STEADY-STATE ANALYSIS
Voltage Gain
Utilizing (2) and (6), by
applying the principle of voltage-second balance on the magnetizing
inductor Lm , (10) can be deduced as following.
()
The voltage across C 1 can be given.
()
Using (6) and (11), the voltage stress of C 2 can
be obtained.
()
From (1) and (5), by applying the principle of voltage-second balance onL 1, the voltage gain M can be achieved as
()
Substituting (11) and (12) into (13), the voltage gain M can be
achieved.
()
The correlation among voltage gain M , duty cycle D , and
coupling coefficient k under n =1 is illustrated in Fig. 4.
The coupling coefficient has almost no impacts to the voltage gain.
Hence the coupling coefficient can be setting as k =1. The ideal
voltage gain can be calculated in (15).
()
Fig. . The correlation among
voltage gain M , duty cycle D , and coupling coefficientk .
Semiconductors’ Voltage
Stresses
When power switches are turned
on, using Kirchhoff’s Voltage Law (KVL), from (1), (11), and (12), the
voltage stresses of diodes are derived as
()
()
()
From Fig. 3 (c), (11), (12), and (15), the voltage stresses of power
switches are expressed as
()
()
Semiconductors’ Current
Stresses
During a switching cycle, applying the Kirchhoff’s Current Law (KCL),
the currents of the capacitors Co andC 1 can be written.
()
()
By applying the principle of ampere-second balance capacitorCo , the average current of the inductorL 1 can be achieved as (23).
()
Similarly, based on (22), the average current acrossD 1 in conducting time is presented as
()
From (24), during a switching cycle, we can derive the average current
of D 1 as
()
From Fig. 1 and (23), according to KCL and the principle of
ampere-second balance, the following average currents ofD 3 and D 2 can be given,
respectively.
()
()
Similarly, using (15) and (27), the average currents flowing through the
power switches S 1 and S 2can be written as follows:
()
()
Applying (27) and (28), the average current flowing through the
magnetizing inductor Lm is given similarly
()
Calculating the current ripples of inductors L 1and Lm can be achieved as (31) and (32),
respectively.
()
()
According to (23), (30)-(32), the maximum and minimum currents ofL 1 and Lm are achieved.
()
()
()
()
According to KCL, the currents of diodes D 1,D 2 and D 3 during a
switching cycle can be written as follows:
()
()
()
Utilizing (37)-(39), the root-mean-square (RMS) currents of the diodes
can be derived.
()
()
()
Within one switching cycle, the expressions of the leakage inductor
current iLk and the secondary winding currentiLs through the coupling inductor are as follows,
respectively.
()
()
According to the (23), (43) and (44), the RMS currents of the magnetics
components can be derived.
()
()
()
In a switching cycle, the currents of capacitorsC 1, C 2 andCo can be derived applying KCL.
()
()
()
From (48)-(50), the RMS currents flowing through the capacitors are
expressed as
()
()
()
During a switching cycle, according to KCL, the currents of the power
switches can be derived as.
()
()
From the equations (54) and (55), the RMS
currents flowing through the
power switches can be deduced.
()
()
Due to the power switches are on during Mode II, the peak currents
flowing through the power switches can be presented as
()
()
For the power switches, the current expressions for these two
instantaneous moments can be derived.
()
()