Calculate the capacitor capacity

[oph]

task 2: Derive an expression for the maximum capacitor voltage in dependence on the occurring sizes.

the task has to do with an up-converter and I should determine an equation for the maximum capacitor voltage

this are the new details:

Since the voltage Vo of the battery is lower than the capacitor voltage required, it must be upconverted. One possibility is a so-called step-up converter, as outlined in the following figure.

The switch S opens and closes periodically, where he closed a share g of the period and a fraction 1 - g is open. The period should be very small compared to the time constant of the capacitor-resistor system. The quantity g is called duty cycle.

The drawn, high-impedance resistor R represents the resistive behavior of the capacitor. All components must be assumed to be ideal, in particular, that the diode is fully locked in the reverse direction and causes no voltage drop in the forward direction.

I hope you understand the task now. If not please ask me



(I have already upload a circuit plan at the beginning)

 

[Delphi51]

With periodic shots of energy/charge from the inductor and losses to the resistance, there will come a voltage level when during one period the loss will equal the gain. If you can find this voltage you will have your answer!

 

[oph]

but where should I start?

 

[lewando]

I'm still not sure what, exactly, you are trying to determine.

"Derive is an expression for the maximum adjusting capacitor voltage..."

What do you mean by adjusting capacitor or adjusting capacitor voltage

If you think this somehow means V_c(t) when the capacitor is charging, then please confirm.

"...after some time,..."

I am pretty sure this means "a time when the charger is at steady state", or "at the maximum charging voltage" (there will be some ripple voltage--take the peak, take the average--your call). t=∞ works, but so will much shorter values for t. So Task 2 could be find V_c(∞), then, except you say:

...depending on the sizes which occur".

The sizes of what? There are a few things that can change "sizes", V_o (the battery voltage), L, R<sub>c, g (the duty cycle), f (the frequency of your switch control voltage)

So maybe you are looking for a general expression: Vc(t=∞, Vo, L, Rc, g, f). If so, I think that will be a very difficult thing to do.

Your charging circuit is called a "boost"-type switching regulator. I can operate in two modes: "continuous" (when there is always some current going through the inductor) and discontinuous (when the current in the inductor is allowed to go to zero, periodically). Many posts ago, an expression for Vc(∞) versus Vo and duty cycle, g, was given. This applies to "continuous mode" operation.

You should familiarize yourself with this knowledge. The best link I can find that will help the details is:
http://en.wikipedia.org/wiki/Boost_converter

Study it, let me know what you want to do.</sub>

 

[oph]

Yes, you are right.
I should determine the maximum of Vc and i`m looking for a general expression.

I have really no idea where I should start, can you please give me a tip?

 

[lewando]

Let me refine my comment: A general equation based on all the variable parameters is outside my ability to envision. Depending on what the mode of operation is (continuous/discontinuous conduction), different equations apply.

Here are some tips:
(1) Constrain the problem to simplify the general equation (consider operation in continuous conduction mode only, for example. Assume a 50% duty cycle constraint). Discuss this approach with your instructor.

(2) Have you read the wiki-link in post 54? Do you have any questions about the article? What other research have you done? If possible, share your findings and also any questions you have about them.

 

[oph]

On an other site I have found some information but I don´t know if they are useful to solve the problem.

For the continuous and steady operation the law of induction applies
ΔI_L = \frac{1}{L}V_e ⋅ t₁ = \frac{1}{L} (V_a - V_e) ⋅ (T-t₁)

V_a = V_e \frac{T}{T-t₁}

The output voltage depends only on the duty cycle and the input voltage, it is independent of the load.

Do you have an idea how i can go on?

Maybe it is helpful to know what my next task is:
Determine how large g must be chosen for a capacitance of 100uF with an resistance of 100MΩ and to charge a 12.0 V battery to a voltage of 500 V when the inductance L of the coil is 5,0 mH.

Maybe you have dot an idea