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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 flyback converter using a single inductor instead of a transformer.^{ [1] }

A **DC-to-DC converter** is an electronic circuit or electromechanical device that converts a source of direct current (DC) from one voltage level to another. It is a type of electric power converter. Power levels range from very low to very high.

The **flyback** converter is used in both AC/DC and DC/DC conversion with galvanic isolation between the input and any outputs. The flyback converter is a buck-boost converter with the inductor split to form a transformer, so that the voltage ratios are multiplied with an additional advantage of isolation. When driving for example a plasma lamp or a voltage multiplier the rectifying diode of the boost converter is left out and the device is called a flyback transformer.

- Principle of operation of the inverting topology
- Conceptual overview
- Continuous mode
- Discontinuous mode
- Limit between continuous and discontinuous modes
- Principles of operation of the 4-switch topology
- Non-ideal circuit
- Effect of parasitic resistances
- See also
- References
- Further reading

Two different topologies are called *buck–boost converter*. Both of them can produce a range of output voltages, ranging from much larger (in absolute magnitude) than the input voltage, down to almost zero.

- The inverting topology
- The output voltage is of the opposite polarity than the input. This is a switched-mode power supply with a similar circuit topology to the boost converter and the buck converter. The output voltage is adjustable based on the duty cycle of the switching transistor. One possible drawback of this converter is that the switch does not have a terminal at ground; this complicates the driving circuitry. However, this drawback is of no consequence if the power supply is isolated from the load circuit (if, for example, the supply is a battery) because the supply and diode polarity can simply be reversed. When they can be reversed, the switch can be on either the ground side or the supply side.
- A buck (step-down) converter combined with a boost (step-up) converter
- The output voltage is typically of the same polarity of the input, and can be lower or higher than the input. Such a non-inverting buck-boost converter may use a single inductor which is used for both the buck inductor mode and the boost inductor mode, using switches instead of diodes,.

^{ [2] }^{ [3] } sometimes called a **"four-switch buck-boost converter"**,^{ [4] } it may use multiple inductors but only a single switch as in the SEPIC and Ćuk topologies.

The **Ćuk converter** is a type of DC/DC converter that has an output voltage magnitude that is either greater than or less than the input voltage magnitude. It is essentially a boost converter followed by a buck converter with a capacitor to couple the energy.

The basic principle of the inverting buck–boost converter is fairly simple (see figure 2):

- while in the On-state, the input voltage source is directly connected to the inductor (L). This results in accumulating energy in L. In this stage, the capacitor supplies energy to the output load.
- while in the Off-state, the inductor is connected to the output load and capacitor, so energy is transferred from L to C and R.

Compared to the buck and boost converters, the characteristics of the inverting buck–boost converter are mainly:

A **buck converter** is a DC-to-DC power converter which steps down voltage from its input (supply) to its output (load). It is a class of switched-mode power supply (SMPS) typically containing at least two semiconductors and at least one energy storage element, a capacitor, inductor, or the two in combination. To reduce voltage ripple, filters made of capacitors are normally added to such a converter's output and input.

A **boost converter** is a DC-to-DC power converter that steps up voltage from its input (supply) to its output (load). It is a class of switched-mode power supply (SMPS) containing at least two semiconductors and at least one energy storage element: a capacitor, inductor, or the two in combination. To reduce voltage ripple, filters made of capacitors are normally added to such a converter's output and input.

- polarity of the output voltage is opposite to that of the input;
- the output voltage can vary continuously from 0 to (for an ideal converter). The output voltage ranges for a buck and a boost converter are respectively to 0 and to .

Like the buck and boost converters, the operation of the buck-boost is best understood in terms of the inductor's "reluctance" to allow rapid change in current. From the initial state in which nothing is charged and the switch is open, the current through the inductor is zero. When the switch is first closed, the blocking diode prevents current from flowing into the right hand side of the circuit, so it must all flow through the inductor. However, since the inductor doesn't like rapid current change, it will initially keep the current low by dropping most of the voltage provided by the source. Over time, the inductor will allow the current to slowly increase by decreasing its voltage drop. Also during this time, the inductor will store energy in the form of a magnetic field.

If the current through the inductor *L* never falls to zero during a commutation cycle, the converter is said to operate in continuous mode. The current and voltage waveforms in an ideal converter can be seen in Figure 3.

From to , the converter is in On-State, so the switch *S* is closed. The rate of change in the inductor current (*I*_{L}) is therefore given by

At the end of the On-state, the increase of *I*_{L} is therefore:

*D* is the duty cycle. It represents the fraction of the commutation period *T* during which the switch is On. Therefore *D* ranges between 0 (*S* is never on) and 1 (*S* is always on).

During the Off-state, the switch *S* is open, so the inductor current flows through the load. If we assume zero voltage drop in the diode, and a capacitor large enough for its voltage to remain constant, the evolution of *I*_{L} is:

Therefore, the variation of *I*_{L} during the Off-period is:

As we consider that the converter operates in steady-state conditions, the amount of energy stored in each of its components has to be the same at the beginning and at the end of a commutation cycle. As the energy in an inductor is given by:

it is obvious that the value of *I*_{L} at the end of the Off state must be the same with the value of *I*_{L} at the beginning of the On-state, i.e. the sum of the variations of *I*_{L} during the on and the off states must be zero:

Substituting and by their expressions yields:

This can be written as:

This in return yields that:

From the above expression it can be seen that the polarity of the output voltage is always negative (because the duty cycle goes from 0 to 1), and that its absolute value increases with D, theoretically up to minus infinity when *D* approaches 1. Apart from the polarity, this converter is either step-up (a boost converter) or step-down (a buck converter). Thus it is named a buck–boost converter.

In some cases, the amount of energy required by the load is small enough to be transferred in a time smaller than the whole commutation period. In this case, the current through the inductor falls to zero during part of the period. The only difference in the principle described above is that the inductor is completely discharged at the end of the commutation cycle (see waveforms in figure 4). Although slight, the difference has a strong effect on the output voltage equation. It can be calculated as follows:

Because the inductor current at the beginning of the cycle is zero, its maximum value (at ) is

During the off-period, *I*_{L} falls to zero after δ.T:

Using the two previous equations, δ is:

The load current is equal to the average diode current (). As can be seen on figure 4, the diode current is equal to the inductor current during the off-state. Therefore, the output current can be written as:

Replacing and δ by their respective expressions yields:

Therefore, the output voltage gain can be written as:

Compared to the expression of the output voltage gain for the continuous mode, this expression is much more complicated. Furthermore, in discontinuous operation, the output voltage not only depends on the duty cycle, but also on the inductor value, the input voltage and the output current.

As told at the beginning of this section, the converter operates in discontinuous mode when low current is drawn by the load, and in continuous mode at higher load current levels. The limit between discontinuous and continuous modes is reached when the inductor current falls to zero exactly at the end of the commutation cycle. with the notations of figure 4, this corresponds to :

In this case, the output current (output current at the limit between continuous and discontinuous modes) is given by:

Replacing by the expression given in the *discontinuous mode* section yields:

As is the current at the limit between continuous and discontinuous modes of operations, it satisfies the expressions of both modes. Therefore, using the expression of the output voltage in continuous mode, the previous expression can be written as:

Let's now introduce two more notations:

- the normalized voltage, defined by . It corresponds to the gain in voltage of the converter;
- the normalized current, defined by . The term is equal to the maximum increase of the inductor current during a cycle; i.e., the increase of the inductor current with a duty cycle D=1. So, in steady state operation of the converter, this means that equals 0 for no output current, and 1 for the maximum current the converter can deliver.

Using these notations, we have:

- in continuous mode, ;
- in discontinuous mode, ;
- the current at the limit between continuous and discontinuous mode is . Therefore the locus of the limit between continuous and discontinuous modes is given by .

These expressions have been plotted in figure 5. The difference in behavior between the continuous and discontinuous modes can be seen clearly.

The 4-switch converter combines the buck and boost converters. It can operate in either the buck or the boost mode. In either mode, only one switch controls the duty cycle, another is for commutation and must be operated inversely to the former one, and the remaining two switches are in a fixed position. A 2-switch buck-boost converter can be built with two diodes, but upgrading the diodes to FET transistor switches doesn't cost much extra while due to lower voltage drop the efficiency improves.

In the analysis above, no dissipative elements (resistors) have been considered. That means that the power is transmitted without losses from the input voltage source to the load. However, parasitic resistances exist in all circuits, due to the resistivity of the materials they are made from. Therefore, a fraction of the power managed by the converter is dissipated by these parasitic resistances.

A **resistor** is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active elements, and terminate transmission lines, among other uses. High-power resistors that can dissipate many watts of electrical power as heat, may be used as part of motor controls, in power distribution systems, or as test loads for generators. Fixed resistors have resistances that only change slightly with temperature, time or operating voltage. Variable resistors can be used to adjust circuit elements, or as sensing devices for heat, light, humidity, force, or chemical activity.

In electrical networks, a **parasitic element** is a circuit element that is possessed by an electrical component but which it is not desirable for it to have for its intended purpose. For instance, a resistor is designed to possess resistance, but will also possess unwanted parasitic capacitance.

For the sake of simplicity, we consider here that the inductor is the only non-ideal component, and that it is equivalent to an inductor and a resistor in series. This assumption is acceptable because an inductor is made of one long wound piece of wire, so it is likely to exhibit a non-negligible parasitic resistance (*R*_{L}). Furthermore, current flows through the inductor both in the on and the off states.

Using the state-space averaging method, we can write:

where and are respectively the average voltage across the inductor and the switch over the commutation cycle. If we consider that the converter operates in steady-state, the average current through the inductor is constant. The average voltage across the inductor is:

When the switch is in the on-state, . When it is off, the diode is forward biased (we consider the continuous mode operation), therefore . Therefore, the average voltage across the switch is:

The output current is the opposite of the inductor current during the off-state. the average inductor current is therefore:

Assuming the output current and voltage have negligible ripple, the load of the converter can be considered purely resistive. If R is the resistance of the load, the above expression becomes:

Using the previous equations, the input voltage becomes:

This can be written as:

If the inductor resistance is zero, the equation above becomes equal to the one of the *ideal* case. But when *R*_{L} increases, the voltage gain of the converter decreases compared to the ideal case. Furthermore, the influence of *R*_{L} increases with the duty cycle. This is summarized in figure 6.

A **rectifier** is an electrical device that converts alternating current (AC), which periodically reverses direction, to direct current (DC), which flows in only one direction.

A **switched-mode power supply** is an electronic power supply that incorporates a switching regulator to convert electrical power efficiently. Like other power supplies, an SMPS transfers power from a DC or AC source to DC loads, such as a personal computer, while converting voltage and current characteristics. Unlike a linear power supply, the pass transistor of a switching-mode supply continually switches between low-dissipation, full-on and full-off states, and spends very little time in the high dissipation transitions, which minimizes wasted energy. Ideally, a switched-mode power supply dissipates no power. Voltage regulation is achieved by varying the ratio of on-to-off time. In contrast, a linear power supply regulates the output voltage by continually dissipating power in the pass transistor. This higher power conversion efficiency is an important advantage of a switched-mode power supply. Switched-mode power supplies may also be substantially smaller and lighter than a linear supply due to the smaller transformer size and weight.

A **differential amplifier** is a type of electronic amplifier that amplifies the difference between two input voltages but suppresses any voltage common to the two inputs. It is an analog circuit with two inputs and and one output in which the output is ideally proportional to the difference between the two voltages

The **Josephson effect** is the phenomenon of supercurrent, a current that flows indefinitely long without any voltage applied, across a device known as a **Josephson junction (JJ)**, which consists of two or more superconductors coupled by a weak link. The weak link can consist of a thin insulating barrier, a short section of non-superconducting metal (S-N-S), or a physical constriction that weakens the superconductivity at the point of contact (S-s-S).

In electronics, a **chopper** circuit is used to refer to numerous types of electronic switching devices and circuits used in power control and signal applications. A chopper is a device that converts fixed DC input to a variable DC output voltage directly. Essentially, a chopper is an electronic switch that is used to interrupt one signal under the control of another.

**Delta-sigma** modulation is a method for encoding analog signals into digital signals as found in an analog-to-digital converter (ADC). It is also used to convert high bit-count, low-frequency digital signals into lower bit-count, higher-frequency digital signals as part of the process to convert digital signals into analog as part of a digital-to-analog converter (DAC).

A **low-dropout** or **LDO ** regulator is a DC linear voltage regulator that can regulate the output voltage even when the supply voltage is very close to the output voltage.

**Ripple** in electronics is the residual periodic variation of the DC voltage within a power supply which has been derived from an alternating current (AC) source. This ripple is due to incomplete suppression of the alternating waveform after rectification. Ripple voltage originates as the output of a rectifier or from generation and commutation of DC power.

A **Wilson current mirror** is a three-terminal circuit that accepts an input current at the input terminal and provides a "mirrored" current source or sink output at the output terminal. The mirrored current is a precise copy of the input current. It may be used as a **Wilson current source** by applying a constant bias current to the input branch as in Fig. 2. The circuit is named after George R. Wilson, an integrated circuit design engineer who worked for Tektronix. Wilson devised this configuration in 1967 when he and Barrie Gilbert challenged each other to find an improved current mirror overnight that would use only three transistors. Wilson won the challenge.

The **commutation cell** is the basic structure in power electronics. It is composed of an electronic switch and a diode. It was traditionally referred to as a chopper, but since switching power supplies became a major form of power conversion, this new term has become more popular.

The **Early effect**, named after its discoverer James M. Early, is the variation in the effective width of the base in a bipolar junction transistor (BJT) due to a variation in the applied base-to-collector voltage. A greater reverse bias across the collector–base junction, for example, increases the collector–base depletion width, thereby decreasing the width of the charge carrier portion of the base.

The **single-ended primary-inductor converter** (**SEPIC**) is a type of DC/DC converter that allows the electrical potential (voltage) at its output to be greater than, less than, or equal to that at its input. The output of the SEPIC is controlled by the duty cycle of the control transistor.

The **hybrid-pi model** is a popular circuit model used for analyzing the small signal behavior of bipolar junction and field effect transistors. Sometimes it is also called **Giacoletto model** because it was introduced by L.J. Giacoletto in 1969. The model can be quite accurate for low-frequency circuits and can easily be adapted for higher frequency circuits with the addition of appropriate inter-electrode capacitances and other parasitic elements.

An **integrating ADC** is a type of analog-to-digital converter that converts an unknown input voltage into a digital representation through the use of an integrator. In its basic implementation, the dual-slope converter, the unknown input voltage is applied to the input of the integrator and allowed to ramp for a fixed time period. Then a known reference voltage of opposite polarity is applied to the integrator and is allowed to ramp until the integrator output returns to zero. The input voltage is computed as a function of the reference voltage, the constant run-up time period, and the measured run-down time period. The run-down time measurement is usually made in units of the converter's clock, so longer integration times allow for higher resolutions. Likewise, the speed of the converter can be improved by sacrificing resolution.

The **primary line constants** are parameters that describe the characteristics of conductive transmission lines, such as pairs of copper wires, in terms of the physical electrical properties of the line. The primary line constants are only relevant to transmission lines and are to be contrasted with the secondary line constants, which can be derived from them, and are more generally applicable. The secondary line constants can be used, for instance, to compare the characteristics of a waveguide to a copper line, whereas the primary constants have no meaning for a waveguide.

In electronics, a transimpedance amplifier, (TIA) is a current to voltage converter, almost exclusively implemented with one or more operational amplifiers. It is also possible to construct a transimpedance amplifier with discrete components using a Field effect transistor for the gain element. This has been done where a very low noise figure was required. The TIA can be used to amplify the current output of Geiger–Müller tubes, photo multiplier tubes, accelerometers, photo detectors and other types of sensors to a usable voltage. Current to voltage converters are used with sensors that have a current response that is more linear than the voltage response. This is the case with photodiodes where it is not uncommon for the current response to have better than 1% nonlinearity over a wide range of light input. The transimpedance amplifier presents a low impedance to the photodiode and isolates it from the output voltage of the operational amplifier. In its simplest form a transimpedance amplifier has just a large valued feedback resistor, R_{f}. The gain of the amplifer is set by this resistor and because the amplifier is in an inverting configuration, has a value of -R_{f}. There are several different configurations of transimpedance amplifiers, each suited to a particular application. The one factor they all have in common is the requirement to convert the low-level current of a sensor to a voltage. The gain, bandwidth, as well as current and voltage offsets change with different types of sensors, requiring different configurations of transimpedance amplifiers.

- ↑ The Flyback Converter - Lecture notes - ECEN4517 - Department of Electrical and Computer Engineering - University of Colorado, Boulder.
- ↑ ST AN2389: "An MCU-based low cost non-inverting buck-boost converter for battery chargers"
- ↑ Motorola Semiconductor. "Application note AN954: A Unique Converter Configuration provides step-up/down functions". 1985. "... a unique step-up/down configuration can be created ... which still employs a single inductor for the voltage transformation."
- ↑ Haifeng Fan. "Wide VIN and High-Power Challenges with Buck-Boost Converters". 2015.

- Daniel W. Hart, "Introduction to Power Electronics", Prentice Hall, Upper Saddle River, New Jersey USA, 1997 ISBN 0-02-351182-6
- Christophe Basso,
*Switch-Mode Power Supplies: SPICE Simulations and Practical Designs*. McGraw-Hill. ISBN 0-07-150858-9. - Frede Blaabjerg,
*Analysis, control and design of a non-inverting buck-boost converter: A bump-less two-level T–S fuzzy PI control*. ISA Transactions. ISSN 0019-0578.

The **International Standard Book Number** (**ISBN**) is a numeric commercial book identifier which is intended to be unique. Publishers purchase ISBNs from an affiliate of the International ISBN Agency.

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