Can anyone tell me how to generalize the PWM formulation ?

Or is there any equation that does this ?

I am really interested in knowing this because I am working on the project that deals with PWM.

If anyone can point me to right direction, appreciate it.

 

Just what are you trying to do?

In power electronics you usually just use a simple gain relationship between input level and output duty cycle.
If your sawtooth goes from 0 to 5 V and you compare this to a DC level, the duty cycle will be simply:
Dutycycle = 1/5 * Vin

This is because 5V compared to a 5V sawtooth will be 100% output while 0V compared to a 5V sawtooth is 0% and it's linear inbetween.

It's of course an idealization since not all PWM's can even do 0 to 100%.

 

I am working on the project called Kinetic energy recovery system.

I am using two batteries (primary and secondary). The primary battery is used to supply voltage to motor or scooter.

The secondary battery is used to charge and discharge to help primary battery.

It is like primary and secondary are used back and forth like PWM implies.

I am using PWM application to stretch out the distance that a scooter travels.

I am trying to get a average voltage between primary and secondary by using PWM.

I am not sure this answers your question.

 

http://www.allaboutcircuits.com/vol_3/chpt_11/1.html

Not sure about what you mean for PWM formulation.

 

When you say primary and secondary battery do you mean non rechargable and rechargable, or just that one is the main battery. What type / capacity are they?

http://en.wikipedia.org/wiki/Primary_battery