- Buck Boost Converter Definition: A buck boost converter is a DC-to-DC power supply that can increase or decrease voltage based on the needs of the circuit.
- Circuit Diagram: The circuit diagram of a buck-boost converter includes an inductor, a switch, a diode, and a capacitor, all crucial for controlling the flow and direction of electrical current.
- Output Voltage Formula: The buck-boost converter’s output voltage is determined by the input voltage, duty cycle (D), and switching interval, illustrating how changes in D directly impact the voltage output.
- Pulse Width Modulation (PWM): PWM controls the timing of the switch in a buck-boost converter, affecting the amount of energy transferred to the output, which is key for efficient power conversion.
- Steady State Analysis: Analyzing the converter in steady state helps ensure that the inductor current changes as needed to maintain a continuous and stable output voltage.
What is a Buck Boost Converter?
The buck-boost converter is a type of DC-to-DC converter (also known as a chopper) that has an output voltage magnitude that is either greater than or less than the input voltage magnitude. It can step the DC voltage up or down. A transformer does the analogous job for AC, not for this DC converter.
The inverting topology is the non-isolated cousin of a flyback converter, using a single inductor instead of a transformer. Two different topologies are called buck-boost converter: the inverting one-switch circuit below, and a cascaded or four-switch non-inverting form.
DC-DC converters, commonly referred to as choppers, include the Buck-Boost converter. This converter can function as either a step-down or step-up converter, depending on its duty cycle, denoted as D. In the inverting CCM case the magnitude ratio is D/(1-D).
Buck Boost Converter Circuit
A typical Buck-Boost converter circuit is shown below:
The input voltage source is connected to a solid state device. The second switch used is a diode. The diode is connected, in reverse to the direction of power flow from source, to a capacitor and the load and the two are connected in parallel as shown in the figure above.
The controlled switch in the converter uses Pulse Width Modulation (PWM) to toggle on and off. PWM may operate based on time or frequency, with time-based being the more common approach.
Frequency-based modulation can work, but it needs a wide range of frequencies to control the switch and thus achieve the desired output voltage.
Time based Modulation is the usual choice for DC-DC converters. The switching frequency stays fixed, which makes the timing easier to design.
The frequency remains constant in this type of PWM modulation. The Buck Boost converter has two modes of operation. The first mode is when the switch is on and conducting.
Mode I : Switch is ON, Diode is OFF
The Switch is ON and therefore represents a short circuit ideally offering zero resistance to the flow of current so when the switch is ON all the current will flow through the switch and the inductor and back to the DC input source.
The inductor stores energy during the time the switch is ON and when the solid state switch is OFF the polarity of the Inductor reverses so that current flows through the load and through the diode and back to the inductor. So the direction of current through the inductor remains the same.
Let us say the switch is on for a time TON and is off for a time TOFF. We define the time period, T, as 
and the switching frequency,
Let us now define another term, the duty cycle, 
Let us analyse the Buck Boost converter in steady state operation for this mode using KVL.
Since the switch is closed for a time TON = DT we can say that Δt = DT.
While performing the analysis of the Buck-Boost converter we have to keep in mind that
- The inductor current is continuous and this is made possible by selecting an appropriate value of L.
- The inductor current in steady state rises from a value with a positive slope to a maximum value during the ON state and then drops back down to the initial value with a negative slope. Therefore the net change of the inductor current over any one complete cycle is zero.
Mode II : Switch is OFF, Diode is ON
In this mode the polarity of the inductor is reversed and the energy stored in the inductor is released and is ultimately dissipated in the load resistance. The input source is disconnected. The inductor alone maintains the flow of current through the load and sets the output voltage. For analysis we keep the original conventions to analyse the circuit using KVL.
Buck Boost Converter Formula
Let us now analyse the Buck Boost converter in steady state operation for Mode II using KVL.
Since the switch is open for a time 
we can say that 
.
The net change of the inductor current over any one complete cycle is zero.
We know that D varies between 0 and 1. For the ideal inverting CCM converter, if D > 0.5, the output voltage magnitude is larger than the input; and if D < 0.5, the output magnitude is smaller than the input. If D = 0.5 the output voltage magnitude is equal to the input voltage.
A circuit of a Buck-Boost converter and its waveforms is shown below.
The inductance, L, is 50mH and the C is 100µF and the resistive load is 50Ω. The switching frequency is 1 kHz. The input voltage is 100 V DC and the duty cycle is 0.5.
The voltage waveforms are as shown above and the current waveforms are as shown in the figure below.
