1. Output voltage is larger than Vin, but output current is smaller
Boost converter
+ v L – i i I i L D
out in L + V V in C
out i C –
Output voltage is larger than Vin, but output current is smaller
Pin is approximately equal to Pout
If the MOSFET gate driver sticks in the “on” position, then there is a short circuit through the MOSFET
If the load is disconnected during operation, so that Iout = 0, then L continues to push power to the right and very quickly charges C up to a high value

3. Switch closed for DT seconds: Charging phase
+ Vin − i I
out i L in L + V V in C
out I
out –
Reverse biased, thus the diode is open
for DT seconds
Note – if the switch stays closed for very long time, the current continues increasing until the limit of switch and/or battery!

4. Switch open for (1 − D)T seconds
+ (Vin − Vout ) − i I
out L i in L + V V in C
out
(iL – Iout) –
Diode closed. Assume continuous conduction.
for (1−D)T seconds

10. Examine the inductor current
Switch closed,
Switch open,
Iavg = Iin is half way between
Imax and Imin iL
Imax
Iavg = Iin ΔI
Imin DT
(1 − D)T T

11. Inductor current rating
Max impact of ΔI on the rms current occurs at the boundary of continuous/discontinuous conduction, where ΔI =2Iin iL
2Iin
Iavg = Iin ΔI
Use max

12. MOSFET and diode currents and current ratings
+ v L – i i I i L D
out in + L V V in C
out i C –
2Iin
2Iin
Use max
Take worst case D for each

13. Capacitor current and current ratingL
out i D in L + V V in C
out i C –
iC = (iD – Iout)
2Iin −Iout
−Iout
Max rms current occurs at the boundary of continuous/discontinuous conduction, where ΔI =2Iout
Use max

14. Worst-case load ripple voltage
iC = (iD – Iout)
−Iout
The worst case is where C provides Iout for most of the period. Then, D~ 1 and

15. Voltage ratings i I i L + V V C – i I i L + V V C – Diode sees Vout
C sees Vout L + V V in C
out – i I
out i L in L + V V in C
out –
MOSFET sees Vout
Diode and MOSFET, sees (worst case) Vout + Vpk
Capacitor also sees a large voltage

16. Continuous current in L; worst caseiL
2Iin
Iavg = Iin
(1 − D)T
Then, considering the worst case (i.e., D → 1),
use max
guarantees continuous conduction
use min

20. Stability and “AC” Response
AC analysis is tricky!
System is very non-linear!
AC is for small signal sinewave waveforms!
This system Is not even close to that!

21. Stability and “AC” Response
Similarly to any AC analysis, we have to assume small signal variations, and define an operating point!
Output of the PWM is duty cycle!
This chart includes resistive losses, otherwise, D=0.7 should result in V-D convertion ratio of approximately 4.

22. Stability and “AC” Response

23. Stability and “AC” Response

28. Impedance matching Iin DC−DC Boost Converter + + Vin − − Source Iin +
Equivalent from source perspective