A confusion in relationship of buck-boost converter

[NexusN]

Homework Statement

On book 'Switching power supplies A to Z' page 73 at the bottom, (please kindly proceed to the link below for that page)
http://books.google.com/books?id=cu...A73#v=onepage&q=switching power supply&f=true

It stated that:

"For the buck-boost, the situation can be analyzed as follows:
■ As the input increases, the duty cycle decreases."

The input here should be referring to the input voltage, but I can hardly understand why an increase in input would put a decrease on the duty cycle, which in turns the on-time.

With duty cycle and voltage relationship formula, it should be

D=Vout/(Vout-Vin),
which an increase in Vin would bring an increase to duty cycle.

I have been trying to figure out why but it seems I have missed something important.
May you kindly point out the fault I have.
Thank you.

Homework Equations

The Attempt at a Solution

 

[NexusN]

After some minutes and having read the changed described on the mentioned book,
they are all the same, Vin increases --> Duty Cycle decreases, I think I've found the trick.

I was wrong to use the Duty Cycle - Voltage formula, instead,
I should apply the voltsecond law,
Von-ton = Voff-toff,
with Voff=Vout in this case, upon an increased Vin, we can only reduce ton and increase toff for regulation, thus resulting in a decrease in Duty Cycle.