I am trying to work out the math of what is the highest cap voltage or capacity I can have to charge from a boost topology in a given time from a source of 5V, 500mA. Here is a rough sketch of what I am describing.
SW1 will be on for 90mS to charge the cap, then will close, then SW2 will open for 10mS to dumb current to a load. So 10Hz duty cycle.
I started to see if I have enough power: (Please correct me if I did this wrong)
I am going to look at this from joules side first.
My source has a 2.5W which is 2.5 joules/s. There for for my duty cycle of 90mS I have 2.5 joules/s * .09 = 0.225 joules/ 90ms.
A cap of 30V 300uF with has energy of 1/2*C*V^2 = 135m joules.
So from energy point of view knowing switching loses and what not, that I have enough energy to charge my capacitor. Is this correct?
This is where it all falls a part when I try to calculate it using constant current capacitor charging equations. The numbers don't add up.
My source is 2.5W, lets assume switching losses of 0.5W to make the math easy.
So I have 2W at the cap. Using P=VI with V=30 and P=2W, I will be 66mA.
Using the equation of charge of the capacitor V = It/C assuming I is constant and solving for t=dVC/I (Note: dv=25V since my 2V buck converter will most likely not work below 5V on the cap. I know this will make the math a bit different but I don't think it should change by that much)
So we solve for t = 25V * 300 / 66mA = 113mS. So it will take me 113mS to charge the cap even though I have almost double the amount of energy needed? Perhaps I am looking at this all wrong and just want someone to point out why my numbers are not adding up and that I am just mixing up two different thing together.
EDIT: The load is a laser of 10A for 6mS 10Hz