USB powered Switch Mode Li-ion Charger

Question

I want to design a Switch Mode Li-ion charger which uses 5V as input and charges a single cell Li-ion cell.
I am referring this AppNote

On page 4 they have given the equation to find inductor value i.e. $$ L = (V_i – V_{sat} – V_o) \times \frac{T_{on}}{2 \times I_{max}} $$ If I use 5V V_in and want to charge at 1A current, the inductor value comes out to be very low. I assume V_o=4.2V. T_on=1.32\$\mu\$s (50% duty cycle) for 376KHz PWM.

So I am confused as to how they use switch mode chargers in mobile phones.

This is the schematic of typical charger:

^{simulate this circuit – Schematic created using CircuitLab}

so I was wondering with 5V input and voltage drops at MOSFET and schottky diode would I have enough voltage to charge the battery?

Answer 1

The inductor in the circuit can be used to create a higher voltage than you had to start with. It stores energy when you put a current through it. When you remove that current, a voltage will appear across its terminals. This can be very much higher than the original voltage.

Circuits which provide a higher DC voltage from the original are known as step-up DC to DC converters. There are also step-down converters.

A feature of switch-mode supplies (and chargers) is they are quite efficient when converting the voltage (up or down), often 90% efficiency or more.