6V/20W Bulb charger & battery design

[Vindhyachal.takniki]

1. Have to design 1 hour backup for 6V/20W  bulb. Have to design a UPS based system.
Bulb: http://www.amscope.com/20w-6v-halogen-bulb-for-microscopes.html

2. What I am thining of using one of below:
   A) 7.4V/5400mAh lithium Ion battery (3.7V/2600mAh) single cell. Total 4 cells
   B) 14.4V/2600mAh lithium Ion battery (3.7V/2600mAh) single cell. Total 4 cells
   
3. A) 7.4V system voltage will vary from 5V-8.4V
   B) 14.4V system voltage will vary from 10V-16.8V   
   
4. Now for 6V/20W, if we consider current then it would be 20W/6V=3.33A
If I use 14.4V/2600mAh battery & use TPS564201DDCR regualtor with it, below find link designed by webbench.
https://drive.google.com/open?id=0B-jbeBk3wfkWM1V0LXhSeXFkak0

System state state Efficieny is 92.977%.

Watts of 14.4V/2600mAh battery is =  14.4*2600mAh = 37.440WattHour
At 92.977% efficieny, Watt I will get = 37.440W_h*92.977% = 34810.5888W_hours

Watts required for 6V/20W bulb for in a hour = 20W_H

So I think this can work. & I can give 1 hour back with this system.

Are the calculations correct. Will system work as per my calculations


5. If I use 7.4V/5200mAh battery, I will use PWM control circuit using 555 & mosfet will be controlled.
System should be such that at 8.4V of battery, PWM out will create 6V at bulb.
So as battery drains outs, voltage at bulb also goes down & its glow will be dimmer.


6. I think 14.4V system is good, since it will always make 6V at the output.
   
7. Any suggestions/comments on it. COst is a concern, need to design around 1K pcs.