Duty-cycle in a Boost Converter

I'm trying to calculate the required input inductance in a boost converter that will be used to charge two lithium-ion based cells in series from a source of 500mA at 5.4V. The battery end-of-charge voltage is 8.2V and it will be allowed to discharge to, say, 7V.

In the expression for the inductance (L=D*T*Vin/Irip, where Irip is the increase in inductor current in the "on"-state), should I use the duty cycle at 8.2V or the duty cycle at 7V, or something in between?

I didn't check your formule for correctness, but it gives you the relation between the parameters and physical values at a certain working point (here Vin and Duty/cycle).

So you have to search your worst case. The worst case depends from design to design. If you for example look for an absolute maximum ripple current, than you will find the minimum inductor to use when the period is at maximum (tolerance), and the D*Vin term is maximum.

I let you serach for that maximum condition, (hint it will be maximum input or minimum input voltage...)

Well, the worst condition is at Vin(min) and Vout(max), the combination of which gives the largest inductor value. Right?

But, in calculating this value I chose a maximum increase in inductor current, Irip, to be (arbitrarily) 20% of the maximum value of 500mA. Since I'm charging a battery on the output, I reckon I want to maximize the output current, Iout = Irip/2 * (1-D), while maintaining the Continuous Current Mode (CCM) of operation. Say I want to maintain CCM down to a level of Iout = Imax*5% = 25mA -- will this requirement then be the dominant one? Is this where the trade-off lies? I mean otherwise I could just make the inductor small by lettering Irip --> Imax, and the inductance would be a sole function of the worst-case duty cycle.

Is it the desire to maintain CCM above a certain minimum current that is the real deciding factor as to how large an inductance I should chose?

It is indeed a trade-off, but continuous current is not an absolute requirement.
There are even controllers especially build for forcing sicontinuous mode (or just on the edge between continuous and discontinuous).

At some points, the discontinuous mode has advantages. There is for example no reverse recovery effect in the diode (since it is not conducting when you turn on the transistor). This can have a good effect on the switching losses.

But if you need to design a converter with a certain rating, the current peaks will be higher when you use discontinuous mode, so components like capacitors and switches will be more stressed. But only if you compare that with the same converter at the same operating point in continuous mode.

When the converter is designed to work in continuous mode on its nominal operating point, and you are happy with that, there is no reason why discontinuous mode is a bad thing on lower load conditions, because the current will be lower anyway.

If you have to design the system as you discribe to be continuous at 25mA, your inductor will be extremely large. (calculate for example with the same formula, and fill in the a value of 25mA for the ripple current, this will give you the inductor for a boundary condition between continuous and discontinuous mode at 25mA).

Stefaan