Research on Multistage Amplifier Frequency Compensation 概括
放大器为模拟设计中的核心功能模块。 CMOS 技术下低电压使得多级成为必然, 频率补 偿用于保证良好的频率特性。 目前所提出的几乎所有的频率补偿技术都是基于 NMC 和 RNMC , 并且围绕着这两种补偿方式在高稳定性, 快速暂态响应, 低功耗, 芯片面积等方面进行优化。 经过对频率补偿的研究,建立了理论框架,熟悉了各种补偿电路 , 完成了初期的理论积 累, 为后期进行深入研究奠定了良好基础。 在这篇文章里, 我将着重谈谈我对各种补偿电路 的研究体会和理解认识,简要推导电路极零点表达式并大概介绍一下其频率特性。
电路分析
一、 (NMC Nest Miller Compensation
Fig 1.Nest Miller Compensation
In the three stage NMC topology, there are two Miller capacitors Cm1and Cm2connected from the output to the output of each stage, respectively. There is a large capacitive load which makes the pole at the output very close to the dominant pole at the output of the first stage. Both poles are located at low frequency, posing a great threat to the stability of the amplifier. Pole-splitting using compensation capacitors and pole-zero cancellation using feed-forward paths seem to be the obvious solutions to remove the effect of the pole. The use of a feed-forward path to cancel this pole is risky because an imperfect pole-zero cancellation at low frequencies creates a pole-zero doublets and
deteriorates the settling time of the amplifier. This leaves us with the only choice of pole splitting using a Miller compensation capacitor. That is why almost all the frequency compensation scheme based on NMC add a capacitor between the output of the first and third stage。
The Miller capacitors Cm1and Cm2form two negative feedback loops to stabilize the amplifier but seriously reduce the high frequency gain. As a result, extra power is needed to compensate this gain reduction. Moreover, the Miller capacitor Cm2that shorts the last stage gives the additional disadvantages that the phase shift reaches 180°as frequency increases, leading to a positive feedback loop involving Cm1, gm2, and Cm2, which is a serious source of instability. Therefore, the trans-conductance gm3must be large enough to counter this shorting effect, thus, it is not suited for low-power applications.
To analyze the stability of the NMC amplifier, the small signal transfer function of the NMC amplifier shown in Fig.1 will be investigated.
首先分析一下我对极点的直观认识。 极点反映在波特图上, 即为增益曲线的拐点。 从能
量的角度看, 电容能量耗散随着频率升高而加剧。 从电压角度看, 电容阻抗随频率升高而降 低导致每一级输出阻抗降低。从电流角度看,频率升高,使电容吸取信号流的能力增强,而 电阻呈现出相对高阻抗。 极点的物理意义可以理解为电阻电容分流的临界点。 在低频处, 高 频极点电容分流低于电阻,故电容可看作开路,信号流近似全部流经电阻,形成直流增益。 在高频处,低频极点电容分流高于电阻,故电容可看作短路,信号流近似全部流经电容,进 行能量耗散。
对图 Fig.1所示 NMC 的极点进行直观分析。 首先每一级的输出寄生电容远小于所连接的 补偿电容,故可看作开路。在主极点 P0附近,高频点处的电容 Cm2, CL看作开路,信号流过对 地电阻形成高电压增益, Vout =gm2R2gm3RLVA。 A 点相对
OUT 点可近似看作零电位, OUT 点通过 Cm1向 A 注入信号流 Vout sCm1,该值应等于 A 点通过到地电阻的分流。因此有 VAgm2R2gm3RLsCm1=VAR1
? (1 即为 P0=1gm2R2gm3RLCm1R1
? (2 在此基础上,当频率继续升高, Cm1看作短路,两端近似等电位。当频率升高至第一次 极点 P1时, B 点达到电阻电容分流临界点。 我们利用 gm2激发的信号流全部流经 Cm2的近似关 系得到次极点 gm2VA=sCm2VA(3 即为 P1=gm2Cm2
? (4 再分析第二次极点 P2,电容 Cm2两端电位近似相等。由 gm3激发的信号全部流经负载电 容 CL。对点 OUT 点有 gm3VB=VBsCL(5 即为 P2=gm3CL
? (6 以上直观的分析方法避免了繁琐的计算, 可以很快地得到极点表达式, 不过有一定误差。 接下来,我将提出更精确的分析方法。该方法可以便利地计算出次极点及零点表达式。 上面的论述中已经分析过多级频率补偿普遍采用弥勒电容分离 P0和 P2。 因此几乎在所有 的补偿电路中主极点都具有相同的表达方式,如式 (2。因此我们需要分析的是三级放大器 中两个次极点。在次级点频率范围内, Cm1两端近似等电位。电容分流占主导,电阻近似看 作开路。只剩下跨导和补偿电容,利用 A 与 OUT 近似等电位的关系可以列出下式
gm2VA+(gm2VA sCm2
+VA (?gm3 =VAsCL(7 With the assumption of gm3? gm2, equation (7 can be simplified as
1+sCm2 gm2 +s2CLCm2 gm2gm3 =0(8
频率补偿研究心得
