Designing a Boost Converter: Finding L for CCM Operation

[jmaack]

Homework Statement

I have some very big difficulties with this assignment, hope someone can give me some clue in the right direction

Design the boost converter represented in and operating in continuous conduction mode (CCM). The usual
hypotheses apply: the output voltage is considered to be constant and equal to Vo, the input voltage is
considered to be constant and equal to Vi, all the components are ideal. Remember to choose a correct value
of inductance in order to guarantee the operation in CCM in the whole range of output current.
Data

Input voltage: Vi = 10 V
Output voltage: Vo = [15; 25] V
Output current range: Io = [2; 5] A
Switching frequency: fs = 50 kHz
Maximum output voltage ripple admitted: Δvo,max = 0.5 V

Questions

1. Switching period: Ts
2. Output power range: Po
3. Inductance: L
4. Duty cycle range: D

Homework Equations

The main problem is that I have no idea on how to find the inductance! I know the solution for a Buck, but not for a boost. I have attached a drawing of the circuit.

Will really appreciate any kind of help or hints!

Best regards!

 

[rude man]

Regarding the load resistor, are we to assume that it can range from 15V/5A = 3 ohms to 25V/2A = 12.5 ohms?

 

[jmaack]

Yes, believe so - but the other way around: 15V/2A = 7.5 to 25V/5A = 5.

But to honest, I have am not at all sure! Do you have any hints then? :-)

 

[rude man]

Once you double-check the above, some things to think about:

* do you understand how the circuit basically works?

* what is the worst case of Vo and Io for the worst-case load R in order for the current thru L to never = 0?

* hint 1: develop 4 equations in 4 unknowns: T1, T2, L and the peak inductor current I(T1) at the end of inductor build-up time T1. T2 is the time the inductor current is fed to the load.

hint 2: net charge addition to C over the time T1 + T2 = 0.

Once you have obtained the largest needed L, you still have to solve 4 equations in 4 unknowns even though you now know L, since the current I0 at the start of T1 is not zero for any conditions other than the worst case. So that initial current now becomes the 4th unknown.

* hint 3: assume C is arbitrarily large so the output voltage is essentially always constant. The size of C is determined solely by the ripple requirement and comes last in your computations.

When you're done you might want to set up a spread sheet where you can input any Vo an R within the permissible range and compute T1, T2, I(T1) and I0.

 

[rude man]

Yes, believe so - but the other way around: 15V/2A = 7.5 to 25V/5A = 5.

But to honest, I have am not at all sure! Do you have any hints then? :-)

You need to find out positively what the (Vo, Io) choices are. Do you believe you need design the circuit for (15V, 2A) and (25V, 5A) ONLY?

EDIT: from the problem statement I think Vo is either +15V or +25V but current can range from 2A to 5A. Notice the word "range" for current in the problem statement.

 

[jmaack]

I need to determine the inductor, and capacitor size, so I can keep it in CCM. I need to do that for all the values of Io and Vo. Meaning, if for example I use LT Spice to simulate the circuit, then it should be in CCM for the lowest values (because then it would also be the point for the other values i guess). Does that make sense?

 

[rude man]

EDIT: I'm sorry, one more change:

You bring up a good point. L needs to be large enough to guarantee continuous current operation (CCM) for the four possibilities: (15V,2A), (15,5), (25,2) and (25,5). Let's assume we don't know which of the four that is.

Looking at the equations I developed it became obvious that there is a direct relation between T₁, T₂ and the duty cycle D = T₁/(T₁+T₂): you can get a very simple equation relating Vout to Vin and D. Use the fact that at t=0 we throw the switch on, so I_L builds up from I₀ to I₀ + ET₁/L. Then, when the switch is switched off, I_L decays until at t=T, I_L(T)= I_L(0) = I₀ again.

So now T1 and T2 are determinable since T1+T2 = T = 1/50KHz. So do this for the two output voltages of 15V and 25V: get D(15V) and D(25V).

You also know load R for the four possible conditions of course.

By realizing that, over one cycle, the net charge into the capacitor must be zero you can now determine L for each of the four conditions. You pick the highest L of the four for your final design.

To double-check that you get CCM operation for all four conditions you now assume a finite I0 and solve again for zero net current flow into the capacitor per cycle. You should get I0 = 0 for the worst case and I0 > 0 for the other three.

You can finally solve for your C value from the output voltage ripple spec. You know charge in during T2 and charge out during T1, and delta Vout = (1/C)(charge in during T2 - charge out during T1).

BTW I don't know how much help your simulation software is for the design phase. But you can certainly check your computations with it.