Boost converter does not work according to the theories

Question

I am still a beginner in this field so I would like to gain some insight about boost converters. I wanted to build a boost converter for a school project with this simple design. The parts were provided by my school.

However, I found out that my circuit does not work according to the theories regarding boost converters.

1. The output voltage and input voltage does not follow the formula \$V_o = \frac{V_i}{(1-D)}\$. According to the formula, I am supposed to get voltage of 3V at \$V_c\$, with \$V_i = 1.5V, D = 0.5\$, but I got around 5V average and 5.5V peak when I run the circuit in LTspice. However, I realized that the inductor current drops to 0 every switch cycle so I tried using the discontinuous mode formula, \$\frac{V_o}{V_i} = \frac{1+\sqrt{1+\frac{4D^2}{K}}}{2}, K = \frac{2L}{RT}\$. According to this formula, I am supposed to get an output voltage of 24.5V, which is very much higher than what I got in the simulation. Is there anything I am missing?

2. I also found out that the my output voltage does not change with duty cycle, D. I tried changing the on-time of the pulse signal to 0.5ms and 1.5ms, but I still obtained around 5V average, and 5.5V peak at the output. However, I found out that the output voltage increases with decreasing period even when the duty cycle is kept the same. According to the DCM formula, shouldn't the gain decrease with decreasing period? What is happening here?
   

3. I also found out that the output voltage increases with load resistance, R2. What is going on here?

Any help would be appreciated! Thanks in advance!

Answer 1

Welcome to Power Electronics! Here's my strategy for moving forward on this:

Replace the transistor and diode with ideal parts, as follows:

1. Replace Q1 (NPN 2SC1815) with an ideal switch, with an on-resistance of 1mΩ, and and OFF resistance of 1MEG-Ω. For assistance refer LTspice help, or this link:
   https://electronics.stackexchange.com/a/103439/341959

2. Replace D1 (1SS270A) with an ideal diode.

3. Increase the load to about 1A, so change R2 to 3Ω, and reduce R1 to 1mΩ.

Next, increase the switching frequency to 100kHz.

This new circuit should behave according to the theory.

After that, replace the ideal diode with the actual diode you will be using, then see how it behaves differently to the ideal case. Next, replace the ideal switch with the transistor you will be using, and give it a suitable control drive (you may need to research that topic a little more) and see again how the circuit behaviour changes compared to the ideal case.