For considerations of swing and performance, a fully differential topology is more popular, therefore, the CM level of the fully differential topology I/O ports is mostly defined with a half supply voltage due to achieved maximum swing. Also, the input signal CM level of next stage is coming from the previous stage, an unbalance common voltage always leads the performance of the next stage out of control or degradation. Hence, achieving a balance and correctness CM level is set by a CMFB (common-mode feedback) scheme. About CMFB schemes are discussed on several textbooks, which have classified with two kinds from whose operational mode as CT (continuous-time) and SC (switched-capacitor). The SC-CMFB scheme always exists some issues as clock feed-through and charge injection from switches, more poor PSRR, and increasing capacitive loading at the output of the fully differential amplifier when it is compared to CT-CMFB [4]. Hence, the SC-CMFB scheme will not be used and discussed here.
More detail about CT-CMFB will be presented in following subsections.
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Up to now, many kinds of the CT-CMFB were presented in many bibliographies, they are usu-ally evolved from four popular frames [5] of CT-CMFB structure which are shown in Fig. 2.5.
Some disadvantages are like that the sensing resistors load at the OTA output, and the re-sistor and the input capacitor of the CM-sense amplifier introduce a pole in the CMFB loop (Fig. 2.6(a)), in Fig. 2.6(b), the OTA output swing is limited since each source-follower transis-tor that connects to an OTA output must remain in the saturation region over the entire output voltage swing, and the non-constant overdrive voltage of the source-follower transistors leads non-linearity issue; another scheme in Fig. 2.5(c) is limited by that the CMFB loop will not function properly whenever the output voltage swing is large enough to turn off either transistor 5 or 6 while the transconductance of 5 and 6 in the triode region is smaller than it is in the saturation region. Then, this structure thus has a lower CMFB loop-gain. The fourth scheme in Fig. 2.6(d) has also limitation on the output voltage swing of the opamp but it does not need sensing resistors and using some transistors operate in the triode region.
On the above, the structure of using resistive divider is not considered in our work due to the resistor be often chosen large to increase the area while to increase the cost. Then, the CMFB using two differential pairs has faster speed and better accuracy than using transistors in the triode region one[6]. Therefore, the structure of using two differential pairs is chosen and used in our work. However, the input swing region and the power consumption of the using two differential pairs structure are the key issues. An improved CMFB structure will be presented later.
A bulk-driven transistor, the signal irrigates from bulk region of transistor, which is used and avoided the inherently limitative swing range of input voltage. Others benefits are more flat transconductor gm that leads a better linearity operating result, and a wide ICMR (input-common-mode-range) by using bulk-driven technique. Also for obtaining a high gain of the CMFB loop and low power consumption, the transistors of input differential pair are used in weak-inversion region (also called subthreshold region; the drain current of a mos is based on the channel diffusion current) which perform a higher bulk-transconductor gmb (or said high gain) than the transistors are operated in the saturation region. For above benefits, which can be verified in simulation results from simple circuits (the circuits are also shown in Fig. 2.6)
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(a) (b)
(c) (d)
Figure 2.5: (a) CMFB using resistive divider and amplifier, (b) the scheme of (a) with source followers as buffers between the OTA outputs and resistors, (c) using transistors in the triode region, and (d) using two differential pairs.
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which are shown in Fig. 2.6. These circuits were simulated in HSpice using BSIM3v3 model of the standard 0.35-µ m n-well CMOS process from TSMC while they compared in the same conditions (supply voltage,Vov (over-drive voltage), tail-current, temperature, and so on.) for each other.
From the simulation results, a CMFB using two differential pairs by bulk-driven is pro-posed while the differential pairs operated in weak-inversion region, the structure is shown in Fig. 2.7(a), where the OTA can be a universal structure and the node Va is a control voltage which connected to a voltage-controlled-current source of the OTA. The nodeVamaintains that the OTA output voltage keeps in a set common level, while the loop is a negative feedback. At the same time, the CMFB structure can be analogized a opamp, we thus care whose DC gain and bandwidth from view points of designing a opamp. A scheme consists of a pmos input dif-ferential pair folded-cascode OTA of bulk-driven and CMFB shown in Fig. 2.7(b) which is used in our work. In [7] which indicates the voltage gain of the operation of circuits in the weak-inversion region approaches a constant value; this result will be appeared more clear due to the Vov is more less variate than non-using bulk-driven technology. Therefore, we can say that the large-signal gain approximates the small-signal gain. At first for the small-signal analysis of the CMFB, we have to get DC operated points, disconnect the CMFB input from the OTA output, and add a large inductance between the two terminals, which inductance keeps the OTA output DC level maintain the set level before the analysis of the CMFB gain. By using typical circuit analysis techniques, it can be found that the small-signal parameters (e.g. gate-transconductor gm and bulk-transconductorgmb) and the loop gain (e.g. differential-input to single-output (at Vo+)) of the proposed CMFB shown in Fig. 2.7(b). In saturation and weak-inversion region, the approximate relation between drain current and gate-to-source voltage are given by [5, 8]
saturation region:
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(a)
(b)
(c)
(d)
Figure 2.6: Comparison between gate-driven and bulk-driven: (a) two kinds simply structure of different input terminal, (b) whose transconductance versus input differential swing range, (c) also versus common mode input voltage, and (d) comparison of transconductance between operated in saturation region and weak-inversion region for using bulk-driven.
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(b)
Figure 2.7: (a) An improved CMFB can be used in universal OTA and (b) a full scheme be used in our work.
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the linearity is quite poor forVDSsmall than3kT /q; hence, it usually chooses VDS ≥ 3kT/q ID ≃ ISW whereIS is the characteristic current,T the absolute temperature, n the inclination of the curve in weak inversion, k Boltzmann constant, q the charge of the electron or hole, γ the body effect coefficient andφF the Fermi potential. Those parameters will be used in the CMFB gain expression. The function of the CMFB gain expression which is gotten by by using the skill of open-circuit time constants method [9] is as following
HCM F B(s) = ACM F B Assuming that gmb,c1=gmb,c2=gmb,c3=gmb,c4 if the Mc1-Mc4 are matching each and the input level is the same asVcm, thus, the formular can be approximated as
ACM F B = −gmb,c1gm,4
gm,c5
Rout; where the gm,4=M · gm,c5
= −M · gmb,c1Rout (2.13)
Dominant pole: at the OTA output node
p1 = 1 RoutCout
(2.14)
Cout= CL+ Cgd,M 6+ Cdb,M 6+ Cgd,M 8+ Cdb,M 8+ Cgb,M c1+ Csb,M c1+ Cdb,M c1
(2.15) Non-dominant pole 1: at the gate of M4
p2 = gm,c5
CA
(2.16)
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Non-dominant pole 2: at the source of M6
p3 = gm,6
CB (2.17)
CB= Cgd,M 2+ Cdb,M 2+ Cgd,M 4+ Cdb,M 4+ Cgs,M 6+ Csb,M 6
(2.18) Zero: at the drain of M4
z1 = gm,M 4
Cgd,M 4 ∈ RHP (2.19)
whereCLandRout are the load capacitance and resistance at the output of the folded-cascode opamp. Notice from (2.14-2.19) that polesp1, p2, andp3 are common to both the CMFB and the differential path of the amplifier itself. On the other hand,z1 is a right half-plane zero and always of higher frequency than p1−3. The CMFB is in contrast with folded-cascode opamp, which adds additional poles that degrade the CMFB loop bandwidth and phase margin. The CMFB GBW (gain-bandwidth) product has to far enough to obtain a less enough settling time;
further, a fine CMFB design should suppress the ac CM output signal, hence, the CMFB GBW product makes the GBW product of the opamp differential mode gain about equal or over it.
Although this goal is difficult to achieve in practice[5], the CMFB GBW product must as far as enough to let the common-mode voltage settle in a time interval. Therefore, poles (p1−3) position of the CMFB will care for guaranteeing an enough GBW and the loop stability.
The differential mode open-loop gain of the opamp and the CMFB open-loop gain are ob-tained from circuit post-layout simulations along with their corresponding phase responses for a load capacitance ofCL=1.3pF , respectively. The performance parameters of the opamp and the proposed CMFB are listed in Table 2.2. Where the post-layout simulations of the CMRR and PSSRR performed by using Monte Carol analysis of 1000 times in HSpice. The parame-ters for simulator are supplied from the TSMC CMOS-0.35-µ m n-well CMOS process while the variation parameters for Monte Carol analysis are obtained from [10]. Another important issue about using bulk-driven technique is the leakage current from bulk terminal due to the
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Table 2.2: Specifications of the opamp and the CMFB for of all corner at Vdd: 3.3 V, and dimension of mosfet and Vdd varied in 3σ of 10% at TT corner.
Parameter OPAmp @CL=1.3pF Unit Note
Differential DC gain (@|Vod| = 0∼1 V) 60∼75 dB
-∆A
A2 (max.) < 162.76µ - the value is referring
to (2.5) for 10-bit linearity
GBW product (min.) 40 MHz
-Phase margin (min.) 73 deg
-Voltage swing of theVod(min.) 1 Volt
-CMRR (min. @DCVo+/− = Vcm) 80 dB
-PSRR+/- (min. @DCVo+/− = Vcm) 75 dB
-Slew rate+/- (min.) 30 V/µs
-Power consumption (max.) 850 µW
-Parameter CMFB @CL=1.3pF Unit Note
Loop DC gain (@|Vod| = 0∼1 V) 55∼70 dB
-GBW product (min. @|Vod| = 0∼1 V) 50 MHz
-Phase margin (min.) 70 deg
-Vo,cmR1 (max. range) 1.63∼1.67 Volt
-Vo,cmR2 (max. range) 1.58∼1.75 Volt
-Bulk leakage current (max.) 500 pA
-Power consumption (max.) 96 µW