shunt_chatgpt.svg

shuntpeaking_chatgpt.m

clear; clc; close all;

% Shunt peaking parameter
m = linspace(0.2, 4, 1000);

% Special values
m_bw_max = sqrt(2);
m_no_peak = 1 + sqrt(2);

%% 1. Bandwidth extension ratio: f_3dB / f_RC
bw_ratio = sqrt( ...
    (2 + 2*m - m.^2 + sqrt((m.^2 - 2*m - 2).^2 + 4*m.^2)) / 2 );

%% 2. Peaking frequency ratio: f_peak / f_RC
fpeak_ratio = nan(size(m));

idx_peak = m < m_no_peak;

fpeak_ratio(idx_peak) = sqrt( ...
    m(idx_peak) .* ...
    (sqrt(1 + 2*m(idx_peak)) - m(idx_peak)) );

% For m >= 1 + sqrt(2), no peaking
fpeak_ratio(~idx_peak) = 0;

%% 3. Peaking gain
Gpeak = ones(size(m));

Gpeak(idx_peak) = sqrt( ...
    1 ./ ( ...
    m(idx_peak) .* ...
    (2*sqrt(1 + 2*m(idx_peak)) - m(idx_peak) - 2) ...
    ) );

Gpeak_dB = 20*log10(Gpeak);

%% Plot
figure('Color','w','Position',[100 100 1400 780]);

tiledlayout(3,1,'TileSpacing','compact','Padding','compact');

% -------------------------
% Bandwidth extension
% -------------------------
nexttile;
plot(m, bw_ratio, 'LineWidth', 2);
grid on;
ylabel('$f_{3\mathrm{dB}}/f_{RC}$', 'Interpreter','latex');
title('Shunt Peaking Trends vs $m = R^2C/L$', ...
    'Interpreter','latex', 'FontSize', 18);

xline(m_bw_max, '--', '$\sqrt{2}$', ...
    'Interpreter','latex', ...
    'LabelVerticalAlignment','bottom', ...
    'LabelHorizontalAlignment','center');

xline(m_no_peak, '--', '$1+\sqrt{2}$', ...
    'Interpreter','latex', ...
    'LabelVerticalAlignment','bottom', ...
    'LabelHorizontalAlignment','center');

ylim([1.4 1.9]);
xlim([0.2 4]);

text(1.48, 1.86, 'max BW near $m=\sqrt{2}$', ...
    'Interpreter','latex', 'FontSize', 12);

% -------------------------
% Peaking frequency
% -------------------------
nexttile;
plot(m, fpeak_ratio, 'LineWidth', 2);
grid on;
ylabel('$f_{peak}/f_{RC}$', 'Interpreter','latex');

xline(m_bw_max, '--');
xline(m_no_peak, '--');

ylim([0 1.0]);
xlim([0.2 4]);

text(2.6, 0.42, 'no peaking beyond $m=1+\sqrt{2}$', ...
    'Interpreter','latex', 'FontSize', 12);

% -------------------------
% Peaking gain
% -------------------------
nexttile;
plot(m, Gpeak_dB, 'LineWidth', 2);
grid on;
ylabel('Peaking gain (dB)');
xlabel('$m = R^2C/L$', 'Interpreter','latex');

xline(m_bw_max, '--');
xline(m_no_peak, '--');

ylim([-0.2 10]);
xlim([0.2 4]);

%% Improve axes appearance
ax = findall(gcf,'Type','axes');
for k = 1:length(ax)
    ax(k).FontSize = 12;
    ax(k).LineWidth = 1;
end