ASSIGNMENT

Q1. A flyback converter is operating in a complete demagnetizing mode. Derive the voltage transfer ratio Vo/Vd in terms of Load Resistance R, Switching frequency f, transformer inductance Lm, and duty ratio.

Q2. A switch-mode power supply is to be designed with following specification.

V_d = 48V±10%

Vo = 5V (Regulated)

Fs = 100 kHz

Pload = 15-50 W

A Forward converter operating in a Continuous-Conduction Mode with a demagnetizing winding (N3=N1) is chosen. Assume all components to be ideal except for the presence of transformer demagnetization inductance.

(a) Calculate N2/N1 if this turn ratio is desired to be as small as possible.

(b) Calculate the minimum value of the filter inductance.

Q3. A flyback converter is operating in an incomplete demagnetizing mode with a duty ratio of 0.4. In the same application, another option may be to parallel two half size flyback converters as shown in Figure 1. Compare the ripple in the input current id and the output stage current io waveforms in these two options, assuming a very large output capacitor such that vo(t) = Vo.

Q4. Optimal reset of the forward converter transformer. As illustrated in Figure 2, it is possible to reset the transformer of the forward converter using a voltage source other than the dc input Vg. By optimally choosing the value of the reset voltage Vr, the peak voltage stresses imposed on transistor Q1 and diode D2 can be reduced. The maximum duty cycle can also be increased, leading to a lower transformer turns ratio and lower transistor current. The resulting improvement in converter cost and efficiency can be significant when the dc input voltage varies over a wide range.

(a) As a function of Vg, the transistor duty cycle D, and the transformer turns ratios, what is the minimum value of Vr that causes the transformer magnetizing current to be reset to zero by the end of the switching period?

(b) For your choice of Vr from part (a), what is the peak voltage imposed on transistor Q1? This converter is to be used in a universal-input off-line application, with the following specifications.

The input voltage Vg can vary between 127V and 380 V. The load voltage is regulated by variation of the duty cycle, and is equal to 12 V. The load power is 480 W.

(c) Choose the turns ratio n3/n1 such that the total active switch stress is minimized. For your choice of n3/n1 over what range will the duty cycle vary? What is the peak transistor current?

(d) Compare your design of Part (c) with the conventional scheme in which n1 =n2 and Vr = Vg. Compare the worst-case peak transistor voltage and peak transistor current.

(e) Suggest a way to implement the voltage source Vr. Give a schematic of the power-stage components of your implementation. Use a few sentences to describe the control-circuit functions required by your implementation, if any.

Q5. The forward converter shown in Figure 3 below has following parameters:

Vs = 100V,

N1/N2 = N1/N3 = 1,

Lm = 1mH,

Lx = 70µH,

R = 20?,

C = 33µF

D = 0.45

If the switching frequency of the converter is 150 kHz and it is operating in continuous conduction mode, determine the following:

a) the output voltage and output voltage ripple,

b) the average, maximum, and minimum values of the current in Lx,

c) the peak current in Lm in the transformer model

d) the peak current in the switch

Q6. The forward converter of Figure 4 operates from a dc input of Vg = 325V and supplies 20 A to its 5Vdc load. The turns ratio n3/n1 is chosen such that the converter produces the required output voltage at a transistor duty cycle of D = 0.4. The MOSFET has on-resistance of 5Ω. The secondary-side schottky diodes have forward voltage drops of Vf = 0.5V. All other elements can be considered ideal.

a) Derive an equivalent circuit for the forward converter, which models the semiconductor conduction losses described above.

b) Solve your model for the case described above and determine numerical values of the turn's ratio n3/n1 and for the efficiency.

c) The secondary-side Schottky diodes are replaced by MOSFETs operating as synchronous rectifiers. The MOSFETs each have an on-resistance of 4m?. Determine the new numerical values of the turn's ratio n3/n1 and the efficiency.