On-time (switch closed): When the switch (usually a MOSFET) is closed or turned on, the input voltage (Vin) is connected to the inductor (L). The current through the inductor starts to increase linearly, and the inductor stores energy in its magnetic field. During this time, the diode (D) is reverse-biased, preventing current from flowing to the output.

Off-time (switch open): When the switch is opened or turned off, the current flow through the inductor is disrupted, and the collapsing magnetic field induces a voltage across the inductor. The polarity of the induced voltage is opposite to the input voltage, which forward-biases the diode and allows the current to flow to the output capacitor (Cout) and the load.

The output voltage of a buck-boost converter depends on the duty cycle (D) of the switch, which is the ratio of the on-time to the total switching period (on-time + off-time). The output voltage can be approximated using the following formula:

Vout ≈ -Vin * D / (1 – D)

Note that the output voltage has a negative sign in the formula, which means the output voltage is inverted with respect to the input voltage. However, a non-inverting buck-boost converter can be designed using additional switches or integrated converter ICs.

The control circuitry, typically using a dedicated PWM controller or a microcontroller, monitors the output voltage and adjusts the duty cycle to maintain a stable output voltage. The control loop usually consists of a voltage reference, an error amplifier, and a PWM generator. By comparing the output voltage to a reference voltage and adjusting the duty cycle accordingly, the control circuitry ensures that the output voltage remains stable, even with variations in input voltage or load conditions.

The efficiency of a buck-boost converter depends on the switching frequency, component quality, and design. It is essential to optimize component selection, such as inductor value, diode type, and output capacitor value, to achieve the desired efficiency, output voltage ripple, and transient response. Typical efficiencies for buck-boost converters range from 75% to 95%.