Mode 2: switch open

Now the diode is forward biased, and circuit appears as shown in figure bellow.

Observe that i=i

_{L}, and solving for di_{L}/dt results in
Since we know v

_{0}is constant, we see again that the rate of change of current is constant! Therefore the current must change linearly while the switch is open. But does it increase or decrease, that is, is di_{L}/dt positive or negative?
The answer to that question depends on whether v

_{o}is larger or smaller than V_{s}. So let’s see if we can relate v_{o}to V_{s}.**Relation between v**

_{0}and V_{s}
Since current must change linearly while switch is open, we can write:

Consider peak-to-peak ripple current. It must be the negative as that given by mode 1 condition.

Now we have 2 different expressions for the peak-peak ripple current:

From mode 1 analysis:From mode 2 analysis:

So equate them!

Bring V

_{s}to the left.
Multiply by L and collect like terms.

Express v

_{o}
Consider the case of k=0. What does this mean in terms of the circuit? It means the moment when the switch opens is Is always open!

Now what happens as k increases from 0? v

_{0}gets larger It BOOSTS the voltage!
What happens when k→0?

Theoretically, , as shown.

.

Practically, parasitic elements become influential, and the output voltage is unstable for values of k approaching 1.0.

**Consideration of Power Transfer**

Let’s replace the load in our circuit with a battery.

How to deliver power to the battery?

Without the chopping action, V

_{s}must be greater than E for transferring power from V_{s}to E. But with the boost chopper circuit, we can transfer power even if V_{s}<E.
At Relation between v

_{0}and V_{s}we have_{}

Replacing v

_{o}by E:For this to be the case, V

_{s}-E < 0.

For this to be the case, V

_{s}< E.

So power transfer (positive current) occurs when source voltage is LESS than the battery voltage!

Previous Boost Regulators – analysis of switch closed

next Step-Down/Step-Up (Buck-Boost) Converter

## 0 comments:

## Post a Comment

Please wait for approval of your comment .......