The Design of an Ultralow-Power Ultra-wideband (5 GHz–10 GHz) Low Noise Amplifier in 0.13 μ米CMOS技术

抽象

提出了一种超低功率低噪声放大器的设计计算方法。LNA的工作频率从5 GHz到10 GHz，采用正向体偏置技术降低电路功耗。设计围绕输入阻抗、输出阻抗和电路增益的精确计算展开。利用MATLAB和高级设计系统(ADS)对LNA进行了设计和仿真。此外，台积电为0.13μ米CMOS工艺在ADS使用。LNA被以降低功耗偏置与两个不同的电压源。Noise Figure (NF), input matching (S11), gain (S21), IIP3, and power dissipation are 1.46 dB–2.27 dB, −11.25 dB, 13.82 dB, −8.5, and 963 μW，分别。

1.简介

低噪声放大器(LNAs)是每个接收机的组成部分。根据操作的频率，可以将它们分为两个不同的类。事实上，LNA被称为超宽带(UWB)，前提是它能在一系列频率上工作。从3.1 GHz到10.6 GHz工作的系统被认为是一个超宽带系统。UWB接收机和发射机的主要结构如图所示1。该电路由RF带通滤波器（BPF RF），低噪声放大器（LNA），可变增益放大器（VGA），和混合器的。该BPF选择两个期望的频率之间的信号。由于BPF损耗和混频器的高噪声指数的时，LNA应当明显降低噪声系数。此外，它应在期望频率适当地放大该信号。此外，VGA应该控制其自身的增益适当，以便产生用于模拟 - 数字转换器（ADC）的适当信号电平。

为了达到系统所要求的适当目标，已经提出了许多工作。换言之，诸如低功耗、平坦增益、带宽期间的噪声系数、稳定性和线性度等标准得到了广泛的关注。使用了由切比雪夫滤波器放大器、反馈放大器和分布式放大器组成的不同技术[1-10]。事实上，通过利用切比雪夫滤波器[获得的最小功率消耗7]。然而，最佳功率增益是通过反馈放大器获得的[8]。此外，分布式放大器拥有所有作品中最好的输入阻抗匹配[8]。最终，反馈放大器的噪声系数最好[10]. 由于LNA的预期寿命取决于其功耗，因此功耗应大大降低。采用电流复用拓扑和前向体偏置技术等成功的方法降低功耗[11-15]. 本文采用切比雪夫滤波器、前向体偏置技术、共源共栅低噪声放大器和共源低噪声放大器，在0.13 μ米CMOS技术。

2.拟议LNA

所提出的LNA由三个主要部分组成，即，一个带通滤波器，共源极LNA，和共源共栅LNA，在图证明2。此外，共源共栅LNA的等效电路在图中描绘了3. 每一部分都被分开分析，以便更精确地审查。

一个带通滤波器或切比雪夫滤波器被用来协助LNA将信号放大到所需的频率，如图所示4。

在过滤器中的电感器和电容器是通过计算

这里，F1C较低通带频率和F2C较高通频带频率。

第二部分，另外，是一种共源极（CS）LNA。用于计算电路的输入阻抗最有名的公式由下式给出[16-18]

证明了公式具有两个虚部和实部的急剧错误[19，20]. 由于Lg、Ls和Ld是由Zin、Zout和gain公式设计的，由此产生的误差给上述元素的计算带来了极大的误差。因此，需要进行新的、精确的计算，以减小由方程引起的误差(2)。共源极LNA和其等效电路中演示图五和6。为切比雪夫滤波器的计算值是在该电路的输入和输出使用。换言之，设计用于电路的输入端的滤波器是相同的在电路中的输出中使用的过滤器。

在解决图中所示的电路后6共源LNA的增益、输入阻抗和输出阻抗由方程给出(3） - （五)。

numgain(cs) = ld × zo2 × (cgs × cgd × ls × rout × cgs × cds × ls × rout × cgd × cds × ls × rout) × s^4 × ld × zo2 × (cgs × ls × cgd × ls × cgd × gm × ls × rout) × s^3 × cgd × ld × rout × zo2 × s^2-gm × ld × rout × zo2 × s.

dengain (cs) = (cgs×cgd×ld××公司lg×ls×溃败×zo2 cd研究生院理事会××××公司ld lg××ls×溃败×zo2×cgd lg×××公司ld××cd ls×溃败×zo2)×s ^ 6×(cgs×cgd×ld lg ls×××溃败研究生院理事会×××cd ld lg××ls×溃败×cgd××cd ld lg××ls×溃败研究生院理事会×××公司ld lg××ls×zo2×cgd×ld××公司lg×ls×zo2×cgd通用×××公司ld lg ls××××扰乱zo2研究生院理事会××cgd××公司ld ls××溃败×佐薇×zo2研究生院理事会×××公司ld××cd ls×溃败×佐薇×zo2×cgd cds××公司×ld×ls×溃败×佐薇×zo2)×s ^ 5×(cgs×ld ls lg×××cgd×ld ls lg×××通用cgd××ld lg××ls×溃败研究生院理事会××cgd×ld lg××溃败×zo2研究生院理事会×××cd ld lg××溃败×zo2×cgd××cd ld lg××溃败×zo2研究生院理事会××cgd×ld ls××溃败×佐薇研究生院理事会×××cd ld×ls×溃败×佐薇研究生院理事会××cgd×ld ls××溃败×zo2×cgd××cd ld×ls×溃败×佐薇研究生院理事会×××cd ld×ls×溃败×zo2×cgd××cd ld×ls×溃败×zo2研究生院理事会××cgd lg ls×××溃败×zo2研究生院理事会×××cd lg×ls×溃败×zo2×cgd lg×××cd ls××扰乱研究生院理事会zo2×××公司ld lg××溃败×zo2×cgd lg××ld××公司溃败×zo2研究生院理事会×××公司ld×ls×溃败×zo2 cds××公司×ld×ls×溃败×zo2研究生院理事会×××公司ld×ls×佐薇×zo2×cgd××公司ld ls××佐薇×zo2×cgd通用×××公司ld×ls×溃败×佐薇×zo2)×s ^ 4×(cgs×ld lg××溃败×cgd×ld lg××溃败研究生院理事会××ld×ls×溃败××cd ld×ls×溃败研究生院理事会××ld lg××zo2×cgd×ld lg××zo2研究生院理事会××ld ls××佐薇×cgd×ld ls××佐薇研究生院理事会××ld ls××zo2×cgd×ld ls××zo2研究生院理事会××lg×ls×zo2×cgd ls lg×××zo2××公司ld×ls×zo2×cgd通用××ld lg××溃败×zo2×cgd通用××ld×ls×溃败×佐薇×cgd通用××ld×ls×溃败×zo2×cgd通用lg×××ls×溃败×zo2通用×××公司ld×ls×溃败×zo2研究生院理事会××cgd×ld×溃败×佐薇×zo2研究生院理事会×××cd ld×溃败×佐薇×zo2×cgd××cd ld×溃败×佐薇×zo2研究生院理事会××cgd×ls×溃败×佐薇×zo2研究生院理事会×××cd ls×溃败×佐薇×zo2×cgd××cd ls×溃败×佐薇×zo2研究生院理事会×××公司ld×溃败×佐薇×zo2×cgd×ld××公司溃败×佐薇×zo2)××s ^ 3ls通用ls (ld×××ld××溃败研究生院理事会××ld×溃败×佐薇×cgd×ld×溃败×佐薇×cgd×ld×溃败×zo2××cd ld×溃败×zo2研究生院理事会××lg×溃败×zo2×cgd lg××溃败×zo2 ls研究生院理事会××××扰乱zo2××cd ls×溃败×zo2×ld××公司溃败×zo2研究生院理事会××ld×佐薇×zo2×cgd×ld×佐薇×zo2 ls研究生院理事会×××佐薇×zo2×cgd ls××佐薇×zo2×cgd通用××ld×溃败×佐薇×zo2×cgd ls通用×××溃败×佐薇×zo2)×s ^ 2×(ld×溃败×ld×zo2 ls××zo2 ls通用×××溃败×zo2研究生院理事会××溃败×佐薇×zo2×cgd×溃败×zo×zo2)×s×溃败×zo2

numzout(cs) = (cgs × cgd × ld × lg × ls× rout + cgs × cds × ld  ×  lg  ×  ls  ×  rout  +  cgd  ×  cds  × ld  ×  lg × ls × rout) × s^5 + (cgs × ld × lg × ls + cgd × ld × lg × ls + cgd × gm × ld × lg × ls × rout + cgs × cgd × ld × ls × rout × zo + cgs × cds × ld × ls ×rout × zo + cgd × cds × ld × ls × rout × zo) × s^4 + (cgs × ld × lg× rout + cgd × ld × lg × rout + cgs × ld × ls × rout  + cds  × ld  ×ls × rout + cgs × ld × ls × zo + cgd × ld × ls  × zo  + cgd  ×  gm  ×ld × ls × rout × zo) × s^3 + (ld × ls + gm × ld × ls × rout + cgs × ld × rout × zo + cgd × ld × rout × zo) × s^2 + ld × rout × s.

denzout (cs) = (cgs×cgd×ld××公司lg×ls×溃败+ cgs lg×××公司ld××cd ls×溃败+ cgd lg×××公司ld××cd ls×溃败)×s ^ 6 + (cgs××ld lg××ls + cgd×ld××公司lg×ls + cgd通用×××公司ld ls lg×××溃败+ cgs×cgd××公司ld ls××溃败×佐薇ls + cgs cds××公司ld××××扰乱佐薇cd + cgd×××公司ld ls××溃败×佐薇)×s ^ 5 + (cgs×cgd×ld lg××溃败+ cgs××cd ld lg××溃败+ cgd××cd ld lg××溃败+ cgs×cgd×ld ls××溃败+ cgs××cd ld×ls×溃败+ cgd××cd ld×ls×溃败+ cgs×cgd lg××ls×溃败+ cgs lg×××cd ls×溃败+ cgd lg×××cd ls×溃败+ cgs lg××ld××公司溃败+ cgd lg××ld××公司溃败+ cgs××公司ld×ls×溃败+ cd××公司ld×ls×溃败+ cgs××公司ld×ls×佐薇+ cgd××公司ld×ls×佐薇+ cgd通用×××公司ld×ls×溃败×佐薇)×s ^ 4 + (cgs×ld lg + cgd××ld×lg + cgs×ld×ls + cgd×ld cgs lg×××ls + ls + cgd lg××ls +公司×ld×ls +通用cgd××ld lg××溃败+通用cgd××ld×ls×溃败+ cgd通用lg×××ls×溃败+有限公司通用××ld×ls×溃败+ cgs×cgd×ld×溃败×佐薇+ cgs××cd ld×溃败×佐薇+ cgd××cd ld×溃败×佐薇+ cgs×cgd ls××溃败cgs cds×××佐薇+ ls×溃败cgd cds×××佐薇+ ls×溃败×佐薇+ cgs×ld××公司溃败×佐薇+ cgd×ld××公司溃败×佐薇)×s ^ 3 + (cgd×ld×溃败+ cd×ld×溃败+ cgs lg××溃败+ cgd lg××溃败+ cgs×ls×溃败+ cd×ls×溃败+公司×ld×溃败+ cgs×ld×佐薇+ cgd×ld cgs××佐薇+ ls + cgd××佐薇ls×佐薇+通用cgd××ld×溃败通用cgd×××佐薇+ ls×溃败×佐薇)×s ^ 2 + (ld + ls +通用×ls×溃败+ cgs×溃败×佐薇+ cgd×溃败×佐薇)×s +溃败

；+ cgd×cds×ld×lg×ls×rout + cgs×co×ld×lg×；+ cgs×cds×ld×lg×rout×zo2 + cgd×cds×ld×lg×rout×8201；+ cgs×co×ld×lg×rout×zo2 + cgd×co×ld×lg×rout× + cgd×ld×lg×zo2 + cgs×ld×ls×zo2 + cgd×ld×ls×zo2 + cgs  （ld×ls + gm×ld×ls×rout + cgd×ld×rout×zo2 + cds×ld×）cgs×lg×lg××rout×zo2̵̵̵̵cgs×ls×ls×L×ls×rout×rout×zo2×zo2 + gm×ls×rout×zo2）×s + rout×zo2。

denzin(cs) = (cgs × cgd × co × ld × ls × rout × zo2 + cgs × cds × co × ld × ls × rout × zo2 + cgd × cds × co × ld × ls × rout × zo2) × s^5 + (cgs × cgd × ld × ls × rout + cgs × cds × ld × ls × rout + cgd × cds × ld × ls × rout + cgs × co × ld × ls × zo2 + cgd × co × ld × ls × zo2 + cgd × co × gm × ld × ls × rout × zo2) × s^4 + (cgs × ld × ls + cgd × ld × ls + cgd × gm × ld × ls × rout + cgs × cgd × ld × rout × zo2 + cgs × cds × ld × rout × zo2 + cgd × cds × ld × rout × zo2 + cgs × cgd × ls × rout × zo2 + cgs × cds × ls × rout × zo2 + cgd × cds × ls × rout × zo2 + cgs × co × ld × rout × zo2 + cgd × co × ld × rout × zo2) × s^3 + (cgs × ld × rout + cgd × ld × rout + cgs × ld × zo2 + cgd × ld × zo2 + cgs × ls × zo2 + cgd × ls × zo2 + cgd × gm × ld × rout × zo2 + cgd × gm × ls × rout × zo2) × s^2 + (cgs × rout × zo2 + cgd × rout × zo2) × s.

这里，击溃是M1的输出电阻，zo2为输出端阻抗，CGD是通过栅极 - 漏极M1的看到的电容器，cds是从漏极到M1源的电容，cgs是M1的门到源的电容，gm是M1的跨导， ，f是频率。

为了证明由于输入阻抗、输出阻抗或增益计算错误而产生的相当大的误差，用HSPICE对输入阻抗进行了模拟，并与用于计算Lg、Ls和Ld的公式进行了比较，如图所示7。

如可在图中观察到7中，寻的两个虚部和实部分被证实。的电路中，在图五，is designed at 7 GHz for the best S11. Hence, the real part of Zin should be 50 and the imaginary part should be 0. The elements are designed by the precise formulas and the output is demonstrated in Figure7. 在7 GHz时，虚部是-169.7，来自先前的公式，而-0.079来自精确的方程(五）本文提出了与HSPICE仿真。In addition, the real part, at 7 GHz, is 86.9 calculated by previous formula versus 50.04 calculated with both proposed formula and HSPICE simulation. It can be obviously observed that the error between imaginary parts and real parts of the precise formulas, calculated in this paper, and HSPICE simulation is zero. The previous formula, on the other hand, has more than 100% error in calculation. The aforementioned comments are applicable to both gain and output impedance. Hence, barely can elements be accurately designed by the formulas which have been proposed so far. Indeed, the more precise the formulas are, the more accurate the design will be.

所提出的LNA的输出是共源共栅LNA。LNA和其等效电路在图中示出8和9。

共源共栅LNA被用来显著降低S12，从而使LNA更稳定。此外，它还用于增强s21。因此，共源共栅LNA的主要目的是适当地放大信号。因此，增益的计算是通过求解图中存在的电路来计算的9。cascode LNA的增益由

numcas = ((cgs1 × cgd1 × cds2 × ls × lo × ro1 × ro2 × zo + cgs1 × cds1 × cds2 × ls × lo × ro1 × ro2 × zo + cgd1 × cds1 × cds2 × ls × lo × ro1 × ro2 × zo) × s^5 + (cgs1 × cgd1 × ls × lo × ro1 × zo + cgs1 × cds1 × ls × lo × ro1 × zo + cgs1 × cds2 × ls × lo × ro2 × zo + cgd1 × cds1 × ls × lo × ro1 × zo + cgd1 × cds2 × ls × lo × ro2 × zo + cgs1 × cgd1 × gm2 × ls × lo × ro1 × ro2 × zo + cgs1 × cds1 × gm2 × ls × lo × ro1 × ro2 × zo + cgd1 × cds1 × gm2 × ls × lo × ro1 × ro2 × zo + cgd1 × cds2 × gm1 × ls × lo × ro1 × ro2 × zo) × s^4 + (cgs1 × ls × lo × zo + cgd1 × ls × lo × zo + cgs1 × gm2 × ls × lo × ro2 × zo + cgd1 × gm1 × ls × lo × ro1 × zo + cgd1 × gm2 × ls × lo × ro2 × zo + cgd1 × cds2 × lo × ro1 × ro2 × zo + cgd1 × gm1 × gm2 × ls × lo × ro1 × ro2 × zo) × s^3 + (cgd1 × lo × ro1 × zo + cgd1 × gm2 × lo × ro1 × ro2 × zo-cds2 × gm1 × lo × ro1 × ro2 × zo) × s^2-(gm1 × lo × ro1 × zo-gm1 × gm2 × lo × ro1 × ro2 × zo) × s).

dencas = ((cgs1 × cgs2 × cgd1 × cgd2 × ls × lg × lo × ro1 × ro2 × zo × cgs1 × cgs2 × cgd1 × cds2 × ls × lg × lo × ro1 × ro2 × zo × cgs1 × cgs2 × cgd2 × cds1 × ls × lg × lo × ro1 × ro2 × zo × cgs1 × cgs2 × cds1 × cds2 × ls × lg × lo × ro1 × ro2 × zo × cgs1 × cgd1 × cgd2 × cds2 × ls × lg × lo × ro1 × ro2 × zo × cgs2 × cgd1 × cgd2 × cds1 × ls × lg × lo × ro1 × ro2 × zo × cgs1 × cgd2 × cds1 × cds2 × ls × lg × lo × ro1 × ro2 × zo × cgs2 × cgd1 × cds1 × cds2 × ls × lg × lo × ro1 × ro2 × zo × cgd1 × cgd2 × cds1 × cds2 × ls × lg × lo × ro1 × ro2 × zo × cgs1 × cgs2 × cgd1 × co × ls × lg × lo × ro1 × ro2 × zo × cgs1 × cgs2 × cds1 × co × ls × lg × lo × ro1 × ro2 × zo × cgs1 × cgd1 × cds2 × co × ls × lg × lo × ro1 × ro2 × zo × cgs2 × cgd1 × cds1 × co × ls × lg × lo × ro1 × ro2 × zo × cgs1 × cds1 × cds2 × co × ls × lg × lo × ro1 × ro2 × zo × cgd1 × cds1 × cds2 × co × ls × lg × lo × ro1 × ro2 × zo) × s^7 × (cgs1 × cgs2 × cgd1 × ls × lg × lo × ro1 × ro2 × cgs1 × cgs2 × cds1 × ls × lg × lo × ro1 × ro2 × cgs1 × cgd1 × cds2 × ls × lg × lo × ro1 × ro2 × cgs2 × cgd1 × cds1 × ls × lg × lo × ro1 × ro2 × cgs1 × cds1 × cds2 × ls × lg × lo × ro1 × ro2 × cgd1 × cds1 × cds2 × ls × lg × lo × ro1 × ro2 × cgs1 × cgs2 × cgd1 × ls × lg × lo × ro1 × zo × cgs1 × cgs2 × cgd2 × ls × lg × lo × ro2 × zo × cgs1 × cgs2 × cds1 × ls × lg × lo × ro1 × zo × cgs1 × cgd1 × cgd2 × ls × lg × lo × ro1 × zo × cgs1 × cgs2 × cds2 × ls × lg × lo × ro2 × zo × cgs2 × cgd1 × cgd2 × ls × lg × lo × ro2 × zo × cgs1 × cgd2 × cds1 × ls × lg × lo × ro1 × zo × cgs2 × cgd1 × cds1 × ls × lg × lo × ro1 × zo × cgs1 × cgd2 × cds2 × ls × lg × lo × ro2 × zo × cgs2 × cgd1 × cds2 × ls × lg × lo × ro2 × zo × cgd1 × cgd2 × cds1 × ls × lg × lo × ro1 × zo × cgd1 × cgd2 × cds2 × ls × lg × lo × ro2 × zo × cgs1 × cgs2 × co × ls × lg × lo × ro2 × zo × cgs1 × cgd1 × co × ls × lg × lo × ro1 × zo × cgs2 × cgd1 × co × ls × lg × lo × ro2 × zo × cgs1 × cds1 × co × ls × lg × lo × ro1 × zo × cgs1 × cds2 × co × ls × lg × lo × ro2 × zo × cgd1 × cds1 × co × ls × lg × lo × ro1 × zo × cgd1 × cds2 × co × ls × lg × lo × ro2 × zo × cgs1 × cgs2 × cgd1 × cgd2 × ls × lo × ro1 × ro2 × zo^2 × cgs1 × cgs2 × cgd1 × cds2 × ls × lo × ro1 × ro2 × zo^2 × cgs1 × cgs2 × cgd2 × cds1 × ls × lo × ro1 × ro2 × zo^2 × cgs1 × cgs2 × cds1 × cds2 × ls × lo × ro1 × ro2 × zo^2 × cgs1 × cgd1 × cgd2 × cds2 × ls × lo × ro1 × ro2 × zo^2 × cgs2 × cgd1 × cgd2 × cds1 × ls × lo × ro1 × ro2 × zo^2 × cgs1 × cgd2 × cds1 × cds2 × ls × lo × ro1 × ro2 × zo^2 × cgs2 × cgd1 × cds1 × cds2 × ls × lo × ro1 × ro2 × zo^2 × cgd1 × cgd2 × cds1 × cds2 × ls × lo × ro1 × ro2 × zo^2 × cgs1 × cgs2 × cgd1 × co × ls × lo × ro1 × ro2 × zo^2 × cgs1 × cgs2 × cds1 × co × ls × lo × ro1 × ro2 × zo^2 × cgs1 × cgd1 × cds2 × co × ls × lo × ro1 × ro2 × zo^2 × cgs2 × cgd1 × cds1 × co × ls × lo × ro1 × ro2 × zo^2 × cgs1 × cds1 × cds2 × co × ls × lo × ro1 × ro2 × zo^2 × cgd1 × cds1 × cds2 × co × ls × lo × ro1 × ro2 × zo^2 × cgs1 × cgd1 × cgd2 × gm2 × ls × lg × lo × ro1 × ro2 × zo × cgs2 × cgd1 × cgd2 × gm1 × ls × lg × lo × ro1 × ro2 × zo × cgs1 × cgd2 × cds1 × gm2 × ls × lg × lo × ro1 × ro2 × zo × cgs2 × cgd1 × cds2 × gm1 × ls × lg × lo × ro1 × ro2 × zo × cgd1 × cgd2 × cds1 × gm2 × ls × lg × lo × ro1 × ro2 × zo × cgd1 × cgd2 × cds2 × gm1 × ls × lg × lo × ro1 × ro2 × zo × cgs1 × cgd1 × co × gm2 × ls × lg × lo × ro1 × ro2 × zo × cgs2 × cgd1 × co × gm1 × ls × lg × lo × ro1 × ro2 × zo × cgs1 × cds1 × co × gm2 × ls × lg × lo × ro1 × ro2 × zo × cgd1 × cds1 × co × gm2 × ls × lg × lo × ro1 × ro2 × zo × cgd1 × cds2 × co × gm1 × ls × lg × lo × ro1 × ro2 × zo) × s^6 × (cgs1 × cgs2 × ls × lg × lo × ro2 × cgs1 × cgd1 × ls × lg × lo × ro1 × cgs2 × cgd1 × ls × lg × lo × ro2 × cgs1 × cds1 × ls × lg × lo × ro1 × cgs1 × cds2 × ls × lg × lo × ro2 × cgd1 × cds1 × ls × lg × lo × ro1 × cgd1 × cds2 × ls × lg × lo × ro2 × cgs1 × cgs2 × ls × lg × lo × zo × cgs1 × cgd2 × ls × lg × lo × zo × cgs2 × cgd1 × ls × lg × lo × zo × cgd1 × cgd2 × ls × lg × lo × zo × cgs1 × co × ls × lg × lo × zo × cgd1 × co × ls × lg × lo × zo × cgs1 × cgs2 × cgd1 × ls × lo × ro1 × zo^2 × cgs1 × cgs2 × cgd2 × ls × lo × ro2 × zo^2 × cgs1 × cgs2 × cds1 × ls × lo × ro1 × zo^2 × cgs1 × cgd1 × cgd2 × ls × lo × ro1 × zo^2 × cgs1 × cgs2 × cds2 × ls × lo × ro2 × zo^2 × cgs2 × cgd1 × cgd2 × ls × lo × ro2 × zo^2 × cgs1 × cgd2 × cds1 × ls × lo × ro1 × zo^2 × cgs2 × cgd1 × cds1 × ls × lo × ro1 × zo^2 × cgs1 × cgd2 × cds2 × ls × lo × ro2 × zo^2 × cgs2 × cgd1 × cds2 × ls × lo × ro2 × zo^2 × cgd1 × cgd2 × cds1 × ls × lo × ro1 × zo^2 × cgd1 × cgd2 × cds2 × ls × lo × ro2 × zo^2 × cgs1 × cgs2 × co × ls × lo × ro2 × zo^2 × cgs1 × cgd1 × co × ls × lo × ro1 × zo^2 × cgs2 × cgd1 × co × ls × lo × ro2 × zo^2 × cgs1 × cds1 × co × ls × lo × ro1 × zo^2 × cgs1 × cds2 × co × ls × lo × ro2 × zo^2 × cgd1 × cds1 × co × ls × lo × ro1 × zo^2 × cgd1 × cds2 × co × ls × lo × ro2 × zo^2 × cgs1 × cgd1 × gm2 × ls × lg × lo × ro1 × ro2 × cgs2 × cgd1 × gm1 × ls × lg × lo × ro1 × ro2 × cgs1 × cds1 × gm2 × ls × lg × lo × ro1 × ro2 × cgd1 × cds1 × gm2 × ls × lg × lo × ro1 × ro2 × cgd1 × cds2 × gm1 × ls × lg × lo × ro1 × ro2 × cgs2 × cgd1 × gm1 × ls × lg × lo × ro1 × zo × cgs1 × cgd2 × gm2 × ls × lg × lo × ro2 × zo × cgd1 × cgd2 × gm1 × ls × lg × lo × ro1 × zo × cgd1 × cgd2 × gm2 × ls × lg × lo × ro2 × zo × cgs1 × co × gm2 × ls × lg × lo × ro2 × zo × cgd1 × co × gm1 × ls × lg × lo × ro1 × zo × cgd1 × co × gm2 × ls × lg × lo × ro2 × zo × cgs1 × cgs2 × cgd1 × ls × lg × ro1 × ro2 × zo × cgs1 × cgs2 × cds1 × ls × lg × ro1 × ro2 × zo × cgs1 × cgd1 × cds2 × ls × lg × ro1 × ro2 × zo × cgs2 × cgd1 × cds1 × ls × lg × ro1 × ro2 × zo × cgs1 × cds1 × cds2 × ls × lg × ro1 × ro2 × zo × cgd1 × cds1 × cds2 × ls × lg × ro1 × ro2 × zo × cgs1 × cgs2 × cgd1 × ls × lo × ro1 × ro2 × zo × cgs1 × cgs2 × cgd2 × ls × lo × ro1 × ro2 × zo × cgs1 × cgs2 × cds1 × ls × lo × ro1 × ro2 × zo × cgs1 × cgd1 × cgd2 × ls × lo × ro1 × ro2 × zo × cgs1 × cgs2 × cds2 × ls × lo × ro1 × ro2 × zo+2.0 × cgs1 × cgd1 × cds2 × ls × lo × ro1 × ro2 × zo × cgs1 × cgd2 × cds1 × ls × lo × ro1 × ro2 × zo × cgs2 × cgd1 × cds1 × ls × lo × ro1 × ro2 × zo × cgs1 × cgd2 × cds2 × ls × lo × ro1 × ro2 × zo × cgs2 × cgd2 × cds1 × ls × lo × ro1 × ro2 × zo+2.0 × cgs1 × cds1 × cds2 × ls × lo × ro1 × ro2 × zo × cgd1 × cgd2 × cds1 × ls × lo × ro1 × ro2 × zo × cgs2 × cds1 × cds2 × ls × lo × ro1 × ro2 × zo+2.0 × cgd1 × cds1 × cds2 × ls × lo × ro1 × ro2 × zo × cgd2 × cds1 × cds2 × ls × lo × ro1 × ro2 × zo × cgs1 × cgs2 × cgd2 × lg × lo × ro1 × ro2 × zo × cgs1 × cgd1 × cgd2 × lg × lo × ro1 × ro2 × zo × cgs1 × cgs2 × cds2 × lg × lo × ro1 × ro2 × zo × cgs2 × cgd1 × cgd2 × lg × lo × ro1 × ro2 × zo × cgs1 × cgd1 × cds2 × lg × lo × ro1 × ro2 × zo × cgs1 × cgd2 × cds1 × lg × lo × ro1 × ro2 × zo × cgs1 × cgd2 × cds2 × lg × lo × ro1 × ro2 × zo × cgs2 × cgd1 × cds2 × lg × lo × ro1 × ro2 × zo × cgs1 × cds1 × cds2 × lg × lo × ro1 × ro2 × zo × cgd1 × cgd2 × cds1 × lg × lo × ro1 × ro2 × zo × cgd1 × cgd2 × cds2 × lg × lo × ro1 × ro2 × zo × cgd1 × cds1 × cds2 × lg × lo × ro1 × ro2 × zo × cgs1 × cgs2 × co × ls × lo × ro1 × ro2 × zo × cgs1 × cgd1 × co × ls × lo × ro1 × ro2 × zo × cgs1 × cds1 × co × ls × lo × ro1 × ro2 × zo × cgs1 × cds2 × co × ls × lo × ro1 × ro2 × zo × cgs2 × cds1 × co × ls × lo × ro1 × ro2 × zo × cgd1 × cds1 × co × ls × lo × ro1 × ro2 × zo × cds1 × cds2 × co × ls × lo × ro1 × ro2 × zo × cgs1 × cgs2 × co × lg × lo × ro1 × ro2 × zo × cgs1 × cgd1 × co × lg × lo × ro1 × ro2 × zo × cgs2 × cgd1 × co × lg × lo × ro1 × ro2 × zo × cgs1 × cds1 × co × lg × lo × ro1 × ro2 × zo × cgs1 × cds2 × co × lg × lo × ro1 × ro2 × zo × cgd1 × cds1 × co × lg × lo × ro1 × ro2 × zo × cgd1 × cds2 × co × lg × lo × ro1 × ro2 × zo × cgs1 × cgd1 × cgd2 × gm2 × ls × lo × ro1 × ro2 × zo^2 × cgs2 × cgd1 × cgd2 × gm1 × ls × lo × ro1 × ro2 × zo^2 × cgs1 × cgd2 × cds1 × gm2 × ls × lo × ro1 × ro2 × zo^2 × cgs2 × cgd1 × cds2 × gm1 × ls × lo × ro1 × ro2 × zo^2 × cgd1 × cgd2 × cds1 × gm2 × ls × lo × ro1 × ro2 × zo^2 × cgd1 × cgd2 × cds2 × gm1 × ls × lo × ro1 × ro2 × zo^2 × cgs1 × cgd1 × co × gm2 × ls × lo × ro1 × ro2 × zo^2 × cgs2 × cgd1 × co × gm1 × ls × lo × ro1 × ro2 × zo^2 × cgs1 × cds1 × co × gm2 × ls × lo × ro1 × ro2 × zo^2 × cgd1 × cds1 × co × gm2 × ls × lo × ro1 × ro2 × zo^2 × cgd1 × cds2 × co × gm1 × ls × lo × ro1 × ro2 × zo^2 × cgd1 × cgd2 × gm1 × gm2 × ls × lg × lo × ro1 × ro2 × zo × cgd1 × co × gm1 × gm2 × ls × lg × lo × ro1 × ro2 × zo) × s^5 × (cgs1 × ls × lg × lo × cgd1 × ls × lg × lo × cgs1 × cgs2 × ls × lo × zo^2 × cgs1 × cgd2 × ls × lo × zo^2 × cgs2 × cgd1 × ls × lo × zo^2 × cgd1 × cgd2 × ls × lo × zo^2 × cgs1 × co × ls × lo × zo^2 × cgd1 × co × ls × lo × zo^2 × cgs1 × gm2 × ls × lg × lo × ro2 × cgd1 × gm1 × ls × lg × lo × ro1 × cgd1 × gm2 × ls × lg × lo × ro2 × cgs1 × cgs2 × ls × lo × ro1 × ro2 × cgs1 × cgd1 × ls × lo × ro1 × ro2 × cgs1 × cds1 × ls × lo × ro1 × ro2 × cgs1 × cds2 × ls × lo × ro1 × ro2 × cgs2 × cds1 × ls × lo × ro1 × ro2 × cgd1 × cds1 × ls × lo × ro1 × ro2 × cds1 × cds2 × ls × lo × ro1 × ro2 × cgs1 × cgs2 × lg × lo × ro1 × ro2 × cgs1 × cgd1 × lg × lo × ro1 × ro2 × cgs2 × cgd1 × lg × lo × ro1 × ro2 × cgs1 × cds1 × lg × lo × ro1 × ro2 × cgs1 × cds2 × lg × lo × ro1 × ro2 × cgd1 × cds1 × lg × lo × ro1 × ro2 × cgd1 × cds2 × lg × lo × ro1 × ro2 × cgs1 × cgs2 × ls × lg × ro2 × zo × cgs1 × cgd1 × ls × lg × ro1 × zo × cgs2 × cgd1 × ls × lg × ro2 × zo × cgs1 × cds1 × ls × lg × ro1 × zo × cgs1 × cds2 × ls × lg × ro2 × zo × cgd1 × cds1 × ls × lg × ro1 × zo × cgd1 × cds2 × ls × lg × ro2 × zo × cgs1 × cgs2 × ls × lo × ro1 × zo × cgs1 × cgs2 × ls × lo × ro2 × zo+2.0 × cgs1 × cgd1 × ls × lo × ro1 × zo × cgs1 × cgd2 × ls × lo × ro1 × zo × cgs1 × cgd2 × ls × lo × ro2 × zo × cgs2 × cgd1 × ls × lo × ro2 × zo × cgs2 × cgd2 × ls × lo × ro2 × zo+2.0 × cgs1 × cds1 × ls × lo × ro1 × zo × cgs2 × cds1 × ls × lo × ro1 × zo+2.0 × cgs1 × cds2 × ls × lo × ro2 × zo × cgd1 × cgd2 × ls × lo × ro2 × zo × cgs2 × cds2 × ls × lo × ro2 × zo+2.0 × cgd1 × cds1 × ls × lo × ro1 × zo × cgd2 × cds1 × ls × lo × ro1 × zo+2.0 × cgd1 × cds2 × ls × lo × ro2 × zo × cgd2 × cds2 × ls × lo × ro2 × zo × cgs1 × cgs2 × lg × lo × ro1 × zo × cgs1 × cgd1 × lg × lo × ro1 × zo × cgs1 × cgd2 × lg × lo × ro1 × zo × cgs2 × cgd1 × lg × lo × ro1 × zo × cgs1 × cgd2 × lg × lo × ro2 × zo × cgs1 × cds1 × lg × lo × ro1 × zo × cgd1 × cgd2 × lg × lo × ro1 × zo × cgs1 × cds2 × lg × lo × ro2 × zo × cgd1 × cgd2 × lg × lo × ro2 × zo × cgd1 × cds1 × lg × lo × ro1 × zo × cgd1 × cds2 × lg × lo × ro2 × zo × cgs1 × co × ls × lo × ro1 × zo × cgs1 × co × ls × lo × ro2 × zo × cgs2 × co × ls × lo × ro2 × zo × cgd1 × co × ls × lo × ro2 × zo × cds1 × co × ls × lo × ro1 × zo × cds2 × co × ls × lo × ro2 × zo × cgs1 × co × lg × lo × ro1 × zo × cgs1 × co × lg × lo × ro2 × zo × cgd1 × co × lg × lo × ro1 × zo × cgd1 × co × lg × lo × ro2 × zo × cgs2 × cgd1 × gm1 × ls × lo × ro1 × zo^2 × cgs1 × cgd2 × gm2 × ls × lo × ro2 × zo^2 × cgd1 × cgd2 × gm1 × ls × lo × ro1 × zo^2 × cgd1 × cgd2 × gm2 × ls × lo × ro2 × zo^2 × cgs1 × co × gm2 × ls × lo × ro2 × zo^2 × cgd1 × co × gm1 × ls × lo × ro1 × zo^2 × cgd1 × co × gm2 × ls × lo × ro2 × zo^2 × cgs1 × cgs2 × cgd1 × ls × ro1 × ro2 × zo^2 × cgs1 × cgs2 × cds1 × ls × ro1 × ro2 × zo^2 × cgs1 × cgd1 × cds2 × ls × ro1 × ro2 × zo^2 × cgs2 × cgd1 × cds1 × ls × ro1 × ro2 × zo^2 × cgs1 × cds1 × cds2 × ls × ro1 × ro2 × zo^2 × cgd1 × cds1 × cds2 × ls × ro1 × ro2 × zo^2 × cgs1 × cgs2 × cgd2 × lo × ro1 × ro2 × zo^2 × cgs1 × cgd1 × cgd2 × lo × ro1 × ro2 × zo^2 × cgs1 × cgs2 × cds2 × lo × ro1 × ro2 × zo^2 × cgs2 × cgd1 × cgd2 × lo × ro1 × ro2 × zo^2 × cgs1 × cgd1 × cds2 × lo × ro1 × ro2 × zo^2 × cgs1 × cgd2 × cds1 × lo × ro1 × ro2 × zo^2 × cgs1 × cgd2 × cds2 × lo × ro1 × ro2 × zo^2 × cgs2 × cgd1 × cds2 × lo × ro1 × ro2 × zo^2 × cgs1 × cds1 × cds2 × lo × ro1 × ro2 × zo^2 × cgd1 × cgd2 × cds1 × lo × ro1 × ro2 × zo^2 × cgd1 × cgd2 × cds2 × lo × ro1 × ro2 × zo^2 × cgd1 × cds1 × cds2 × lo × ro1 × ro2 × zo^2 × cgs1 × cgs2 × co × lo × ro1 × ro2 × zo^2 × cgs1 × cgd1 × co × lo × ro1 × ro2 × zo^2 × cgs2 × cgd1 × co × lo × ro1 × ro2 × zo^2 × cgs1 × cds1 × co × lo × ro1 × ro2 × zo^2 × cgs1 × cds2 × co × lo × ro1 × ro2 × zo^2 × cgd1 × cds1 × co × lo × ro1 × ro2 × zo^2 × cgd1 × cds2 × co × lo × ro1 × ro2 × zo^2 × cgd1 × gm1 × gm2 × ls × lg × lo × ro1 × ro2 × cgs1 × cgd1 × gm2 × ls × lg × ro1 × ro2 × zo × cgs2 × cgd1 × gm1 × ls × lg × ro1 × ro2 × zo × cgs1 × cds1 × gm2 × ls × lg × ro1 × ro2 × zo × cgd1 × cds1 × gm2 × ls × lg × ro1 × ro2 × zo × cgd1 × cds2 × gm1 × ls × lg × ro1 × ro2 × zo × cgs1 × cgd1 × gm2 × ls × lo × ro1 × ro2 × zo × cgs2 × cgd1 × gm1 × ls × lo × ro1 × ro2 × zo × cgs1 × cgd2 × gm2 × ls × lo × ro1 × ro2 × zo × cgs2 × cgd2 × gm1 × ls × lo × ro1 × ro2 × zo × cgs1 × cds1 × gm2 × ls × lo × ro1 × ro2 × zo × cgd1 × cgd2 × gm1 × ls × lo × ro1 × ro2 × zo × cgs2 × cds2 × gm1 × ls × lo × ro1 × ro2 × zo × cgd1 × cds1 × gm2 × ls × lo × ro1 × ro2 × zo+2.0 × cgd1 × cds2 × gm1 × ls × lo × ro1 × ro2 × zo × cgd2 × cds1 × gm2 × ls × lo × ro1 × ro2 × zo × cgd2 × cds2 × gm1 × ls × lo × ro1 × ro2 × zo × cgs1 × cgd2 × gm2 × lg × lo × ro1 × ro2 × zo × cgd1 × cgd2 × gm1 × lg × lo × ro1 × ro2 × zo × cgd1 × cgd2 × gm2 × lg × lo × ro1 × ro2 × zo × cgd1 × cds2 × gm1 × lg × lo × ro1 × ro2 × zo × cgs1 × co × gm2 × ls × lo × ro1 × ro2 × zo × cgs2 × co × gm1 × ls × lo × ro1 × ro2 × zo × cgd1 × co × gm1 × ls × lo × ro1 × ro2 × zo × cds1 × co × gm2 × ls × lo × ro1 × ro2 × zo × cds2 × co × gm1 × ls × lo × ro1 × ro2 × zo × cgs1 × co × gm2 × lg × lo × ro1 × ro2 × zo × cgd1 × co × gm1 × lg × lo × ro1 × ro2 × zo × cgd1 × co × gm2 × lg × lo × ro1 × ro2 × zo × cgd1 × cgd2 × gm1 × gm2 × ls × lo × ro1 × ro2 × zo^2 × cgd1 × co × gm1 × gm2 × ls × lo × ro1 × ro2 × zo^2) × s^4 × (cgs1 × ls × lo × ro1 × cgs1 × ls × lo × ro2 × cgs2 × ls × lo × ro2 × cgd1 × ls × lo × ro2 × cds1 × ls × lo × ro1 × cds2 × ls × lo × ro2 × cgs1 × lg × lo × ro1 × cgs1 × lg × lo × ro2 × cgd1 × lg × lo × ro1 × cgd1 × lg × lo × ro2 × cgs1 × ls × lg × zo × cgd1 × ls × lg × zo+2.0 × cgs1 × ls × lo × zo × cgs2 × ls × lo × zo+2.0 × cgd1 × ls × lo × zo × cgd2 × ls × lo × zo × cgs1 × lg × lo × zo × cgd1 × lg × lo × zo × co × ls × lo × zo × cgs1 × cgs2 × ls × ro2 × zo^2 × cgs1 × cgd1 × ls × ro1 × zo^2 × cgs2 × cgd1 × ls × ro2 × zo^2 × cgs1 × cds1 × ls × ro1 × zo^2 × cgs1 × cds2 × ls × ro2 × zo^2 × cgd1 × cds1 × ls × ro1 × zo^2 × cgd1 × cds2 × ls × ro2 × zo^2 × cgs1 × cgs2 × lo × ro1 × zo^2 × cgs1 × cgd1 × lo × ro1 × zo^2 × cgs1 × cgd2 × lo × ro1 × zo^2 × cgs2 × cgd1 × lo × ro1 × zo^2 × cgs1 × cgd2 × lo × ro2 × zo^2 × cgs1 × cds1 × lo × ro1 × zo^2 × cgd1 × cgd2 × lo × ro1 × zo^2 × cgs1 × cds2 × lo × ro2 × zo^2 × cgd1 × cgd2 × lo × ro2 × zo^2 × cgd1 × cds1 × lo × ro1 × zo^2 × cgd1 × cds2 × lo × ro2 × zo^2 × cgs1 × co × lo × ro1 × zo^2 × cgs1 × co × lo × ro2 × zo^2 × cgd1 × co × lo × ro1 × zo^2 × cgd1 × co × lo × ro2 × zo^2 × cgs1 × gm2 × ls × lo × ro1 × ro2 × cgs2 × gm1 × ls × lo × ro1 × ro2 × cgd1 × gm1 × ls × lo × ro1 × ro2 × cds1 × gm2 × ls × lo × ro1 × ro2 × cds2 × gm1 × ls × lo × ro1 × ro2 × cgs1 × gm2 × lg × lo × ro1 × ro2 × cgd1 × gm1 × lg × lo × ro1 × ro2 × cgd1 × gm2 × lg × lo × ro1 × ro2 × cgs1 × gm2 × ls × lg × ro2 × zo × cgd1 × gm1 × ls × lg × ro1 × zo × cgd1 × gm2 × ls × lg × ro2 × zo × cgs2 × gm1 × ls × lo × ro1 × zo × cgs1 × gm2 × ls × lo × ro2 × zo+2.0 × cgd1 × gm1 × ls × lo × ro1 × zo × cgd2 × gm1 × ls × lo × ro1 × zo × cgd1 × gm2 × ls × lo × ro2 × zo × cgd2 × gm2 × ls × lo × ro2 × zo × cgd1 × gm1 × lg × lo × ro1 × zo × co × gm1 × ls × lo × ro1 × zo × co × gm2 × ls × lo × ro2 × zo × cgs1 × cgs2 × ls × ro1 × ro2 × zo × cgs1 × cgd1 × ls × ro1 × ro2 × zo × cgs1 × cds1 × ls × ro1 × ro2 × zo × cgs1 × cds2 × ls × ro1 × ro2 × zo × cgs2 × cds1 × ls × ro1 × ro2 × zo × cgd1 × cds1 × ls × ro1 × ro2 × zo × cds1 × cds2 × ls × ro1 × ro2 × zo × cgs1 × cgs2 × lg × ro1 × ro2 × zo × cgs1 × cgd1 × lg × ro1 × ro2 × zo × cgs2 × cgd1 × lg × ro1 × ro2 × zo × cgs1 × cds1 × lg × ro1 × ro2 × zo × cgs1 × cds2 × lg × ro1 × ro2 × zo × cgd1 × cds1 × lg × ro1 × ro2 × zo × cgd1 × cds2 × lg × ro1 × ro2 × zo × cgs1 × cgs2 × lo × ro1 × ro2 × zo × cgs1 × cgd1 × lo × ro1 × ro2 × zo × cgs2 × cgd1 × lo × ro1 × ro2 × zo × cgs2 × cgd2 × lo × ro1 × ro2 × zo × cgs1 × cds1 × lo × ro1 × ro2 × zo × cgs1 × cds2 × lo × ro1 × ro2 × zo × cgd1 × cgd2 × lo × ro1 × ro2 × zo × cgs2 × cds2 × lo × ro1 × ro2 × zo × cgd1 × cds1 × lo × ro1 × ro2 × zo+2.0 × cgd1 × cds2 × lo × ro1 × ro2 × zo × cgd2 × cds1 × lo × ro1 × ro2 × zo × cgd2 × cds2 × lo × ro1 × ro2 × zo × cds1 × cds2 × lo × ro1 × ro2 × zo × cgs2 × co × lo × ro1 × ro2 × zo × cgd1 × co × lo × ro1 × ro2 × zo × cds1 × co × lo × ro1 × ro2 × zo × cds2 × co × lo × ro1 × ro2 × zo × cgs1 × cgd1 × gm2 × ls × ro1 × ro2 × zo^2 × cgs2 × cgd1 × gm1 × ls × ro1 × ro2 × zo^2 × cgs1 × cds1 × gm2 × ls × ro1 × ro2 × zo^2 × cgd1 × cds1 × gm2 × ls × ro1 × ro2 × zo^2 × cgd1 × cds2 × gm1 × ls × ro1 × ro2 × zo^2 × cgs1 × cgd2 × gm2 × lo × ro1 × ro2 × zo^2 × cgd1 × cgd2 × gm1 × lo × ro1 × ro2 × zo^2 × cgd1 × cgd2 × gm2 × lo × ro1 × ro2 × zo^2 × cgd1 × cds2 × gm1 × lo × ro1 × ro2 × zo^2 × cgs1 × co × gm2 × lo × ro1 × ro2 × zo^2 × cgd1 × co × gm1 × lo × ro1 × ro2 × zo^2 × cgd1 × co × gm2 × lo × ro1 × ro2 × zo^2 × cgd1 × gm1 × gm2 × ls × lg × ro1 × ro2 × zo × cgd1 × gm1 × gm2 × ls × lo × ro1 × ro2 × zo × cgd2 × gm1 × gm2 × ls × lo × ro1 × ro2 × zo × co × gm1 × gm2 × ls × lo × ro1 × ro2 × zo) × s^3 × (ls × lo × cgs1 × ls × zo^2 × cgd1 × ls × zo^2 × cgs1 × lo × zo^2 × cgd1 × lo × zo^2 × gm1 × ls × lo × ro1 × gm2 × ls × lo × ro2 × cgs2 × lo × ro1 × ro2 × cgd1 × lo × ro1 × ro2 × cds1 × lo × ro1 × ro2 × cds2 × lo × ro1 × ro2 × cgs1 × ls × ro1 × zo × cgs1 × ls × ro2 × zo × cgs2 × ls × ro2 × zo × cgd1 × ls × ro2 × zo × cds1 × ls × ro1 × zo × cds2 × ls × ro2 × zo × cgs1 × lg × ro1 × zo × cgs1 × lg × ro2 × zo × cgd1 × lg × ro1 × zo × cgd1 × lg × ro2 × zo × cgs1 × lo × ro1 × zo × cgs1 × lo × ro2 × zo × cgs2 × lo × ro1 × zo+2.0 × cgd1 × lo × ro1 × zo × cgd1 × lo × ro2 × zo × cgd2 × lo × ro1 × zo × cgd2 × lo × ro2 × zo × cds1 × lo × ro1 × zo × cds2 × lo × ro2 × zo × co × lo × ro1 × zo × co × lo × ro2 × zo × cgs1 × gm2 × ls × ro2 × zo^2 × cgd1 × gm1 × ls × ro1 × zo^2 × cgd1 × gm2 × ls × ro2 × zo^2 × cgd1 × gm1 × lo × ro1 × zo^2 × cgs1 × cgs2 × ro1 × ro2 × zo^2 × cgs1 × cgd1 × ro1 × ro2 × zo^2 × cgs2 × cgd1 × ro1 × ro2 × zo^2 × cgs1 × cds1 × ro1 × ro2 × zo^2 × cgs1 × cds2 × ro1 × ro2 × zo^2 × cgd1 × cds1 × ro1 × ro2 × zo^2 × cgd1 × cds2 × ro1 × ro2 × zo^2 × gm1 × gm2 × ls × lo × ro1 × ro2 × cgs1 × gm2 × ls × ro1 × ro2 × zo × cgs2 × gm1 × ls × ro1 × ro2 × zo × cgd1 × gm1 × ls × ro1 × ro2 × zo × cds1 × gm2 × ls × ro1 × ro2 × zo × cds2 × gm1 × ls × ro1 × ro2 × zo × cgs1 × gm2 × lg × ro1 × ro2 × zo × cgd1 × gm1 × lg × ro1 × ro2 × zo × cgd1 × gm2 × lg × ro1 × ro2 × zo × cgs1 × gm2 × lo × ro1 × ro2 × zo × cgd1 × gm1 × lo × ro1 × ro2 × zo × cgd1 × gm2 × lo × ro1 × ro2 × zo × cgd2 × gm2 × lo × ro1 × ro2 × zo × co × gm2 × lo × ro1 × ro2 × zo × cgd1 × gm1 × gm2 × ls × ro1 × ro2 × zo^2) × s^2 × (lo × ro1 × lo × ro2 × ls × zo × lo × zo × cgs1 × ro1 × zo^2 × cgs1 × ro2 × zo^2 × cgd1 × ro1 × zo^2 × cgd1 × ro2 × zo^2 × gm2 × lo × ro1 × ro2 × gm1 × ls × ro1 × zo × gm2 × ls × ro2 × zo × cgs2 × ro1 × ro2 × zo × cgd1 × ro1 × ro2 × zo × cds1 × ro1 × ro2 × zo × cds2 × ro1 × ro2 × zo × cgs1 × gm2 × ro1 × ro2 × zo^2 × cgd1 × gm1 × ro1 × ro2 × zo^2 × cgd1 × gm2 × ro1 × ro2 × zo^2 × gm1 × gm2 × ls × ro1 × ro2 × zo) × s × ro1 × zo × ro2 × zo × gm2 × ro1 × ro2 × zo).

这里，RO1是M1的输出电阻，RO2是M2的输出电阻，ZO是输入或输出端口的阻抗时，是使Cgd1通过栅极 - 漏极M1的看到的电容器，cds1是M1漏源极的电容，cgs1是M1的门到源的电容，cgd2是通过栅极 - 漏极M2的看到的电容器，CDS2是通过漏极 - 源M2的看到的电容器，CGS2是通过栅极 - 源M2的看到的电容器，gm1是M1的跨导，GM2是M2的跨导， ，f是频率。

所计算的公式可能是冗长而复杂的。但是由于所有的公式都是用MATLAB来求解的，所以都比较容易求解。

3。结果与讨论

其中一个建议LNA的主要目标是具有最低的功耗。因此，偏压技术和电压供给是至关重要显著。如可在图中观察到1，LNA有两个不同的电压源：第一个VDD1 = 0.3伏；第二个VDD2 = 0.6伏。该技术降低了共源LNA的功耗，从而降低了整个电路的功耗。此外，每一个晶体管都在不同的区域有偏压。通过分配Vbb1 = 0.3伏，M1在弱反转下工作。因此，第一阶段的功耗为325 μW. M2 is designed to work in moderate inversion by Vbb2 = 0.5 volts. Moreover, M3 is put in strong inversion by Vbb3 = 0.3 volts. The power consumption in the second stage of the LNA is 638 μW.因此，建议在LNA的功耗为963 μW. The proposed LNA is designed to operate from 5 GHz to 10 GHz. The simulated results are depicted in Figures10-15。

该电路的稳定性已被评估

保证设置在LNA的稳定性，这μ大于1，在图展示了10。噪声图如图所示11和it varies from 2.27 dB to 1.466 dB. The noise performance of the LNA is better at higher frequencies. The input impedance matching, S11, is less than −10 dB. On average, on the other hand, S11 is −11.52 dB. The power gain of the circuit, S21, is more than 13 dB and in average is 13.82 dB. The cascode LNA makes S12 less than −32 dB, making the LNA more stable.

在7.5 GHz下对LNA进行线性仿真，如图所示15。为了评估综合考虑更多结果的LNA，我们提出了一个优点值(FOM) [21]。

所有结果和FOM与表中其他工作进行了比较1。的FOM是由于功耗和适当噪声系数​​的明显增强。此外，噪声系数的最大速率被用来计算FOM。与往常一样，取舍可以在所有参数被提及。For instance, if VDD1 is increased to 0.6 volts, noise figure is between 1.42 dB and 2 dB. Besides, power gain increases to more than 14 dB. In fact, the trade-off is between power consumption and power gain and noise figure. Indeed, by increasing VDD1 to 0.6 volts the power consumption has increased to 1.4 mW. In addition, even in comparison to other works, the power consumption is acceptable.

4。结论

超宽带超低功耗LNA在此提出。计算和功率消耗是本文的主要目标。晶体管的尺寸已经缩小到纳米级，并在本文提出的计算是适用于CMOS晶体管的所有尺寸。既然目的是计算和设计，执行不执行。然而，许多作品都证明了仿真结果和实测结果几乎接近对方。

数据可用性

用来支持这项研究的结果的数据可从作者Hemad Heidari Jobaneh在通过他的电子邮件请求：emehhj@gmail.com。

利益冲突

作者声明没有利益冲突。

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