Electrical Engineering - Buck Converter, Prevent Saturation

[YoshiMoshi]

Homework Statement

I need help with part b-

A buck regulator is supplied from a 12VDC source and outputs 5VDC at 4 A with a PWM switching frequency is 100 kHz. Answer the following then:
a- Determine the continuous conduction mode inductance (L_CCM).
b- Compute the inductance for the converter in with the requirement that the inductor current not exceed 10A to prevent saturation.

Homework Equations

The Attempt at a Solution

a.
V_s = 12 V, V_o = 5 V, I_o = 4 A, f = 100*10^3 Hz

D = V_o/V_s = 5/12
R = V_o/I_o = 5/4 ohm
L_CCM = ( (1 - D)R ) / ( 2f ) = ( (1 - 5/12)( 5/4 ) ) / ( 2*100*10^3 ) ~ 3.646*10^(-6) H

b.
R = V_o / I_o = 5/10 = .5 ohm
lambda = I_o / ( I_max - I_o ) = 4/(10 - 4) = 2/3
lambda = L / L_CCM, L = lambda * L_CCM = ( 2/3 )( 3.646*10^(-6) ) ~ 2.431*10^(-6) H

So this was my answers to the assignment. Apparently my answer to question a. is correct, and my answer to question b is wrong. I'm not sure what I'm doing wrong. My textbook provides me the lambda formula that I used in question b.

Since the value I found for L is less than L_CCM, and L has to be greater than L_CCM (not so sure), my answer to question b should be the same value as L_CCM upon realizing that the value I found for L is less than L_CCM?

Thanks for any help, much appreciated.

 

[Baluncore]

The average output current will flow through the inductor. The current will rise and fall as the PWM changes phase, between the switch and the freewheel diode. What will the waveform of the current in the inductor be? What is the minimum inductance that will average 4A without exceeding 10A?