- #1
dvscrobe
- 51
- 11
- Homework Statement
- This problem comes out of a EET course called Power Electronics. See equation 3.48a. The text doesn’t show the derivation and I could not figure it out even after asking the instructor. This is for learning how DC-DC buck converters operate in a discontinuous mode. A buck converter uses transistors and passive components to step DC voltages down.
- Relevant Equations
- Power in = Power out
Let K=2Lfs and Pin=Pout,
Have,
(Vin-Vo)/k D^2 Vin =Vo ^2/R
(I am fine up to this part. I am equating input power to output power)
V^2=D^2 + D^2 R/2 Vo Vin - R/k D ^2 Vin =0
(This is where the instructor takes over. Can’t figure out how he got to V^2. Where did that come from? Thought I was just dealing with Vin and Vout.)
Let M=D^2 R/k
Vo=Vin/2 (sqrt(M^2+4M ) -M)
Have,
(Vin-Vo)/k D^2 Vin =Vo ^2/R
(I am fine up to this part. I am equating input power to output power)
V^2=D^2 + D^2 R/2 Vo Vin - R/k D ^2 Vin =0
(This is where the instructor takes over. Can’t figure out how he got to V^2. Where did that come from? Thought I was just dealing with Vin and Vout.)
Let M=D^2 R/k
Vo=Vin/2 (sqrt(M^2+4M ) -M)