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A buck converter (step-down converter) is a DC-to-DC power converter which steps down voltage (while stepping up current) from its input (supply) to its output (load). It is a class of
switched-mode power supply A switched-mode power supply (switching-mode power supply, switch-mode power supply, switched power supply, SMPS, or switcher) is an electronic power supply that incorporates a switching regulator to convert electrical power efficiently. Lik ...
(SMPS) typically containing at least two semiconductors (a
diode A diode is a two-terminal electronic component that conducts current primarily in one direction (asymmetric conductance); it has low (ideally zero) resistance in one direction, and high (ideally infinite) resistance in the other. A diode ...
and a
transistor upright=1.4, gate (G), body (B), source (S) and drain (D) terminals. The gate is separated from the body by an insulating layer (pink). A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch e ...
, although modern buck converters frequently replace the diode with a second transistor used for synchronous rectification) and at least one energy storage element, a
capacitor A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals. The effect of ...
,
inductor An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a c ...
, or the two in combination. To reduce voltage ripple, filters made of capacitors (sometimes in combination with inductors) are normally added to such a converter's output (load-side filter) and input (supply-side filter). Its name derives from the inductor that “bucks” or opposes the supply voltage. Switching converters (such as buck converters) provide much greater power efficiency as DC-to-DC converters than
linear regulator In electronics, a linear regulator is a voltage regulator used to maintain a steady voltage. The resistance of the regulator varies in accordance with both the input voltage and the load, resulting in a constant voltage output. The regulating circ ...
s, which are simpler circuits that lower voltages by dissipating power as heat, but do not step up output current. The efficiency of buck converters can be very high, often over 90%, making them useful for tasks such as converting a computer's main
supply Supply may refer to: *The amount of a resource that is available **Supply (economics), the amount of a product which is available to customers **Materiel, the goods and equipment for a military unit to fulfill its mission *Supply, as in confidenc ...
voltage, which is usually 12V, down to lower voltages needed by
USB Universal Serial Bus (USB) is an industry standard that establishes specifications for cables, connectors and protocols for connection, communication and power supply (interfacing) between computers, peripherals and other computers. A broad ...
,
DRAM Dynamic random-access memory (dynamic RAM or DRAM) is a type of random-access semiconductor memory that stores each bit of data in a memory cell, usually consisting of a tiny capacitor and a transistor, both typically based on metal-oxid ...
and the CPU, which are usually 5, 3.3 or 1.8V. Buck convertors typically operate with a switching frequency range from 100 kHz to a few MHz. A higher switching frequency allows for use of smaller inductors and capacitors, but also increases lost efficiency to more frequent transistor switching.


Theory of operation

The basic operation of the buck converter has the current in an
inductor An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a c ...
controlled by two switches (fig. 2). In a physical implementation, these switches are realized by a transistor and a diode, or two transistors (which avoids the loss associated with the diode's voltage drop).


Concept: explained for the idealised case

To simplify the explanation an idealised converter is assumed: ie certain real world factors are ignored (in the same way that explaining a car engine may ignore friction in the bearings, say). The assumptions here *(A) All the components are considered to be perfect. Specifically, the switch and the diode have zero voltage drop when on and zero current flow when off, and the inductor has zero series resistance. *(B) the input and output voltages do not change over the course of a cycle, which would imply the output capacitance as being
infinite Infinite may refer to: Mathematics * Infinite set, a set that is not a finite set *Infinity, an abstract concept describing something without any limit Music *Infinite (group), a South Korean boy band *''Infinite'' (EP), debut EP of American m ...
. Given those assumptions, the conceptual model of the buck converter is best understood in terms of the relation between current and voltage of the inductor. Beginning with the switch open (off-state), the current in the circuit is zero. When the switch is first closed (on-state), the current will begin to increase, and the inductor will produce an opposing voltage across its terminals in response to the changing current. This voltage drop counteracts the voltage of the source and therefore reduces the net voltage across the load. Over time, the rate of change of current decreases, and the voltage across the inductor also then decreases, increasing the voltage at the load. During this time, the inductor stores energy in the form of a
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
. If the switch is opened while the current is still changing, then there will always be a voltage drop across the inductor, so the net voltage at the load will always be less than the input voltage source. When the switch is opened again (off-state), the voltage source will be removed from the circuit, and the current will decrease. The decreasing current will produce a voltage drop across the inductor (opposite to the drop at on-state), and now the inductor becomes a current source. The stored energy in the inductor's magnetic field supports the current flow through the load. This current, flowing while the input voltage source is disconnected, when appended to the current flowing during on-state, totals to current greater than the average input current (being zero during off-state). The "increase" in average current makes up for the reduction in voltage, and ideally preserves the power provided to the load. During the off-state, the inductor is discharging its stored energy into the rest of the circuit. If the switch is closed again before the inductor fully discharges (on-state), the voltage at the load will always be greater than zero.


Continuous mode

Buck converters operate in continuous mode if the current through the inductor (I_\text) never falls to zero during the commutation cycle. In this mode, the operating principle is described by the plots in figure 4: * When the switch pictured above is closed (top of figure 2), the voltage across the inductor is V_\text = V_\text - V_\text. The current through the inductor rises linearly (in approximation, so long as the voltage drop is almost constant). As the diode is reverse-biased by the voltage source V, no current flows through it; * When the switch is opened (bottom of figure 2), the diode is forward biased. The voltage across the inductor is V_\text = - V_\text (neglecting diode drop). Current I_\text decreases. The energy stored in inductor L is :E = \frac L I_\text^2 Therefore, it can be seen that the energy stored in L increases during on-time as I_\text increases and then decreases during the off-state. L is used to transfer energy from the input to the output of the converter. The rate of change of I_\text can be calculated from: :V_\text = L\frac With V_\text equal to V_\text - V_\text during the on-state and to -V_\text during the off-state. Therefore, the increase in current during the on-state is given by: :\begin \Delta I_ &= \int_0^ \frac\, \mathrmt = \frac t_\text, & t_\text &= DT \end where D is a scalar called the duty cycle with a value between 0 and 1. Conversely, the decrease in current during the off-state is given by: :\begin \Delta I_ &= \int_^\frac\, \mathrmt = -\frac t_\text, & t_\text &= (1 - D)T \end Assuming that the converter operates in the steady state, the energy stored in each component at the end of a commutation cycle T is equal to that at the beginning of the cycle. That means that the current I_\text is the same at t = 0 and at t = T (figure 4). So, from the above equations it can be written as: :\begin \Delta I_ + \Delta I_ &= 0 \\ \fract_\text - \fract_\text &= 0 \end The above integrations can be done graphically. In figure 4, \Delta I_ is proportional to the area of the yellow surface, and \Delta I_ to the area of the orange surface, as these surfaces are defined by the inductor voltage (red lines). As these surfaces are simple rectangles, their areas can be found easily: \left(V_\text - V_\text\right) t_\text for the yellow rectangle and -V_\text t_\text for the orange one. For steady state operation, these areas must be equal. As can be seen in figure 4, t_\text = DT and t_\text = (1 - D)T. This yields: :\begin \left(V_\text - V_\text\right)DT - V_\text(1 - D)T &= 0 \\ DV_\text - V_\text &= 0 \\ \Rightarrow D &= \frac \end From this equation, it can be seen that the output voltage of the converter varies linearly with the duty cycle for a given input voltage. As the duty cycle D is equal to the ratio between t_\text and the period T, it cannot be more than 1. Therefore, V_\text \leq V_\text. This is why this converter is referred to as ''step-down converter''. So, for example, stepping 12 V down to 3 V (output voltage equal to one quarter of the input voltage) would require a duty cycle of 25%, in this theoretically ideal circuit.


Discontinuous mode

In some cases, the amount of energy required by the load is too small. 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 figure 5). This has, however, some effect on the previous equations. The inductor current falling below zero results in the discharging of the output capacitor during each cycle and therefore higher . A different control technique known as
pulse-frequency modulation Pulse-frequency modulation (PFM) is a modulation method for representing an analog signal using only two levels (1 and 0). It is analogous to pulse-width modulation (PWM), in which the magnitude of an analog signal is encoded in the duty cycle ...
can be used to minimize these losses. We still consider that the converter operates in steady state. Therefore, the energy in the inductor is the same at the beginning and at the end of the cycle (in the case of discontinuous mode, it is zero). This means that the average value of the inductor voltage (VL) is zero; i.e., that the area of the yellow and orange rectangles in figure 5 are the same. This yields: :\left(V_\text - V_\text\right)DT - V_\text\delta T = 0 So the value of δ is: :\delta = \fracD The output current delivered to the load (I_\text) is constant, as we consider that the output capacitor is large enough to maintain a constant voltage across its terminals during a commutation cycle. This implies that the current flowing through the capacitor has a zero average value. Therefore, we have : :\overline = I_\text Where \overline is the average value of the inductor current. As can be seen in figure 5, the inductor current waveform has a triangular shape. Therefore, the average value of IL can be sorted out geometrically as follows: :\begin \overline &= \left(\fracI_DT + \fracI_ \delta T\right)\frac\\ &= \fracI_\left(D + \delta\right)\\ &= I_\text \end The inductor current is zero at the beginning and rises during ton up to ILmax. That means that ILmax is equal to: :I_ = \frac DT Substituting the value of ILmax in the previous equation leads to: :I_\text = \frac And substituting δ by the expression given above yields: :I_\text = \frac This expression can be rewritten as: :V_\text = V_\text\frac It can be seen that the output voltage of a buck converter operating in discontinuous mode is much more complicated than its counterpart of the continuous mode. Furthermore, the output voltage is now a function not only of the input voltage (Vi) and the duty cycle D, but also of the inductor value (L), the commutation period (T) and the output current (Io).


From discontinuous to continuous mode (and vice versa)

As mentioned 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. Using the notations of figure 5, this corresponds to : :\begin DT + \delta T &= T \\ \Rightarrow D + \delta &= 1 \end Therefore, the output current (equal to the average inductor current) at the limit between discontinuous and continuous modes is (see above): :I_ = \frac\left(D + \delta\right) = \frac Substituting ILmax by its value: :I_ = \frac D T On the limit between the two modes, the output voltage obeys both the expressions given respectively in the continuous and the discontinuous sections. In particular, the former is :V_\text = DV_\text So Iolim can be written as: :I_ = \fracDT Let's now introduce two more notations: * the normalized voltage, defined by \left, V_\text\ = \frac. It is zero when V_\text = 0, and 1 when V_\text = V_\text ; * the normalized current, defined by \left, I_\text\ = \fracI_\text. The term \frac 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 \left, I_\text\ equals 0 for no output current, and 1 for the maximum current the converter can deliver. Using these notations, we have: * in continuous mode: *:\left, V_\text\ = D * in discontinuous mode: *:\begin \left, V_\text\ &= \frac\\ &= \frac\\ &= \frac \end the current at the limit between continuous and discontinuous mode is: :\begin I_ &= \fracD\left(1 - D\right)T\\ &= \frac D\left(1 - D\right) \end Therefore, the locus of the limit between continuous and discontinuous modes is given by: :\frac = 1 These expressions have been plotted in figure 6. From this, it can be deduced that in continuous mode, the output voltage does only depend on the duty cycle, whereas it is far more complex in the discontinuous mode. This is important from a control point of view. On the circuit level, the detection of the boundary between CCM and DCM are usually provided by an inductor current sensing, requiring high accuracy and fast detectors as:


Concept: handling the real-world differences to the assumptions made above

The analysis above was conducted with the assumptions: * The output capacitor has enough capacitance to supply power to the load (a simple resistance) without any noticeable variation in its voltage. * The voltage drop across the diode when forward biased is zero * No commutation losses in the switch nor in the diode These assumptions can be fairly far from reality, and the imperfections of the real components can have a detrimental effect on the operation of the converter.


Output voltage ripple (continuous mode)

Output voltage ripple is the name given to the phenomenon where the output voltage rises during the On-state and falls during the Off-state. Several factors contribute to this including, but not limited to, switching frequency, output capacitance, inductor, load and any current limiting features of the control circuitry. At the most basic level the output voltage will rise and fall as a result of the output capacitor charging and discharging: :dV_\text = \frac We can best approximate output ripple voltage by shifting the output current versus time waveform (continuous mode) down so that the average output current is along the time axis. When we do this, we see the AC current waveform flowing into and out of the output capacitor (sawtooth waveform). We note that ''V'' (where ''V'' is the capacitor voltage) occurs at ''t''/2 (just after capacitor has discharged) and ''V'' at ''t''/2. By integrating ''I''d''t'' (= d''Q'' ; as ''I'' = d''Q''/d''t'', ''C'' = ''Q''/''V'' so d''V'' = d''Q''/''C'') under the output current waveform through writing output ripple voltage as d''V'' = ''I''d''t''/''C'' we integrate the area above the axis to get the peak-to-peak ripple voltage as: Δ''V'' = Δ''I'' ''T''/8''C'' (where Δ''I'' is the peak-to-peak ripple current and ''T'' is the time period of ripple. A full explanation is given there.) We note from basic AC circuit theory that our ripple voltage should be roughly sinusoidal: capacitor impedance times ripple current peak-to-peak value, or Δ''V'' = Δ''I'' / (2ω''C'') where ω = 2π''f'', ''f'' is the ripple frequency, and ''f'' = 1/''T'', ''T'' the ripple period. This gives: Δ''V'' = Δ''I'' ''T''/2π''C''), and we compare to this value to confirm the above in that we have a factor of 8 vs a factor of ~ 6.3 from basic AC circuit theory for a sinusoid. This gives confidence in our assessment here of ripple voltage. The paragraph directly below pertains that directly above and may be incorrect. Use the equations in this paragraph. Once again, please see talk tab for more: pertaining output ripple voltage and AoE (Art of Electronics 3rd edition). During the Off-state, the current in this equation is the load current. In the On-state the current is the difference between the switch current (or source current) and the load current. The duration of time (d''T'') is defined by the duty cycle and by the switching frequency. For the on-state: :dT_\text = DT = \frac For the off-state: :dT_\text = (1 - D)T = \frac Qualitatively, as the output capacitance or switching frequency increase, the magnitude of the ripple decreases. Output voltage ripple is typically a design specification for the power supply and is selected based on several factors. Capacitor selection is normally determined based on cost, physical size and non-idealities of various capacitor types. Switching frequency selection is typically determined based on efficiency requirements, which tends to decrease at higher operating frequencies, as described below in
Effects of non-ideality on the efficiency Effect may refer to: * A result or change of something ** List of effects ** Cause and effect, an idiom describing causality Pharmacy and pharmacology * Drug effect, a change resulting from the administration of a drug ** Therapeutic effect, a ...
. Higher switching frequency can also raise EMI concerns. Output voltage ripple is one of the disadvantages of a switching power supply, and can also be a measure of its quality.


Effects on the efficiency

The simplified analysis above, does not account for non-idealities of the circuit components nor does it account for the required control circuitry. Power losses due to the control circuitry are usually insignificant when compared with the losses in the power devices (switches, diodes, inductors, etc.) The non-idealities of the power devices account for the bulk of the power losses in the converter. Both static and dynamic power losses occur in any switching regulator. Static power losses include I^2R (conduction) losses in the wires or PCB traces, as well as in the switches and inductor, as in any electrical circuit. Dynamic power losses occur as a result of switching, such as the charging and discharging of the switch gate, and are proportional to the switching frequency. It is useful to begin by calculating the duty cycle for a non-ideal buck converter, which is: :D = \frac where: * ''V''sw is the voltage drop on the power switch, * ''V''sw,sync is the voltage drop on the synchronous switch or diode, and * ''V''L is the voltage drop on the inductor. The voltage drops described above are all static power losses which are dependent primarily on DC current, and can therefore be easily calculated. For a diode drop, ''V''sw and ''V''sw,sync may already be known, based on the properties of the selected device. :\begin V_\text &= I_\text R_\text = DI_\text R_\text \\ V_\text &= I_\text R_\text = (1 - D)I_\text R_\text \\ V_\text &= I_\text R_\text \end where: * ''R''on is the ON-resistance of each switch, and * ''R''DC is the DC resistance of the inductor. The duty cycle equation is somewhat recursive. A rough analysis can be made by first calculating the values ''V''sw and ''V''sw,sync using the ideal duty cycle equation. For a MOSFET voltage drop, a common approximation is to use RDSon from the MOSFET's datasheet in Ohm's Law, V = IDSRDSon(sat). This approximation is acceptable because the MOSFET is in the linear state, with a relatively constant drain-source resistance. This approximation is only valid at relatively low VDS values. For more accurate calculations, MOSFET datasheets contain graphs on the VDS and IDS relationship at multiple VGS values. Observe VDS at the VGS and IDS which most closely match what is expected in the buck converter. In addition, power loss occurs as a result of leakage currents. This power loss is simply :P_\text = I_\textV where: * ''I''leakage is the leakage current of the switch, and * ''V'' is the voltage across the switch. Dynamic power losses are due to the switching behavior of the selected pass devices (
MOSFET The metal–oxide–semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET) is a type of field-effect transistor (FET), most commonly fabricated by the controlled oxidation of silicon. It has an insulated gate, the voltage of which d ...
s,
power transistor A power semiconductor device is a semiconductor device used as a switch or rectifier in power electronics (for example in a switch-mode power supply). Such a device is also called a power device or, when used in an integrated circuit, a power IC ...
s, IGBTs, etc.). These losses include turn-on and turn-off switching losses and switch transition losses. Switch turn-on and turn-off losses are easily lumped together as :P_\text = \frac where: * ''V'' is the voltage across the switch while the switch is off, * ''t''rise and ''t''fall are the switch rise and fall times, and * ''T'' is the switching period but this does not take into account the parasitic capacitance of the MOSFET which makes the ''Miller plate''. Then, the switch losses will be more like: :P_\text = \frac When a MOSFET is used for the lower switch, additional losses may occur during the time between the turn-off of the high-side switch and the turn-on of the low-side switch, when the body diode of the low-side MOSFET conducts the output current. This time, known as the non-overlap time, prevents "shootthrough", a condition in which both switches are simultaneously turned on. The onset of shootthrough generates severe power loss and heat. Proper selection of non-overlap time must balance the risk of shootthrough with the increased power loss caused by conduction of the body diode. Many MOSFET based buck converters also include a diode to aid the lower MOSFET body diode with conduction during the non-overlap time. When a diode is used exclusively for the lower switch, diode forward turn-on time can reduce efficiency and lead to voltage overshoot. Power loss on the body diode is also proportional to switching frequency and is :P_\text = V_\text I_\text t_\text f_\text where: * ''VF'' is the forward voltage of the body diode, and * ''tno'' is the selected non-overlap time. Finally, power losses occur as a result of the power required to turn the switches on and off. For MOSFET switches, these losses are dominated by the energy required to charge and discharge the capacitance of the MOSFET gate between the
threshold voltage The threshold voltage, commonly abbreviated as Vth or VGS(th), of a field-effect transistor (FET) is the minimum gate-to-source voltage (VGS) that is needed to create a conducting path between the source and drain terminals. It is an important s ...
and the selected gate voltage. These switch transition losses occur primarily in the gate driver, and can be minimized by selecting MOSFETs with low gate charge, by driving the MOSFET gate to a lower voltage (at the cost of increased MOSFET conduction losses), or by operating at a lower frequency. :P_\text = Q_\text V_\text f_\text where: * ''Q''G is the gate charge of the selected MOSFET, and * ''V''GS is the peak gate-source voltage. For N-MOSFETs, the high-side switch must be driven to a higher voltage than ''Vi''. To achieve this, MOSFET gate drivers typically feed the MOSFET output voltage back into the gate driver. The gate driver then adds its own supply voltage to the MOSFET output voltage when driving the high-side MOSFETs to achieve a ''VGS'' equal to the gate driver supply voltage. Because the low-side ''VGS'' is the gate driver supply voltage, this results in very similar ''VGS'' values for high-side and low-side MOSFETs. A complete design for a buck converter includes a
tradeoff analysis A trade-off (or tradeoff) is a situational decision that involves diminishing or losing one quality, quantity, or property of a set or design in return for gains in other aspects. In simple terms, a tradeoff is where one thing increases, and anot ...
of the various power losses. Designers balance these losses according to the expected uses of the finished design. A converter expected to have a low switching frequency does not require switches with low gate transition losses; a converter operating at a high duty cycle requires a low-side switch with low conduction losses.


Specific structures


Synchronous rectification

A synchronous buck converter is a modified version of the basic buck converter circuit topology in which the diode, D, is replaced by a second switch, S2. This modification is a tradeoff between increased cost and improved efficiency. In a standard buck converter, the
flyback diode A flyback diode is any diode connected across an inductor used to eliminate flyback, which is the sudden voltage spike seen across an inductive load when its supply current is suddenly reduced or interrupted. It is used in circuits in which ind ...
turns on, on its own, shortly after the switch turns off, as a result of the rising voltage across the diode. This voltage drop across the diode results in a power loss which is equal to :P_\text = V_\text (1 - D) I_\text where: * ''V''D is the voltage drop across the diode at the load current ''Io'', * ''D'' is the duty cycle, and * ''Io'' is the load current. By replacing the diode with a switch selected for low loss, the converter efficiency can be improved. For example, a MOSFET with very low ''R''DSon might be selected for ''S''2, providing power loss on switch 2 which is :P_ = I_\text^2 R_\text (1 - D) In both cases, power loss is strongly dependent on the duty cycle, D. Power loss on the freewheeling diode or lower switch will be proportional to its on-time. Therefore, systems designed for low duty cycle operation will suffer from higher losses in the freewheeling diode or lower switch, and for such systems it is advantageous to consider a synchronous buck converter design. Consider a
computer power supply A power supply unit (PSU) converts mains AC to low-voltage regulated DC power for the internal components of a computer. Modern personal computers universally use switched-mode power supplies. Some power supplies have a manual switch for select ...
, where the input is 5 V, the output is 3.3 V, and the load current is 10A. In this case, the duty cycle will be 66% and the diode would be on for 34% of the time. A typical diode with forward voltage of 0.7 V would suffer a power loss of 2.38 W. A well-selected MOSFET with RDSon of 0.015 Ω, however, would waste only 0.51 W in conduction loss. This translates to improved efficiency and reduced heat generation. Another advantage of the synchronous converter is that it is bi-directional, which lends itself to applications requiring
regenerative braking Regenerative braking is an energy recovery mechanism that slows down a moving vehicle or object by converting its kinetic energy into a form that can be either used immediately or stored until needed. In this mechanism, the electric traction mo ...
. When power is transferred in the "reverse" direction, it acts much like a
boost converter A boost converter (step-up converter) is a DC-to-DC power converter that steps up voltage (while stepping down current) from its input (supply) to its output (load). It is a class of switched-mode power supply (SMPS) containing at least two semi ...
. The advantages of the synchronous buck converter do not come without cost. First, the lower switch typically costs more than the freewheeling diode. Second, the complexity of the converter is vastly increased due to the need for a complementary-output switch driver. Such a driver must prevent both switches from being turned on at the same time, a fault known as "shootthrough". The simplest technique for avoiding shootthrough is a time delay between the turn-off of S1 to the turn-on of S2, and vice versa. However, setting this time delay long enough to ensure that S1 and S2 are never both on will itself result in excess power loss. An improved technique for preventing this condition is known as adaptive "non-overlap" protection, in which the voltage at the switch node (the point where S1, S2 and L are joined) is sensed to determine its state. When the switch node voltage passes a preset threshold, the time delay is started. The driver can thus adjust to many types of switches without the excessive power loss this flexibility would cause with a fixed non-overlap time. Both low side and high side switches may be turned off in response to a load transient and the body diode in the low side MOSFET or another diode in parallel with it becomes active. The higher voltage drop on the low side switch is then of benefit, helping to reduce current output and meet the new load requirement sooner.


Multiphase buck

The multiphase buck converter is a circuit topology where basic buck converter circuits are placed in parallel between the input and load. Each of the ''n'' "phases" is turned on at equally spaced intervals over the switching period. This circuit is typically used with the synchronous buck topology, described above. This type of converter can respond to load changes as quickly as if it switched ''n'' times faster, without the increase in switching losses that would cause. Thus, it can respond to rapidly changing loads, such as modern microprocessors. There is also a significant decrease in switching ripple. Not only is there the decrease due to the increased effective frequency, but any time that ''n'' times the duty cycle is an integer, the switching ripple goes to 0; the rate at which the inductor current is increasing in the phases which are switched on exactly matches the rate at which it is decreasing in the phases which are switched off. Another advantage is that the load current is split among the ''n'' phases of the multiphase converter. This load splitting allows the heat losses on each of the switches to be spread across a larger area. This circuit topology is used in computer motherboards to convert the 12 VDC
power supply A power supply is an electrical device that supplies electric power to an electrical load. The main purpose of a power supply is to convert electric current from a source to the correct voltage, current, and frequency to power the load. As a r ...
to a lower voltage (around 1 V), suitable for the CPU. Modern CPU power requirements can exceed 200W, can change very rapidly, and have very tight ripple requirements, less than 10mV. Typical CPU power supplies found on mainstream motherboards use 3 or 4 phases, while high-end systems can have 16 or more phases. One major challenge inherent in the multiphase converter is ensuring the load current is balanced evenly across the ''n'' phases. This current balancing can be performed in a number of ways. Current can be measured "losslessly" by sensing the voltage across the inductor or the lower switch (when it is turned on). This technique is considered lossless because it relies on resistive losses inherent in the buck converter topology. Another technique is to insert a small resistor in the circuit and measure the voltage across it. This approach is more accurate and adjustable, but incurs several costs—space, efficiency and money. Finally, the current can be measured at the input. Voltage can be measured losslessly, across the upper switch, or using a power resistor, to approximate the current being drawn. This approach is technically more challenging, since switching noise cannot be easily filtered out. However, it is less expensive than having a sense resistor for each phase.


Efficiency factors

There are two main phenomenon impacting the efficiency: conduction losses and switching losses. Conduction losses happen when current is flowing through the components and thus depend on the load. They are caused by
Joule effect Joule effect and Joule's law are any of several different physical effects discovered or characterized by English physicist James Prescott Joule. These physical effects are not the same, but all are frequently or occasionally referred to in the lit ...
in the resistance when the transistor or MOSFET switch is conducting, the inductor winding resistance, and the capacitor equivalent series resistance. Losses are proportional to the square of the current in this case. Conduction losses are also generated by the diode forward voltage drop (usually or for
schottky diode The Schottky diode (named after the German physicist Walter H. Schottky), also known as Schottky barrier diode or hot-carrier diode, is a semiconductor diode formed by the junction of a semiconductor with a metal. It has a low forward voltag ...
), and are proportional to the current in this case. Switching losses happen in the transistor and diode when the voltage and the current overlap during the transitions between closed and open states. A schottky diode can be used to minimize the switching losses caused by the reverse recovery of a regular PN diode. The switching losses are proportionnal to the switching frequency. In a complete real-world buck converter, there is also a command circuit to regulate the output voltage or the inductor current. This circuit and the MOSFET gate controller have a power consumption, impacting the overall efficiency of the converter. 090424 ee.iitb.ac.in


Impedance matching

A buck converter can be used to maximize the power transfer through the use of
impedance matching In electronics, impedance matching is the practice of designing or adjusting the input impedance or output impedance of an electrical device for a desired value. Often, the desired value is selected to maximize power transfer or minimize signal ...
. An application of this is in a ''
maximum power point tracker Maximum power point tracking (MPPT) or sometimes just power point tracking (PPT), is a technique used with variable power sources to maximize energy extraction as conditions vary. The technique is most commonly used with photovoltaic (PV) solar sy ...
'' commonly used in
photovoltaic Photovoltaics (PV) is the conversion of light into electricity using semiconducting materials that exhibit the photovoltaic effect, a phenomenon studied in physics, photochemistry, and electrochemistry. The photovoltaic effect is commercially us ...
systems. By the equation for
electric power Electric power is the rate at which electrical energy is transferred by an electric circuit. The SI unit of power is the watt, one joule per second. Standard prefixes apply to watts as with other SI units: thousands, millions and billions o ...
: :V_\text I_\text = \eta V_\text I_\text where: * ''V''o, ''V''i are the output and input voltages * ''I''o, ''I''i are the output and input currents * ''η'' is the power efficiency (ranging from 0 to 1) By
Ohm's law Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equat ...
: :\begin I_\text &= \frac \\ I_\text &= \frac \end where: * ''Z''o, ''Z''i are the output and input impedances. Substituting these expressions for ''I''o and ''I''i into the power equation yields: :\frac = \frac As was previously shown for the continuous mode, (where ''I''L > 0): :V_\text = D V_\text where: *''D'' is the duty cycle Substituting this equation for ''V''o into the previous equation, yields: :\frac = \frac which reduces to: :\frac = \frac and finally: :D = \sqrt This shows that it is possible to adjust the impedance ratio by adjusting the duty cycle. This is particularly useful in applications where the impedances are dynamically changing.


See also

*
Split-pi topology In electronics, a split-pi topology is a pattern of component interconnections used in a kind of power converter that can theoretically produce an arbitrary output voltage, either higher or lower than the input voltage. In practice the upper volt ...


References


Bibliography

* * * * * *


External links

* https://www.ipes.ethz.ch/mod/lesson/view.php?id=2 Interactive Power Electronics Seminar (iPES)] Many Java applets demonstrating the operation of converters
Model based control of digital buck converter
Description and working
VisSim VisSim is a visual block diagram program for simulation of dynamical systems and model-based design of embedded systems, with its own visual language. It is developed by Visual Solutions of Westford, Massachusetts. Visual Solutions was acquired ...
source code diagram for low cost digital control of DC-DC buck converters
SPICE simulation of the buck converter


- Detailed article on DC-DC converters which gives a more formal and detailed analysis of the Buck including the effects of non-ideal switching (but, note that the diagram of the buck-boost converter fails to account for the inversion of the polarity of the voltage between input and output).
DC-DC Power Converter Case study

On the Power Efficiency Optimization

Multiphase DC-DC converter
{{DEFAULTSORT:Buck Converter Voltage regulation Choppers