Buck converter

model). The basic concept of a buck converter is: • Use the higher-than-needed voltage of the source to quickly induce a current into an inductor ("on" in fig. 2 and 4). • Disconnect the source and use the inertia of the current in the inductor to provide more current than the source delivers ("off" in fig. 2 and 4). To close the circuit with the source disconnected, a second switch, usually a diode, is needed. During on-state, the source may need to momentarily provide more current than its rating for constant load allows, but the on-time is too short for the source to take damage. During off-state, no current is drawn from the source, and the components can cool down. The average current draw over both states needs to be below the source specification. To even out voltage spikes from the switching between on-state and off-state, a capacitor is used on the output side. A mechanical analogy for a buck converter would be to pedal a bicycle in single, strong bursts (Force ~ Voltage), and let the bicycle roll in between (inertia ~ inductor). The basic operation of the buck converter has the current in an inductor 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). Idealised case 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. 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{L}) never falls to zero during the commutation cycle. In this mode, the operating principle is described by the plots in figure 4: Real-world factors 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{o} = \frac{idT}{C} 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 Idt (= dQ ; as I = dQ/dt, C = Q/V so dV = dQ/C) under the output current waveform through writing output ripple voltage as dV = Idt/C we integrate the area above the axis to get the peak-to-peak ripple voltage as: ΔV = ΔI T/8C (where ΔI 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 ΔV = ΔI / (ωC) where ω = 2πf, f is the ripple frequency, and f = 1/T, T the ripple period. This gives: ΔV = ΔI T/2πC), 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 (dT) is defined by the duty cycle and by the switching frequency. For the on-state: :dT_\text{on} = DT = \frac{D}{f} For the off-state: :dT_\text{off} = (1 - D)T = \frac{1 - D}{f} 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. 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{V_\text{o} + (V_\text{sw,sync} + V_\text{L})}{V_\text{i} - V_\text{sw} + V_\text{sw,sync}} where: • Vsw is the voltage drop on the power switch, • is the voltage drop on the synchronous switch or diode, and • VL 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, Vsw and may already be known, based on the properties of the selected device. :\begin{align} V_\text{sw} &= I_\text{sw} R_\text{on} = DI_\text{o} R_\text{on} \\ V_\text{sw,sync} &= I_\text{sw,sync} R_\text{on} = (1 - D)I_\text{o} R_\text{on} \\ V_\text{L} &= I_\text{L} R_\text{DC} \end{align} where: • Ron is the ON-resistance of each switch, and • RDC 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 Vsw and 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{leakage} = I_\text{leakage}V where: • Ileakage 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 (MOSFETs, power transistors, 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{SW} = \frac{VI_\text{o} (t_\text{rise} + t_\text{fall})}{6T} where: • V is the voltage across the switch while the switch is off, • trise and tfall 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{SW} = \frac{VI_\text{o} \left(t_\text{rise} + t_\text{fall}\right)}{2T} 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 "shoot-through", a condition in which both switches are simultaneously turned on. The onset of shoot-through generates severe power loss and heat. Proper selection of non-overlap time must balance the risk of shoot-through 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{D,body} = V_\text{F} I_\text{o} t_\text{no} f_\text{SW} 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 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{Gdrive} = Q_\text{G} V_\text{GS} f_\text{SW} where: • QG is the gate charge of the selected MOSFET, and • VGS 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 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 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{D} = V_\text{D} (1 - D) I_\text{o} where: • VD 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 RDSon might be selected for S2, providing power loss on switch 2 which is :P_{S_2} = I_\text{o}^2 R_\text{DSon} (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, 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. When power is transferred in the "reverse" direction, it acts much like a boost converter. 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 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 ==