the benefits of the two OTAs from which it is created, but without sharing their limitations. It is named the recycling foldedcascode as it reconfigures the same devices of an FC and reuses previously idle current in the signal path with virtually no increase in silicon area. In the FC OTA of Figure 5, the NMOS transistors and conduct the most current yet act as current sinks only. The modifications present in Figure 8 are intended to use and as driving transistors. First the original drivers, and (Figure 5), are split in half to produce transistors and (Figure 8). Each pair of and in Figure 8 is driven by the same input, and thus the input capacitance remains the same as that of the original FC. Next, and (Figure 5) are split with aโโ1:Nโโratio, and the diode connected and (Figure 8) are used to create an inversion and drive and , such that the small signal currents added at the sources of and are in phase. To keep the same current consumption as the original FC and simplify the forthcoming analysis, is equal to 3.
Now it can be shown that the transconductance of the RFC is given by (11), where is the same as that of the original FC , and is the lumped capacitance at the source of. By applying the value of , the lowfrequency transconductance of the RFC is found to be twice that of the original FC for the same power consumption. When compared to the currentmirror OTA, the increase in the RFC transconductance was not on the expense of increasing the output current and reducing the output impedance. As far as bandwidth is concerned, the input signal follows two paths to the output: โ โ โ creates a currentmirror OTA, while the feedforward path โ creates an FC OTA. Since the signal parts add in phase at the source of , an LHP zero is created by the feedforward path, which partially compensates the negative phase shift induced by . Since all the poles and zero of the RFC are associated with NMOS devices, they are naturally at high frequencies and will not introduce slow settling components as long as is kept moderately small. In fact, the polezero pair associated with the current mirrors and can be placed beyond the OTA unity gain frequency, . Suppose that a condition is imposed such that , then an upper boundary is placed on N as described by (12):
Given the RFC modifications, the slew rate is also improved. Assuming a singleended load , the slew rate of the original FC and the currentmirror OTAs is and , respectively. Now consider the RFC when a large signal is applied at the input. As approaches , transistors shut off, which forces transistors and to shut off. Hence the total current available to charge the capacitance at is and is provided by . On the other hand, with and off, is pushed into deep triode conducting negligible current and hence all the tail current, , is forced to flow through . This current is in turn mirrored from to by a factor of . Thus, is sourcing while is sinking , resulting in the capacitance at to be discharged by . This differential imbalance in the charging and discharging of and is quickly converted to a common mode error and fixed by the common mode feedback (CMFB), and the result is a maximum symmetrical slew rate of . While it is clear that the slew rate of the RFC is enhanced over that of the original FC, the same may not be so obvious when it comes to the currentmirror OTA. But, if we consider the same power consumption, the value of N used in the currentmirror OTA is 1 whereas for the RFC, is 3; the slew rate is also enhanced over that of the currentmirror OTA. In the design of any OTA however, the slew rate will be restricted by the size and biasing conditions of the devices in the signal path, which will limit the slew rate to a smaller value than in theory, especially for lowvoltage implementations.
An aspect worth examining is the overall efficiency. If we define efficiency as the ratio of generated smallsignal current to total DC current, that is, , then the efficiencies of the original FC, currentmirror, and RFC OTAs can be given by (13). The RFC is clearly the most efficient OTA. Although the currentmirror OTA is almost as efficient as the RFC, its increased efficiency comes at the expense of a large which drastically affects its pole locations and limits its bandwidth, whereas the efficiency of the RFC is independent of . More importantly, the efficiency of the RFC is the same as that of a telescopic OTA (total telescopic current is ), but the RFC has a wider input common mode range and larger output swing:
4. FoldedCascode OTA Case Study
This enhanced efficiency of the RFC can be viewed from another angle. If the RFC is able to achieve twice the transconductance and more than twice the slew rate of the original FC while using the same power and silicon area, then the RFC must be able to achieve the same transconductance and slew rate as the original FC using significantly less power and silicon area. Indeed, if we take the RFC of Figure 8 and reduce the width of all devices by a factor of 2, it will achieve a similar performance to the original FC, but using only half the power and half the area, which also means half the input capacitance. To demonstrate this, three OTAs were designed in TSMC CMOS technology with a 1.8โV supply: an FC and two RFC OTAs. One of the recycling foldedcascodes, RFC1, uses the same power and area as the FC, while the second, RFC2, uses only half the power and half the area.
The setup in Figure 9 was used to characterize the different OTA aspects. To preserve the highoutput impedance of the OTAs and limit the DC output current drawn, was set to be 560โ. As for and they were set to 2.2โpF and 2.5โpF, respectively, which yields an overall load of 3.6โpF. As seen in Figure 10, RFC1 indeed has a wider bandwidth, whereas RFC2 has virtually the same bandwidth; this was anticipated according to the analysis in the preceding section. While RFC1 has +6โdB gain due to an enhanced , RFC2 has +6โdB gain because it consumes half the current; the additional 2โ4โdB improvement is attributed to the enhanced output impedance. The gain enhancement seen in is due to the increased of and , as they conduct less current compared to their counterparts and of the FC. Therefore, an overall lowfrequency gain enhancement of 8โ10โdB can be seen in the RFC compared to the FC as seen in Figure 10.
(a)
(b)
(a)
(b)
The phase response shows some degradation for both RFC1 and RFC2 with respect to the FC. This is to be expected. As discussed earlier, the addition of current mirrors in the signal path introduces a polezero pair. However, by satisfying the condition set by (12) for the upper limit of , the degradation in the phase margin should not significantly affect the transient response of the amplifiers; here the phase margins of the FC, RFC1 and RFC2 are , , and , respectively. For the transient response shown in Figure 11, the input signal was a 500โmVpp 10โMHz pulse with a common mode level of 450โmV. Undoubtedly, RFC1 has a superior slew rate performance than FC as seen in Figure 11(a). RFC2 too has a better slew rate performance, which is seen more clearly in Figure 11(b) as a higher peak output current. Moreover, the settling behavior of both RFC1 and RFC2 was not affected by the phase margin degradation in comparison to FC.
(a)
(b)
As for noise, RFC1 shows better performance over the FC. Intuitively, the enhanced transconductance of the RFC1 reduces the noise when referred to the input. This, however, is counteracted by an increased output noise due to contributions by and , which actually are amplified by . Considering that the output current thermal and flicker noise PSD of an MOS device can be expressed as (14), it can be demonstrated that the input referred thermal () noise PSD of the FC and RFC1 given by (15) and (16).
The noise performance improvement of RFC1 is hence explained by two smaller terms in (17) compared to their counterpart in (15) for the FC:
A summary of the discussed results is shown in Table 1.

5. Multistage OTAs with no Miller Capacitors
Amplifiers with cascaded gain stages are very popular for SC applications as well [6, 19โ24]. Several compensation schemes have been reported in literature for multistage amplifiers [22, 23]; one of them is shown in Figure 12. The inverting amplifiers are not needed if differential stages are used. DC gains of 90โ100โdB can be achieved. Due to the three highimpedance nodes, double Miller compensation might be required for adequate phase margin. The classic twostage Miller compensation scheme is shown in Figure 13. The openloop dominant pole, , is pushed to lower frequencies by the increase in effective capacitance formed by the compensation capacitor, Cm, and the gain of the second stage, . This decreases the open loop unity gain frequency (~) and results in a slower settling time. The nondominant pole is mainly given by . For good stability, the condition must be satisfied. However, highfrequency SC circuits may require large load capacitors that force a large and further increase the power consumption and capacitor .
Feedforward compensation techniques have been used to boost the DC gain of OTAs, especially for lowfrequency applications [25], [29]. Figure 14 shows the simplified schematic of the compensation scheme. The NCFF compensation scheme does not employ any compensation capacitor but uses a Left plane (LHP) zero for obtaining good phase response. It can be found that the openloop small signal transconductance gain is
where is the DC gain of the first stage , and the dominant pole of the first stage is located at . The DC transconductance is approximately given by . By using this OTA in the amplifier configuration shown in Figure 1(a), and according to (1), (2), (5), (6), and (25), the closedloop zero and poles are located at the following frequencies:
Real poles are obtained if is further increased, but the frequency of the closedloop zero decreases, and slow components might appear. The dominant pole and zero are close enough (mismatch ) if
Additional computations show that under this condition, the poles are located at
Notice that under these conditions, and with sufficient feedback, and are very close to each other regardless of the absolute value of the load capacitors used; the rootlocus is similar to the one depicted in Figure 3. The frequency of both and increases, increasing the speed, if the parasitic capacitance at the output of the first stage, , is reducedโthis is an important design consideration. If is reduced, then complex poles might appear, but these can be tolerated; although some ringing appears in the transient response, fast response results if the real part of the poles is sufficiently large. The SC amplifier of Figure 1(a) has been simulated using the NCFF architecture with transconductances g_{m1}, g_{m2,}and g_{m3} set at 1mA/V, 4โmA/V, and 10โmA/V, respectively. The amplifier DC gain is around 90โdB, because a telescopic amplifier is used for the first stage. Shown in Figure 15(a) is the transient response for the NCFF amplifier for and and
(a)
(b)
Although the variations in parameters are large, the settling time is around 3.2 nanosecods for cases 1 and 4. The pulse response is slow if increases, cases 2 and 3, where the settling is 3.3 and 7 nanosecods, respectively. For comparison, a twostage Miller amplifier with large transconductance stages was designed; the transconductances used are and a nominal of 2โpF; a nulling resistor optimized for RHP zero cancellation is used. The amplifier DC gain is set at 90โdB. Shown in Figure 15(b) are three simulated cases for the Miller amplifier :
(1)input and integrating capacitors of 0.5โpF, 1โpF, and ;(2)input and integrating capacitors of 1โpF, 2โpF, and ;(3)input and integrating capacitors of 1โpF, 2โpF, and .Notice that the NCFF approach (nominal case, ) can be faster than the Miller amplifier, even if the latter structure uses larger transconductances.
6. Experimental and Simulated Results
The aforementioned FC, RFC1, and RFC2 OTA prototypes have been fabricated in TSMC 0.18โ CMOS process; a microphotograph of the chip is shown in Figure 16. The silicon area of the amplifiers is 4700โ, 4950โ, and 3000โ, and they were biased with a total current of 800โ, 800โ, and 400โ, respectively. Input, integrating and load capacitors of 2.2โpF, 2.2โpF, and 2.5โpF, respectively, were used. Equipment and PCB routing parasitics contribute an additional 2.1โpF, 3.4โpF, and 2.2โpF to the FC, RFC1, and RFC2, respectively. The amplifiers pulse response is depicted in Figure 17 with no observable overshoot. The settlingtime is 20.7 nanosecods, 13.7 nanosecods and 20.8 nanosecods respectively.
A twostage OTA using NCFF compensation scheme was implemented in AMI 0.5โ CMOS technology with supply voltages of ; the schematic is shown in Figure 18. The active area for the amplifier is around 0.16โ. The bias current for the first stage is only 50, and the one used in the second stage is . For the feedforward stage the tail current is . The transistor aspect ratios are 960โ/0.6โ for the first differential pair, 600โ/0.9โ for the second stage, and 120โ/0.9โ for the feedforward path. According to [25] and [27] the polezero matching should be fairly good. Postlayout simulations show that for a load capacitance of 8โpF and a step of 300โmV, the settling time of the OTA was 5.1 nanoseconds. Neither overshoots nor lowfrequency components were observed. The postlayout simulation results for a singleended OTA show a DC gain of 91โdB, GBW of 325โMHz and slew rate of 140โV/.
An inverting amplifier, similar to the one shown in Figure 1(a), was experimentally tested. For the test setup, external capacitors of 5โpF were employed. The total effective load capacitance was 12โpF (estimated capacitance of measurement equipment probe capacitance and package bondpad capacitance). Transient postlayout results for a 400โmV peak signal are shown in Figure 19(a); the amplifier response corresponds to a typical firstorder system. The settling time is around 6.5 nanosecods; the first 1 nanosecod is associated with slew rate limitations while 5.6 nanosecods correspond to linear settling. The chip was measured and the settling time for an input step of 800โmV was 17 nanosecods, as depicted in Figure 19(b), which divides to roughly 12 nanosecods in the slew rate limited and 5 nanosecods in the bandwidth limited settling phases. For these results, the input edge had a fall time of around 3 nanosecods due to PCB, bondpad parasitic (DIP40 package was used), and equipment loading effects. The output step response has no ringing, which shows a good phase margin. Postlayout simulation results for the amplifier with a 4 nanosecods fall time input step, and parasitic capacitors at the OTA input of 3pF and load capacitor of 12โpF show a settling time of around 13.5 nanosecods, which is in good agreement with the measured results.
(a)
(b)
7. Conclusions
Feedforward techniques can improve the speed of closed loop switchedcapacitor networks. It has been shown that the recycling foldedcascode OTA presents higher slew rate and superior settling performance than the conventional foldedcascode OTA for the same power consumption. The polezero pair present in feedforward topologies must be placed at high frequencies to avoid slow settling components. Another important advantage of feedforward schemes is that gain enhancement and smaller parasitic capacitor presented at the input reduce the error after settling than that obtained with the regular foldedcascode OTA. The NCFF compensation scheme enables both high gain and fast settling time, resulting in accurate and fast step response. LHP zeros are used to cancel the phase shift of poles to obtain a good phase margin. The effect of polezero mismatches on feedforward amplifierโs performance was studied, and it was shown that the polezero cancellation should occur at high frequencies for best settling time performance. Simulation and experimental results for the amplifiers are in accordance with the theoretical derivations.
References
 S.I. Liu, C.H. Kuo, R.Y. Tsai, and J. Wu, โA doublesampling pseudotwopath bandpass $\mathrm{\Delta}\sum $ modulator,โ IEEE Journal of SolidState Circuits, vol. 35, no. 2, pp. 276โ280, 2000. View at: Publisher Site  Google Scholar
 P. Cusinato, D. Tonietto, F. Stefani, and A. Baschirotto, โA 3.3V CMOS 10.7MHz sixthorder bandpass $\sum \mathrm{\Delta}$ modulator with 74dB dynamic range,โ IEEE Journal of SolidState Circuits, vol. 36, no. 4, pp. 629โ638, 2001. View at: Publisher Site  Google Scholar
 T. Salo, T. Hollman, S. Lindfors, and K. Halonen, โAn 80MHz 8th order bandpass modulator with 75 dB SNDR for IS95,โ in Proceedings of IEEE Custom Integrated Circuits Conference (CICC '02), pp. 179โ182, Orlando, Fla, USA, May 2002. View at: Google Scholar
 B. K. Thandri, J. SilvaMartinez, J. M. RochaPerez, and J. Wang, โA 92 MHz, 80 dB peak SNR SC bandpass $\sum \mathrm{\Delta}$ modulator based on a high GBW OTA with no Miller capacitors in 0.35 $\mu $m CMOS technology,โ in Proceedings of IEEE Custom Integrated Circuits Conference (CICC '03), pp. 123โ126, San Jose, Calif, USA, September 2003. View at: Google Scholar
 K. Bult and G. J. G. M. Geelen, โA fastsettling CMOS op amp for SC circuits with 90dB DC gain,โ IEEE Journal of SolidState Circuits, vol. 25, no. 6, pp. 1379โ1384, 1990. View at: Publisher Site  Google Scholar
 R. Eschauzier and J. Huijsing, Frequency Compensation Techniques for LowPower Operational Amplifiers, Kluwer Academic Publishers, Boston, Mass, USA, 1995.
 P. R. Gray and R. G. Meyer, โMOS operational amplifier design—a tutorial overview,โ IEEE Journal of SolidState Circuits, vol. 17, no. 6, pp. 969โ982, 1982. View at: Google Scholar
 T. Wakimoto and Y. Akazawa, โA lowpower wideband amplifier using a new parasitic capacitance compensation technique,โ IEEE Journal of SolidState Circuits, vol. 25, no. 1, pp. 200โ206, 1990. View at: Publisher Site  Google Scholar
 W. Sansen and Z. Y. Chang, โFeedforward compensation techniques for highfrequency CMOS amplifiers,โ IEEE Journal of SolidState Circuits, vol. 25, no. 6, pp. 1590โ1595, 1990. View at: Publisher Site  Google Scholar
 F. Opt' Eynde and W. Sansen, โDesign and optimization of CMOS wide band amplifiers,โ in Proceedings of IEEE Custom Integrated Circuits Conference (CICC '89), pp. 25.7/1โ25.7/4, San Diego, Calif, USA, May 1989. View at: Google Scholar
 J. SilvaMartinez and F. CarretoCastro, โImproving the highfrequency response of the foldedcascode amplifiers,โ in Proceedings of IEEE International Symposium on Circuits and Systems (ISCAS '96), vol. 1, pp. 500โ503, Atlanta, Ga, USA, May 1996. View at: Google Scholar
 S. Setty and C. Toumazou, โFeedforward compensation techniques in the design of low voltage OpAmps and OTAs,โ in Proceedings of IEEE International Symposium on Circuits and Systems (ISCAS '98), vol. 1, pp. 464โ467, Monterey, Calif, USA, May 1998. View at: Google Scholar
 R. H. M. van Veldhoven, โA triplemode continuoustime $\sum \mathrm{\Delta}$ modulator with switchedcapacitor feedback DAC for a GSMEDGE/CDMA2000/UMTS receiver,โ IEEE Journal of SolidState Circuits, vol. 38, no. 12, pp. 2069โ2076, 2003. View at: Publisher Site  Google Scholar
 S.T. Ryu, S. Ray, B.S. Song, G.H. Cho, and K. Bacrania, โA 14b linear capacitor selftrimming pipelined ADC,โ IEEE Journal of SolidState Circuits, vol. 39, no. 11, pp. 2046โ2051, 2004. View at: Publisher Site  Google Scholar
 Y. Yang, A. Chokhawala, M. Alexander, J. Melanson, and D. Hester, โA 114dB 68mW chopperstabilized stereo multibit audio ADC in 5.62 ${\text{mm}}^{2}$,โ IEEE Journal of SolidState Circuits, vol. 38, no. 12, pp. 2061โ2068, 2003. View at: Publisher Site  Google Scholar
 M. D. Pardoen and M. G. Degrauwe, โA railtorail input/output CMOS power amplifier,โ IEEE Journal of SolidState Circuits, vol. 25, no. 2, pp. 501โ504, 1990. View at: Publisher Site  Google Scholar
 G. OlveraRomero and J. SilvaMartinez, โA foldedcascode OTA for highfrequency applications based on complementary differential pairs,โ in Proceedings of IEEE International Workshop on MixedMode Integrated Circuits and Applications, pp. 57โ60, July 1999. View at: Google Scholar
 R. Assaad and J. SilvaMartinez, โEnhancing general performance of folded cascode amplifier by recycling current,โ Electronics Letters, vol. 43, no. 23, pp. 1243โ1244, 2007. View at: Publisher Site  Google Scholar
 L. Wang and S. H. K. Embabi, โLowvoltage highspeed switchedcapacitor circuits without voltage bootstrapper,โ IEEE Journal of SolidState Circuits, vol. 38, no. 8, pp. 1411โ1415, 2003. View at: Publisher Site  Google Scholar
 J. Grilo, I. Gallon, K. Wang, and R. G. Montemayor, โA 12mW ADC deltasigma modulator with 80 dB of dynamic range integrated in a singlechip Bluetooth transceiver,โ IEEE Journal of SolidState Circuits, vol. 37, no. 3, pp. 271โ278, 2002. View at: Publisher Site  Google Scholar
 R. Gaggl, A. Wiesbauer, G. Fritz, C. Schranz, and P. Pessl, โA 85dB dynamic range multibit deltasigma ADC for ADSLCO applications in 0.18$\mu $m CMOS,โ IEEE Journal of SolidState Circuits, vol. 38, no. 7, pp. 1105โ1114, 2003. View at: Publisher Site  Google Scholar
 F. You, S. H. K. Embabi, and E. SánchezSinencio, โMultistage amplifier topologies with nested GmC compensation,โ IEEE Journal of SolidState Circuits, vol. 32, no. 12, pp. 2000โ2011, 1997. View at: Google Scholar
 R. G. H. Eschauzier, L. P. T. Kerklaan, and J. H. Huijsing, โA 100MHz 100dB operational amplifier with multipath nested Miller compensation structure,โ IEEE Journal of SolidState Circuits, vol. 27, no. 12, pp. 1709โ1717, 1992. View at: Publisher Site  Google Scholar
 L. Yao, M. S. J. Steyaert, and W. Sansen, โA 1V 140$\mu $W 88dB audio sigmadelta modulator in 90nm CMOS,โ IEEE Journal of SolidState Circuits, vol. 39, no. 11, pp. 1809โ1818, 2004. View at: Publisher Site  Google Scholar
 B. K. Thandri and J. SilvaMartinez, โA robust feedforward compensation scheme for multistage operational transconductance amplifiers with no Miller capacitors,โ IEEE Journal of SolidState Circuits, vol. 38, no. 2, pp. 237โ243, 2003. View at: Publisher Site  Google Scholar
 B. Y. Kamath, R. G. Meyer, and P. R. Gray, โRelationship between frequency response and settling time of operational amplifiers,โ IEEE Journal of SolidState Circuits, vol. 9, no. 6, pp. 347โ352, 1974. View at: Google Scholar
 H. C. Yang and D. J. Allstot, โConsiderations for fast settling operational amplifiers,โ IEEE Transactions on Circuits and Systems, vol. 37, no. 3, pp. 326โ334, 1990. View at: Publisher Site  Google Scholar
 U. Chilakapati and T. Fiez, โEffect of switch resistance on the SC integrator settling time,โ IEEE Transactions on Circuits and Systems II, vol. 46, no. 6, pp. 810โ816, 1999. View at: Publisher Site  Google Scholar
 A. Thomsen, D. Kasha, and W. Lee, โFive stage chopper stabilized instrumentation amplifier using feedforward compensation,โ in Proceedings of IEEE Symposium on VLSI Circuits, pp. 220โ223, Honolulu, Hawaii, USA, June 1998. View at: Google Scholar
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Copyright © 2009 Rida Assaad and Jose SilvaMartinez. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.