Energy calculation via current signal integration with limits

I want to calculate Energy during applied voltage and recieved current pulse signal at given time

data=load('data.txt'); % Pulse data

T=data(:,1); % Time vector

V=data(:,2); % Voltage in volts

I=data(:,3); %Current in Amp

iVs= find(T>=0,1,'first'); % Voltage/Pulse Signal start index

Vmx=V(iVs); % Value of voltage at signal/pulse start time

iVe=find(T>0 & V<=(Vmx/4),1,'last'); % End of signal/voltage index

w=round((T(iVe)-T(iVs))*1E6); % Pulse width or duration in micro sec

P=I.*V; % Power pulse

% Now we have time, Voltage, Current, start and end time of pulse/signal

% What is enegry delivered in pulse duration (Zero to 43 micro-sec)

% Formula =

Somehow I struglling to apply intergration with time limits ?

Answer 1

[Star Strider]

Add this after your posted code:

idxrng = iVs:iVe;
IntP = cumtrapz(T(idxrng), P(idxrng));

figure
subplot(3,1,1)
yyaxis left
plot(T, V)
ylabel('V')
yyaxis right
plot(T, I)
ylabel('I')
grid
subplot(3,1,2)
plot(T, P)
ylabel('P')
grid
subplot(3,1,3)
plot(T(idxrng), IntP)
text(T(iVe), IntP(end), sprintf('Total Power = %7.3f \n \\downarrow', IntP(end)), 'HorizontalAlignment','right', 'VerticalAlignment','bottom')
ylabel('$\int{P}dt$', 'Interpreter','latex')
grid

producing:

.Add appropriate units (such a ‘VA’) for power.

[Akhtar Rind]

Some confusions,

The above term is Total power or Energy per pulse?

cumtrapz(T(idxrng), P(idxrng)); This is Power and Time integral, which would give us total power per pulse or energy?

[Star Strider]

It is the integrated power of the pulse over time. The units would be for example Watt-seconds (Joules), if that is appropriate for the voltage and current units. The total energy of the pulse (as you defined it) is -0.993.

I plotted the cumtrapz result simply to show the evolution in the context of the limits you stated. Use trapz to get a single value.

[Akhtar Rind]

Fantastic. It worked. Many thanks.

[Star Strider]

As always, my pleasure!