## Graph as a function of time of the Integral of the product of V (R1n.A) * I (R1n.A)

 I would like to have the graph as a function of time of the Integral of the product of V (R1n.A) * I (R1n.A). I studied the article: https://www.circuitlab.com/forums/support/topic/97ez3wx3/power-produced-by-circuit/, but I can't understand how the ustep function works. Thank you very much by luis_presso August 23, 2020 I'm signed into CL but when I look for https://www.circuitlab.com/forums/support/topic/97ez3wx3/power-produced-by-circuit/ I get the message "Error 404: File Not Found". Perhaps the circuit is not public? by EF82 August 24, 2020 Hi @luis_presso, how about something like this: Open it and run the simulation -- I think it will do basically what you're talking about! It plots two curves (note: two different y-axes for scale). The first trace V(R1_POWER) shows the instantaneous power consumption of R1. It's mapped to Volts, but it represents 1V = 1W. The second trace shows V(R1_ENERGY) shows the integral of the first trace. It's also mapped to volts, but it represents 1V = 1J. by mrobbins August 24, 2020 Thanks @mrobbins for interesting suggestion "Integrating power ...". As a result, I learned two new things today. 1] A neat application of the Laplace Block. Wishing I had one in my (real) components box! 2] Prompted by the useful results from 1] I got to grips with the "integral" function on the simulation plot/graph, as per https://www.circuitlab.com/docs/the-basics/#cursors_math_functions I obtained the same numerical result - 162uW*s - by two different methods. Great to have two more tricks in my simulation toolbox. by EF82 August 24, 2020 Thank you very much @mrobbins. With masterful elegance, you resolved the issue. Best regards! by luis_presso August 24, 2020 Dear @EF82, look at this link https://www.circuitlab.com/editor/mde8vk9kr654/, and you will find an easier answer to the topic discussed. Best regards. by luis_presso August 24, 2020 What a good discussion you started @luis_presso , thank you very much. This is such a good learning site. by EF82 August 25, 2020 You are welcome @EF82. The contribution of @mrobbins was really very important. I think that, in the same way that there is an integrator block, there should be a derivative block of functions that, according to my interpretation, would be an ideal inductor of 1 henry. Homework :-) ... and share on this forum ... We keep in touch. by luis_presso August 27, 2020 Another great suggestion @luis_presso , thank you again. It made me think about the duality of voltage <> current in relation to Laplace blocks ("s" for one is "1/s" for the other, if long-ago learning is remembered correctly). If a "perfect" inductor of 1H can be the basis of a differentiator, then why not also a "perfect" capacitor (1F)? So, the result of my "homework" is below - two circuits for the price one one, so to speak! Be sure to read to the end in Description/Testing/2. Lots more work before these gadgets are robust enough for general use... https://www.circuitlab.com/circuit/f55993669a9b/two-differentiators/ by EF82 August 28, 2020 I should have posted this one first, it was what I was working on when your question arrived. Sorry for any back-to-front confusion. https://www.circuitlab.com/circuit/755ujprww2ns/laplace-oscillators-differentiating/ by EF82 August 28, 2020 Excellent contribution @EF82. As you say, new tools for the toolbox. Thank you very much for sharing your circuit and for taking your time for this chat. by luis_presso August 28, 2020