## Working principle

A Buck-Boost converter transforms a positive DC voltage at the input to a negative DC voltage at the output. The circuit operation depends on the conduction state of the MOSFET:

**On-state**: The current through the inductor increases and the diode is in blocking state.**Off-state**: Since the current through the inductor can not abruptly change the diode must carry the current so it commutates and begins conducting. Energy is transferred from the inductor to the capacitor resulting in a decreasing inductor current and a voltage across the resistor with the opposite polarity compared to V_{in}. During steady state the circuit is said to operate:

- in
*discontinuous conduction*mode if the inductor current reaches zero and - in
*continuous conduction*mode if the inductor current never reaches zero.

- in

The circuit has two limits of operation. For a PWM duty cycle D ➝ 0 the output voltage equals zero, and for D ➝ 1 the output voltage grows toward negative infinity. In between those limits the output voltage in continuous conduction mode is given by: V_{out} = -D/(1-D) **· **V_{in}.

Note that the parallel combination of inductor and capacitor as shown above acts as a second order low pass filter reducing the voltage ripple at the output.

### Experiments

- Change the PWM duty cycle of the converter from 0.5 to 0.4 and 0.6 and observe how the average output voltage changes to 16 V and 36 V, respectively.
- Change the resistance value from 10 Ω to 80 Ω and observe how the converter goes into discontinuous conduction mode.