Homework
Lesson 39
Isolated DC / Dc Converters
1. Problem 7.1
a.
b.
c.
First, we determine whether we are in continuous conduction.
The peak to peak current ripple in Lm is
This current ripple indicates continuous conduction.
Average inductor current is already found above:
The maximum current is
The falling current returns to
Output voltage ripple in continuous conduction is approximately
2.
a.
b.
The second part of the problem assumes continuous conduction in the magnetizing inductance.
Rearranging to solve for the turns ratio,
The turns ratio is
N1:N2 = 1.309:1 or 1:0.764.
Checking the continuous current assumption,
The average current is greater than half of the ripple, so the current is continuous.
The minimum current will be 25% of the average inductor current, per the part b problem statement,
Finding the ripple current
We know that the rising part of the current ripple may be found from the following
Rearranging,
Problem 7.3
Calculate the load resistance.
There are many solutions to this problem.
Calculate the duty cycle, as is done in Example 7-2 n page 244.
Calculate the capacitance, as is done in the same example. Any capacitance larger than this will do the job well.
Calculate the inductance, as is likewise done in the same example.
3. Problem 7.6.
a.
The forward converter is a buck converter with a transformer.
Ripple is
b.
Average current in the inductor is the same as the average current in the load because the capacitor's average current must be zero for any complete cycle.
Change in the inductor current is determined from the part of the cycle when inductor Lx current decreases.
Maximum Lx inductor current is
Minimum Lx inductor current is
c.
This is easiest found from the part of the switching cycle when magnetizing current increases.
Because magnetizing current starts at zero, this change is its peak value.
d.
Peak switch current(which is the same as physical transformer primary current) is the sum of the peak magnetizing current and the peak reflected secondary current.
Recall
Reflecting to get the ideal primary winding current,
Add these two components to get the physical transformer primary current.