6.1 What is the relationship between Vo/Vs and the efficiency of the linear converter in section 6.1?
Input power is
Output power is
Calculate efficiency
Simplify the expression by dividing out the current IL.
The energy efficiency is, ideally, equal to the voltage ratio.
Problem 6.2
a.
b.
c.
a.
From the figure we see that the circuit is just a series circuit. The output current is the same as the input current.
Efficiency is power out / power in:
b.
c.
Problem 6.7
a.
b.
c.
d.
a.
b.
Because the capacitor has no average current, the inductor average current is the same as the output average current.
The change in inductor current is found from the inductor's integral relationship:
Calculating the max and min values,
c.
It is also possible to do this from energy conservation.
d.
Problem 6.13
The duty ratio is the ratio of the voltages:
Calculate the output resistance from the given information.
Specify a switching frequency.
Using equation 6-26 in the text handout, we find the minimum inductance for continuous inductor current is ,
We see the output ripple is defined as
Rearrange this to allow us to solve for the remaining unknown, the capacitance,
Problem 6.15
a. Determine the output voltage.
b.
c.
d.
a. Determine the output voltage.
b.
c.
We see the output ripple is defined as
We can also express this a per unit ripple.
d.
Problem 6.17
Inductor current rises from min to max value in a time equal to DTs and then falls back to its min value to complete the cycle by time Ts
Problem 6.20
a.
b.
c.
a.
b.
Another way to do this is to calculate the output and input power, then calculate the input current and, from there, calculate the inductor current.
The change in inductor current is
Max and min inductor currents are
c.
Per unit ripple is