模拟集成电路中的频率补偿(4)

FIRST QUARTER 2011

small-signal equivalent model of the OpAmp. gm1 and gm2 represent the transconductance of M1 and M2, respec-transconductance of M7 and M8 tively, with gm15gm2. The transconductance, is gmb. gmL is the sum of M9 and M10’s

which includes the ac effect of the class-AB stage. The

output conductance of each stage is denoted by gob, go1, and goL, respectively. Cpb, Cp1, and Cp2 that lumped into the load capacitor CL, represent the parasitic capacitances at the corresponding stages. A small Cb amplified by the pro-posed CM has large effective capacitance and causes the two poles associated with the input and output nodes of

the second stage to split apart, leading to widely spaced

dominant and non-dominant poles. The purpose of Cd is to adjust the position of the first non-dominant pole and

handle a wide range of load capacitance. An area-efficient MOSCAP befits Cd for area reduction.

A. Local Feedback Loop

Analysis of the Proposed OpAmp

When the proposed CM is incorporated into the two-stage OpAmp, it introduces a local feedback loop around the second stage. To analyze the stability of the OpAmp under varying capacitive load, the local loop is broken at the node Vb as shown in Fig. 11(b). In addition to the assumptions made for analyzing the proposed CM, the local transfer function TL1s2 is calculated with the fol-lowing assumptions:

1) The gain of all the stages are much greater than 1;2) The parasitic capacitance Cpb, Cp1, and Cp2 are much smaller than Cb, while CL is much larger than Cb.Hence, TL1s2 is given by,TL1s2<

2

sgmL1gmb Rb212Cb

.

ggss

CbCbRbCpbo1oLa11pdba11p1ba11sg1s2b

mbgmb

(12)The magnitude plot of TL1s2 is shown in Fig. 12 with in-creasingly large CL. The dominant pole of the local loop is vpd 5 goL/CL

while the first non-dominant pole is vp1 5 go1/1Cp11Cd2. vµ is the UGF of the local loop and other two high-frequency poles are produced by the CM, which are gmb/Cb, and 1/1RbCpb2, respectively. Of course, they might exhibit the form of two complex poles.

As described in Fig. 12, when CL is small, vm might be located close to, gmb/Cb and 1/1RbCpb2. With much smaller CL, the PM of the local loop worsens to cause a significant peaking in the overall transfer function of the OpAmp [27]. Therefore, the OpAmp has a lower limit for driving capacitive loads. To evaluate the limit, the PM

FIRST QUARTER 2011

of the local loop is assumed to be larger than 45°, and

expressed asvm

PMblocal<90°2arctan

gmb/C. (13)

12

v2$45°mgbCpb

mb/Cb

From (4), gmb/Cb is set to be equal to 1/1RbCpb2 to make

full use of the proposed CM. Solving (13) with this condi-tion, implies that the minimum CL that ensures a stable local loop is

C1"5112gmL1gmbRb212C2b

L5

2gmb1Cp11Cd2

If Cd is not added, the minimum CL is still very large.

So the OpAmp is unable to handle small capacitive load without Cd.

Since vm, gmb/Cb, and 1/1RbCpb2 determine the high-frequency poles of the OpAmp’s overall transfer func-tion, a larger vm suggests a larger PM. As CL increases, vm is reduced, as shown in Fig. 12. Although the local loop’s PM improves, the OpAmp’s PM degrades. This trend continues until the mid-band local loop gain be-comes less than the unity, which is given by

gmL1gmbRb212Cb

g,1. (15)

o1CL

Under this condition, the local loop fails to control the high-frequency behavior of the OpAmp. Therefore, the transfer function of the OpAmp is obtained by mere-ly considering the open loop given below:

g1gmbRb112Cb

m1gmLa11s

A2gmb

v1s2<

gC

p1d

o1goLa11s

gba11sCL

o1

gb

oL

IEEE CIRCUITS AND SYSTEMS MAGAZINE

35

A LHP vz1 5 2gmb/31gmbRb112Cb4 is generated in the OpAmp. The appearance of vz1 is not due to the existence of the local feedback loop. Physically, the presence of such an LHP zero derives from the fact that one part of the signal at the output of gm1 stage is bypassed by the resistor Rb and this part of the signal is in-phase with the signal passing through the main path. From (16) and neglecting the impact of vz1 be-cause of its high location in frequency, the PM of the OpAmp is expressed as

PMmin<arctan

4go11gmbRb212Cb

gm1Cp11CdThe requirement in (19) indicates there are two pos-sibilities to obtain a good PMmin for the OpAmp. One is to reduce the first stage gain of the OpAmp, while increas-ing OpAmp’s offset and noise and lowering the overall gain, and leading to a limited reduction in gm1/go1. The other is to enlarge the ratio 31gmbRb212Cb4/1Cp11Cd2 al-though with a limitation. As observed from Fig. 12, vm is proportional to this ratio and vm also increases with de-vp1creasing CL. The increased vm will approach the values g2o1CL

5arctan PM<arctan

of the high-frequency poles, and significantly degrading Adcvpdgm1gmLCp11Cdthe PM of the local loop. Therefore, the design effort will

Investigating eq. (17), if CL increases further, the posi-imply trade-offs among the first stage gain, power, and tion of the dominant pole goL/CL is shifted to the left the size of Cb and Cd.while the non-dominant pole go1/1Cp11Cd2 remains un-changed. Thus, the PM of the OpAmp increases. For this B. Capacitor Size and Unity-Gain Frequency

case, if the proposed OpAmp is stable for the given value It is worth it to mention that the proposed CM tech-of CL, it is also unconditionally stable for any larger CL.nique further decreases the size of physical capacitor From the varying course of PM versus CL in the by 1gmbRb 212 when compared with the MCCB tech-above cases, a minimum PM of the OpAmp occurs at nique for single-value load capacitance. In other words, TL1jw251 which is …… 此处隐藏：5572字，全部文档内容请下载后查看。喜欢就下载吧 ……