power electronics daniel hart

1. Chapter 7
DC Power Supplies

2. 7.2 TRANSFORMER MODEL
The ideal transformer:

3. 7.2 TRANSFORMER MODEL
The real transformer:

4. 7.2 TRANSFORMER MODEL
B-H curve of Transformer:

5. ISOLATED CONVERTER
Features of Isolated Converters :

6. ISOLATED CONVERTER

7. ISOLATED CONVERTER

8. 7.3 THE FLYBACK CONVERTER
Continuous-current mode:
The overall operation of the circuit is best understood with this simplified transformer
model, therefore only magnetizing inductance is considered in the circuit and ignoring
primary and secondary resistances and inductances.
Note the
polarity by DOT
convention

9. Assumptions for the analysis are made:
1. The output capacitor is very large, resulting in a constant output
voltage Vo.
2. The circuit is operating in the steady state, implying that all voltages
and currents are periodic, beginning and ending at the same points over
one switching period.
3. The duty ratio of the switch is D, being closed for time DT and open for
(1 - D)T.
4. The switch and diode are ideal
7.3 THE FLYBACK CONVERTER

10. 7.3 THE FLYBACK CONVERTER
CCM Analysis: When Switch is closed:
On the source side of the transformer: On load side of the transformer:

11. 7.3 THE FLYBACK CONVERTER
CCM Analysis: When Switch is closed:
Since the diode is off, i2 = 0, which means that i1 = 0. So
while the switch is closed, current is increasing linearly in
the magnetizing inductance Lm, and there is no current in
the windings of the ideal transformer in the model.

12. 7.3 THE FLYBACK CONVERTER
CCM Analysis: When Switch is open:
The current iLm enters the undotted terminal of the primary
and must exit the undotted terminal of the secondary.
This is allowable since the diode current is positive.
Assuming that the output voltage remains constant at Vo, the
transformer secondary voltage v2 becomes -Vo.

13. 7.3 THE FLYBACK CONVERTER
Note that the relation between input and output for the flyback converter is similar to that of the buck-boost
converter but includes the additional term for the transformer ratio. When switch is open:
CCM Analysis: When Switch is open: Since the net change in inductor current must
be zero over one period for steady-state operation

14. CCM Analysis: Finding the average, maximum and minimum inductor current.
7.3 THE FLYBACK CONVERTER
Assuming no power Loss in the converter:
Average Source current and average magnetizing
inductor current is related as: (See the figure)
Substituting IS
Substituting Vo / Vs

15. CCM Analysis: Finding the average, maximum and minimum inductor current.
7.3 THE FLYBACK CONVERTER
Average magnetizing inductor current is:
Maximum magnetizing inductor current is:

16. CCM Design:
7.3 THE FLYBACK CONVERTER
Minimum magnetizing inductor current should be > 0 therefore:
If switching frequency is known then value of magnetizing inductance of transformer is :
Magnetizing Inductance can also be found by change in magnetizing current when switch is closed as
discussed previously:

17. CCM Design:
7.3 THE FLYBACK CONVERTER
The output configuration for the flyback converter is the same as for the buck boost converter, so the output
ripple voltages for the two converters are also the same

18. 7.3 THE FLYBACK CONVERTER

19. 7.4 THE FORWARD CONVERTER
● The switching period is T, the switch is closed for time
DT and open for (1 - D)T. Steady-state operation is
assumed for the analysis of the circuit, and the current
in inductance Lx is assumed to be continuous.
● Leakage inductance and losses are not included in this
simplified transformer model.

20. 7.4 THE FORWARD CONVERTER
● The transformer has three windings: windings 1 and 2 transfer energy from the
source to the load when the switch is closed; winding 3 is used to provide a path
for the magnetizing current when the switch is open and to reduce the magnetizing
current to zero before the start of each switching period.
● Recall that for the flyback converter, energy was stored in Lm when the switch was
closed and transferred to the load when the switch was open. In the forward
converter, Lm is not a parameter that is included in the input-output relationship
and is generally made large.

21. 7.4 THE FORWARD CONVERTER
CCM Analysis: When Switch is closed:
Since VD3 <0 therefore D3 is off. A positive v2 forward-biases D1 and
reverse-biases D2.

22. 7.4 THE FORWARD CONVERTER
CCM Analysis: When Switch is closed:
This inductor will charge. Since V0 is constant:
This inductor will charge. The
voltage across the magnetizing
inductance Lm is also Vs, resulting:

23. 7.4 THE FORWARD CONVERTER
CCM Analysis: When Switch is open:
When D3 is on then:
With v3 established, v1 and v2 become

24. 7.4 THE FORWARD CONVERTER
CCM Analysis: When Switch is open:
With D1 off and positive current in Lx, D2 must be on. With D2 on, the
voltage across Lx is
Resulting:
Therefore, the inductor
current decreases linearly
when the switch is open.

25. 7.4 THE FORWARD CONVERTER
CCM Analysis: When Switch is open:
For steady-state operation, the net change in inductor current over one period must be zero:
Solving for Vo :
This relationship is same as buck converter which also includes turn-ratio. Note that
current in Lx must be continuous for this analysis and equation to be valid.

26. For this following condition must be
met:
7.4 THE FORWARD CONVERTER
CCM Design:
For steady state operation, current in magnetizing inductance must discharge to zero before next charge.
For example, if the ratio N3/N1 = 1 (a
common practice), then the duty ratio D
must be less than 0.5.
Discharging time of magnetizing
inductance can be found as:

27. 7.4 THE FORWARD CONVERTER
CCM Design:
The circuit configuration on the output of the forward converter is the same as that for the buck
converter, so the output voltage ripple based on an ideal capacitance is also the same.

28. CCM Design:
7.4 THE FORWARD CONVERTER

29. 7.4 THE FORWARD CONVERTER

30. 7.4 THE FORWARD CONVERTER