Suggestions for Further Work

The dissertation employs the technique of using a multi-winding transformer to integrate a boost PFC rectifier and an active-clamp DC-DC circuit. Based on the proposed converters, the suggested further work is to realize magnetic integration circuits by integrating the exter-nal inductors and the power transformer with single magnetic core. This implementation will result in smaller size, lighter weight and lower cost as well as more attraction for low power applications.

To further promote the conversion efficiency of the proposed converters, several topics could be the potential further work for this objective. Since the active-clamp circuit can only provide turn-on ZVS for the main switch, the suggested further work is to replace the ac-tive-clamp circuit with advanced soft-switching technique, such as zero-voltage-transition (ZVT) circuit or zero-current-transition (ZCT) circuit, etc. These techniques can effectively achieve soft-switching and voltage spike suppression at turn-off of the power switch. More-over, although this dissertation employs the flyback-forward converter to facilitate the power delivery, there still exists a part of input power is processed two times before reaching final output. The part of input power is first transferred to bulk capacitor via the additional winding N1 and then transferred to output port via the DC-DC cell. Thus, another suggested further work is to achieve the power transfer process in one time delivery from input terminal to out-put port.

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APPENDIX A

Derivation of Equations (3.12) and (3.13)

According to Fig. 3.5(d), KVL and KCL, the circuit equations are given by

( )

t i

( )

t i

( )

t Differentiating (A.1), (A.2) and (A.3) with respect to t yields

( ) ( ) ( )

And rearranging (A.4) yields

( ) ( )

Substituting (A.7), (A.8) and (A.9) into (A.6) yields

( ) ( ) ( ) ( ) ( )

Applying Laplace transform to (A.10), we can obtain (3.12).

Moreover, vc(t) can be derived by using the following equation:

( ) ( ) ( )

The substitution of (A.2) and (A.3) as well as the derivation of (3.12) into (A.11) yields

( ) ( ( ) ( ) ) ( )

b

b c o o

ac

r c o

L

V t v n V

V n n v n t B

t L A

t v n V

n + ⋅ + ⋅ − −

−

⋅ +

⋅

−

=

−

⋅

3 2 3

1 2

2 2 2 2

2 3

2

cos

sinω ω ω

ω . (A.12)

Rearranging (A.12), one can obtain the expression of vc as shown in (3.13). Based on the ini-tial condition

( ) ( )

( ) ( )

⎩⎨

⎧

=

=

2 1

0 0

t v v

t i i

c c

P

P (A.13)

A2 and B2 can be found.

APPENDIX B

Derivation of Equation (3.15)

According to Fig. 3.5(d) and Ampere’s law, the current iLb in State 3 is given by

3

From Fig. 3. 5(d) and KCL, the following equation is given

2 Substituting (B.2) into (B.1) to replace iN2, the integration of (B.1) through the duty-off time

can be obtained as

Replacing the time functions of iLr, iLm, and iN3 with their corresponding voltage expressions yields the charge balance across Cc. Rearranging (B.4), one can obtain the integration of iLb through

(

1−D

)

T_s as

( )

( )

Moreover, iLb can also be expressed as (3.14). The integration of (3.14) through the duty-off time

(

1−D

)

T_s is given by

Equating (B.5) with (B.6), one can obtain A2 as expressed in (3.15).

APPENDIX C

Derivation of Equations (3.19) and (3.20)

The derivation of Equations (3.19) and (3.20) is similar to that described in Appendix A.

The most obvious difference lies in that the resonant capacitance is Cr instead of Cc. Thus, according to Fig. 3.5(e), the circuit equations are given by

( )

t i

( )

t i

( )

t sub-stitution, the equations of resonant current iP(t) and voltage vc(t) can be obtained as

( )

t

respectively. Applying Laplace transform to (C.5), one can obtain iP(t) as expressed in (3.19).

Rearranging (C.6), vCr(t) can be found as shown in (3.20).

APPENDIX D

Derivation of Equation (3.25)

Referring to Fig. 3.5(f), the circuit equations are given by

( )

t i

( )

t i

( )

t Substituting (D.2) and (D.3) into (D.1), and then differentiating (D.1) with respect to t, one can obtain

( ) ( ) ( )

By substituting (D.4), (D.5), and (D.6) into (D.7), one can obtain

( ) ( ) ( ) ( )

Rearranging (D.8), vN2 can be obtained as shown in (3.25).

APPENDIX E

Derivation of Equation (4.2)

According to Figs. 4.4(a) and 4.4(b), the circuit equations are given by

( )

t ni

( )

t Substituting (E.1) into (E.2) to replace iN2 and then differentiating (E.2) with respect to t, one can obtain

( ) ( ) ( )

Substituting (E.3), (E.4), and (E.5) into (E.6) yields

o Rearranging (E.7), vN2,t0 can be obtained as shown in (4.2).

APPENDIX F

Derivation of Equation (4.16)

According to Fig. 4.4(l), the circuit equations are given by

( )

t i

( )

t i

( )

t Substituting (F.1) into (F.2) to replace iN2 and then differentiating (F.2) with respect to t, one can obtain

( ) ( ) ( ) ( )

Substituting (F.3), (F.4), (F.5), and (F.6) into (F.7) yields

( ) ( ) ( ) ( ) ( )

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