Calculate dV/dQ to plot differential voltage analysis curve?

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I have all the required data but do not know how to differentiate my voltage with respect to discharge/charge capacity given.
  5 comentarios
John D'Errico
John D'Errico el 3 de Jun. de 2022
@Alberto Cuadra Lara Comments cannot be accepted as answers. If you want credit for an answer, then you need to post it as an answer.
Alberto Cuadra Lara
Alberto Cuadra Lara el 3 de Jun. de 2022
My mistake, I thought I posted it as an answer. Thanks @John D'Errico!

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Alberto Cuadra Lara
Alberto Cuadra Lara el 3 de Jun. de 2022
Hello Ekagra,
I guess you have numerical values of the voltage as a function of the discharge/charge capacity, right? In this case, you can compute the first derivative numerically, e.g., using finite central differences as follows, where x and y will be Q and V, respectively.
% Definitions
x = linspace(0, 2*pi);
y = sin(x);
% Compute first derivative
dydx = compute_first_derivative(y, x);
% Plot
figure; hold on;
plot(x, y);
plot(x(2:end), dydx);
xlabel('x', 'interpreter', 'latex')
ylabel('y', 'interpreter', 'latex')
legend({'y(x)', 'dy(x)/dx'}, 'interpreter', 'latex', 'location', 'northeastoutside');
% SUB-PASS FUNCTION
function dxdy = compute_first_derivative(x, y)
% Compute first central derivate using a non-uniform grid
%
% Args:
% x (float): Values for the corresponding grid
% y (float): Grid values
%
% Returns:
% dxdy (float): Value of the first derivate for the given grid and its corresponding values
%
% Author: Alberto Cuadra-Lara
h = y(2:end) - y(1:end-1);
hmax = max(h);
mu = h / hmax;
dxdy = zeros(1, length(h));
dxdy(1) = ((x(2) - x(1)) ./ h(1));
for i = 2:length(mu)-1
dxdy(i) = (mu(i)^2 * x(i+1) - (mu(i)^2 - mu(i+1)^2) * x(i) - mu(i+1)^2 * x(i-1)) / ((mu(i)^2 * mu(i+1) + mu(i) * mu(i+1)^2) * hmax);
end
% Direct method
% dxdy(2:end-1) = (mu(2:end-1).^2 .* x(3:end-1) - (mu(2:end-1).^2 - mu(3:end).^2) .* x(2:end-2) - mu(3:end).^2 .* x(1:end-3)) ./ ((mu(2:end-1).^2 .* mu(3:end) + mu(2:end-1) .* mu(3:end).^2) * hmax);
dxdy(end) = ((x(end) - x(end-1)) ./ h(end));
end

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