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7 - L-22 (DP) (Pe) ( (Ee) Nptel)

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change in the magnetic field energy and this in turn will mean infinite magnitude of

instantaneous power, some thing that a practical system cannot support.]

For the idealized circuit considered here, the secondary winding current abruptly rises from zero
to I P N1 N 2 as soon as the switch ‘S’ turns off. N 1 and N 2 denote the number of turns in the
primary and secondary windings respectively. The sudden rise of secondary winding current is
shown in Fig. 22.5(a) and Fig. 22.5(b). The diode connected in the secondary circuit, as shown in
Fig.22.1, allows only the current that enters through the dotted end. It can be seen that the
magnitude and current direction in the secondary winding is such that the mmf produced by the
two windings does not have any abrupt change. The secondary winding current charges the
output capacitor. The + marked end of the capacitor will have positive voltage. The output
capacitor is usually sufficiently large such that its voltage doesn’t change appreciably in a single
switching cycle but over a period of several cycles the capacitor voltage builds up to its steady
state value.

The steady-state magnitude of output capacitor voltage depends on various factors, like,
input dc supply, fly-back transformer parameters, switching frequency, switch duty ratio
and the load at the output. Capacitor voltage magnitude will stabilize if during each switching
cycle, the energy output by the secondary winding equals the energy delivered to the load.

As can be seen from the steady state waveforms of Figs.22.5(a) and 22.5(b), the secondary
winding current decays linearly as it flows against the constant output voltage (VO). The linear
d
decay of the secondary current can be expressed as follows: LSec × iSec = −VO ---------- (22.2),
dt
Where, LSec and iSec are secondary winding inductance and current respectively.
VO is the stabilized magnitude of output voltage.

Under steady-state and under the assumption of zero on-state voltage drop across diode, the
secondary winding voltage during this mode equals VO and the primary winding voltage =
VON1/N2 (dotted ends of both windings being at lower potential). Under this condition, voltage
stress across switch ‘S’ is the sum total of the induced emf in the primary winding and the dc
supply voltage (Vswitch = EDC + VON1/N2).

The secondary winding, while charging the output capacitor (and feeding the load), starts
transferring energy from the magnetic field of the fly back transformer to the power supply
output in electrical form. If the off period of the switch is kept large, the secondary current gets
sufficient time to decay to zero and magnetic field energy is completely transferred to the output
capacitor and load. Flux linked by the windings remain zero until the next turn-on of the switch,
and the circuit is under discontinuous flux mode of operation. Alternately, if the off period of the
switch is small, the next turn on takes place before the secondary current decays to zero. The
circuit is then under continuous flux mode of operation.

During discontinuous mode, after complete transfer of the magnetic field energy to the output,
the secondary winding emf as well as current fall to zero and the diode in series with the winding
stops conducting. The output capacitor however continues to supply uninterrupted voltage to the
load. This part of the circuit operation has been referred to as Mode-3 of the circuit operation.

Version 2 EE IIT, Kharagpur 7

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