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Homework Statement
A boost SMPS has the following design properties:
Input Voltage - Vi = 6.0v
Maximum Output Current - Io(max) = 0.5A
switching frequency - F = 100khz
Inductor = 500μH
Capacitor = 1000μF with ESR 25mΩ
Consider the boost SMPS operating in discontinuous conduction mode with a duty cycle of 0.5.
i) Calculate the energy stored in the inductor at the end of the on-time.
ii) Consider discontinuous conduction mode as in part i) when the boost SMPS has a 600Ω resistor connected at the output. Find the value of the output voltage that the SMPS will adopt.
Homework Equations
1/2CV^2 = Energy stored in a capacitor.
1/2Li^2 = Energy stored in an inductor.
ΔVc = 1/c∫Io.dt = 1/C * Io * δ/F voltage ripple
Assume voltage drop across diode is negligible. I have attached the circuit diagram of a simple boost that we have been using for this course.
The Attempt at a Solution
After having given a lot of thought, I have an attempt but do not think it's correct. I would really appreciate some help with this.
We are operating in discontinuous conduction mode, which means the current flowing when the transistor is in it off state drops to zero before it turns on again. Therefore, all the energy that was built up in the inductor is shipped to the capacitor. Hence, if I am able to work out the voltage ripple across the capacitor, then I can apply the equation E = 1/2CV^2 and obtain the energy that was also stored in the inductor.
I am having some trouble working out this ΔVc. My initial approach was to use ΔVc = 1/c∫Io.dt = 1/c * Io * δ/F where δ is the duty cycle (0.5). This brings into question what should I use as Io ? The question gives Io(max) which is 0.5A but I do not think this is what I should be using?.
Using this gives me an answer of 3nJ which seems far too small. I am also absolutely clueless about whether to take the ESR into account too.
If anyone could shed some light on this I would be extremely grateful ! Some indication of whether my method is correct would be most appreciated too. Many, many thanks and I wish you all a good day :)