gmid设计二级运放

GMID设计二级运放
设计原则与目标
在GMID参数指导下，设计二级运算放大器的关键在于优化gm/ID比率。通过调整晶体管的几何尺寸和其他参数来实现最佳性能指标[^1]。
参数选择策略
对于第二级的设计，需考虑如何提升gmro特性。为了达到这一目的，可采取两种主要措施：一是保持较小的沟道宽度以减少寄生电容；二是维持固定的gm/id比例下增大器件尺寸从而持续增强gmro表现[^3]。
工艺流程概述
具体到实际操作层面，在确定了所需的跨导值(gm)之后，应根据应用需求选取合适的栅极长度(L)，其中短沟道有利于获得更高的速度和更紧凑的布局而长沟道则有助于提高内在增益。随后依据所选gm/id比设定工作电流(Id),并最终计算得出所需宽度(W)[^4]。
% MATLAB Simulation Example for Second Stage Op-Amp Design Using GMID Methodology
clc;
clear all;

% Define parameters based on the requirements and technology constraints.
Vdd = 1.8; % Supply voltage (Volts)
Vgs = 0.7; % Gate-source voltage (Volts)

% Choose L value considering speed vs gain trade-off.
L_short_channel = 0.1e-6; % Short channel length for high-speed applications (Meters)
L_long_channel = 1e-6; % Long channel length for higher intrinsic gain (Meters)

% Set target gm_id ratio according to application needs.
target_gm_id_ratio_high_gain = 2 * 1e-3 / 1e-6; % Higher gm/id for better performance at cost of power consumption
target_gm_id_ratio_low_power = 0.5 * 1e-3 / 1e-6;% Lower gm/id aiming at low-power operation with acceptable signal swing.

% Calculate W using chosen L and desired Id values while keeping gm/id constant.
function Width = calculate_width(CurrentDensity, LengthChannel, TargetGmIdRatio)
mu_n = 400*1e-4; % Mobility factor (cm²/V·s converted into SI units m²/V·s)
Cox = 9.5e-9; % Oxide capacitance per unit area F/m

Vt = 0.4; % Threshold Voltage Volts
Kp = ((mu_n*Cox)/(2*(LengthChannel)));

Desired_Id = CurrentDensity * LengthChannel;
Width = sqrt((Desired_Id/(Kp*((Vgs-Vt)^2)))) ./TargetGmIdRatio;
end

disp('Width calculated for short-channel:');
calculate_width(target_gm_id_ratio_high_gain*L_short_channel,Vgs-L_short_channel,target_gm_id_ratio_high_gain);
disp('Width calculated for long-channel:');
calculate_width(target_gm_id_ratio_low_power*L_long_channel,Vgs-L_long_channel,target_gm_id_ratio_low_power);
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