A buck converter has an input voltage Vin = 24 V, switching frequency fs = 100 kHz, duty ratio d = 50%, load resistance RL = 10 Ω, inductance 100 µH, and capacitance 680 µF.

1. Calculate the following values, and include units in your answers:

a) Average output voltage, Vo
b) Average output current, Io
c) Peak-to-peak current ripple, ΔiL
d) Output current that will cause the converter to enter DCM (I0,crit)
e) Load resistance that will cause the converter to enter DCM (Rcrit)
f) Average voltage across the inductor in steady-state
g) Average current through the inductor in steady-state
h) Peak-to-peak voltage ripple across the capacitor, ΔvC
i) Average voltage across the capacitor in steady-state
j) Average current into the capacitor in steady-state
k) Approximate magnitude of the peak-to-peak ripple in the capacitor current, ΔiC

2. Sketch the following waveforms, and include the theoretical maximum and minimum values of each waveform:

a) q(t)
b) vDS
c) vdiode
d) vL
e) iL
f) iC
g) Output voltage (including ripple)

3. Qualitatively describe the effect on Io, ΔiL, Rcrit, and ΔvC if you:

a) Increase the duty ratio (assume that you're starting at d = 50%)
b) Increase the switching frequency
c) Increase the load resistance

4. If you were trying to make a buck converter enter DCM, but your load resistor could not reach Rcrit, what other controllable parameters (not including Vin) could you change to reduce the lowest value of iL to zero? Explain your reasoning.