Relation Between Input and Output Voltage of FTSMPS
Relation between Input and Output voltage of FTSMPS:
- The equivalent circuits of mode-1 and mode-2 can be used to derive a steady state relation between the input voltage, switch duty ratio (δ) and the output voltage. With the assumption of constant input and output voltage, the instantaneous value of inductor voltage (eL) during mode-1 can be written as:
Where t = 0 is the time instant when mode – 1 of any steady state switching cycle starts,
T is the switching time period that may be assumed to be constant and
δ is the duty ratio of the switch.
- It can be seen that δT is the time duration of mode-1 and (1-δ) T is the time duration of mode-2.
- The inductor voltage during mode-2 may similarly be written as:
Now since voltage across an inductor, averaged over a steady state cycle time, must always be zero, one gets:
- The forward converter output voltage is directly proportional to the switch duty ratio. It may be noticed that except for transformer scaling factor the output voltage relation is same as in a simple dc-to-dc buck converter.
- The output voltage relation across the inductor that we have obtained i.e.
is valid only under the assumption of continuous inductor current.
- For an improperly designed circuit or for very light load at the converter output, the inductor current may decay to zero in the midst of mode-2 resulting into discontinuous inductor current.
- Once the inductor current becomes zero, diode ‘D2’ no longer conducts and the points ‘P’ and ‘N’ of the equivalent circuit are no longer shorted. In fact, the output voltage ‘VO’ will appear across ‘P’ and ‘N’. Thus the inductor voltage equation remains valid only for a part of (1-δ) T period.
- In case of discontinuous inductor current, the output voltage, which is the average of voltage across points ‘P’ and ‘N’ will have a higher magnitude than the one given by the output voltage equation across the inductor.
- Under discontinuous inductor current the relation between output voltage and switch duty ratio becomes non-linear and is load dependent.
- For better control over output voltage discontinuous inductor current mode is generally avoided. With prior knowledge of the load-range and for the desired switching frequency the filter inductor may be suitably chosen to keep the inductor current continuous and preferably with less ripple.