A buck-boost DC-DC converter, shown in the figure below, is used to convert $24V$ battery voltage to $36V$ DC voltage to feed a load of $72W$. It is operated at $20kHz$ with an inductor of $2mH$ and output capacitor of $1000\mu F$. All devices are considered to be ideal. The peak voltage across the solid-state switch (S), in volt, is ____________.

Concept:

Buck - Boost Converter:

The buck–boost converter is a type of DC to DC converter that has an output voltage magnitude that is either greater than or less than the input voltage magnitude. It is equivalent to a Fly-back converter using a single inductor instead of a fly-back Transformer. The opposite voltage is the opposite polarity of that of the input.

The steady-state output voltage Vout of buck-boost converter is

$V_{out}=-V_{in}\left(\frac{D}{1-D}\right)$

Here D = duty cycle



- When Chopper is ON, Current flows from Sending Voltage, Vs to Chopper, CH, Inductor, L and back to Vs
- Energy is stored in the inductor during TON
- When the chopper is OFF, the inductor stored energy now discharges through the path, load, diode D, and L.

Explanation:

When switch is OFF, diode D is ON as shown in below figure,



Using KVL,

peak voltage across switch = 24 + 36 = 60 V