1. Introduction to Linear Regulators and Switching Regulators of the Buck Boost and Inverting Types
In this guide, we describe many well-known topologies (elemental building blocks) that are commonly used to implement linear and switching power supply designs. Each topology has both common and unique properties, and the experienced designer will choose the topology best suited for the intended application. However, for those engineers just starting in this area, the choice may appear rather daunting. It is worth spending some time to develop a basic understanding of the properties, because the correct initial choice will avoid wasting time on a topology that may not be the best for the application.
We will see that some topologies are best used for AC/DC offline converters at lower output powers (say, < 200W),whereas others will be better at higher output powers. Again some will be a better choice for higher AC input voltages (say, = 220 VAC), whereas others will be better at lower AC input voltages. In a similar way, some will have advantages for higher DC output voltages (say, > 200V), yet others are preferred at lower DC voltages. For applications where several output voltages are required, some topologies will have a lower parts count or may offer a trade-off in parts counts versus reliability, while input or output ripple and noise requirements will also be an important factor.
Further, some topologies have inherent limitations that require additional or more complex circuitry, whereas the performance of others can become difficult to analyze in some situations.
So we should now see how helpful it can be in our initial design choice to have at least a working knowledge of the merits and limitations of all the basic topologies. A poor initial choice can result in performance limitation and perhaps in extended design time and cost. Hence it is well worth the time and effort to get to know the basic performance parameters of the various topologies.
In this first section, we describe some of the earliest and most fundamental building blocks that form the basis of all linear and switching power systems. These include the following regulators:
• Linear regulator
• Buck regulator
• Boost regulator
• Inverting regulator (also known as flyback or buck-boost)
We describe the basic operation of each type, show and explain the various waveforms, and describe the merits and limitations of each topology. The peak transistor currents and voltage stresses are shown for various output power and input voltage conditions. We look at the dependence of input current on output power and input voltage.
We examine efficiency, DC and AC switching losses, and some typical applications.
2. Linear Regulator-the Dissipative Regulator
2.1 Basic Operation
To demonstrate the main advantage of the more complex switching regulators, the discussion starts with an examination of the basic properties of what preceded them-the linear or series-pass regulator.
FIG. 1a shows the basic topology of the linear regulator. It consists of a transistor Q1 (operating in the linear, or non-switching-mode) to form an electrically variable resistance between the DC source (Vdc) developed by the 60-Hz isolation transformer, rectifiers, and storage capacitor C f , and the output terminal at Vo that is connected to the external load (not shown).
In FIG. 1a, an error amplifier senses the DC output voltage Vo via a sampling resistor network R1, R2 and compares it with a reference voltage Vref. The error amplifier output drives the base of the series-pass power transistor Q1 via a drive circuit. The phasing is such that if the DC output voltage Vo tends to increase (say, as a result of either an increase in input voltage or a decrease in output load current), the drive to the base of the series-pass transistor is reduced.
This increases the resistance of the series-pass element Q1 and hence controls the output voltage so that the sampled output continues to track the reference voltage. This negative-feedback loop works in the reverse direction for any decreases in output voltage, such that the error amplifier increases the drive to Q1 decreasing the collector-to emitter resistance, thus maintaining the value of Vo constant.
FIG. 1 (a) The linear regulator. The waveform shows the ripple normally
present on the unregulated DC input (Vdc). Transistor Q1, between the
DC source at Cf and the output load at Vo , acts as an electrically variable
resistance. The negative-feedback loop via the error amplifier alters
the effective resistance of Q1 and will keep Vo constant, providing the
input voltage sufficiently exceeds the output voltage. (b) FIG. 1b
shows the minimum input-output voltage differential (or headroom) required
in a linear regulator. With a typical NPN series-pass transistor, a minimum
input-output voltage differential (headroom) of at least 2.5 V is required
between Vo and the bottom of the C f input ripple waveform at minimum
Vac input.
In general, any change in input voltage-due to, for example, AC input line voltage change, ripple, steady-state changes in the input or output, and any dynamic changes resulting from rapid load changes over its designed tolerance band-is absorbed across the series-pass element. This maintains the output voltage constant to an extent determined by the gain in the open-loop feedback amplifier.
Switching regulators have transformers and fast switching actions that can cause considerable RFI noise. However, in the linear regulator the feedback loop is entirely DC-coupled. There are no switching actions within the loop. As a result, all DC voltage levels are predictable and calculable. This lower RFI noise can be a major advantage in some applications, and for this reason, linear regulators still have a place in modern power supply applications even though the efficiency is quite low. Also since the power losses are mainly due to the DC current and the voltage across Q1, the loss and the overall efficiency are easily calculated.
2.2 Some Limitations of the Linear Regulator
This simple, DC-coupled series-pass linear regulator was the basis for a multi-billion-dollar power supply industry until the early 1960s.
However, in simple terms, it has the following limitations:
• The linear regulator is constrained to produce only a lower regulated voltage from a higher non-regulated input.
• The output always has one terminal that is common with the input. This can be a problem, complicating the design when DC isolation is required between input and output or between multiple outputs.
• The raw DC input voltage (Vdc in FIG. 1a) is usually de rived from the rectified secondary of a 60-Hz transformer whose weight and volume was often a serious system constraint.
• As shown next, the regulation efficiency is very low, resulting in a considerable power loss needing large heat sinks in relatively large and heavy power units.
2.3 Power Dissipation in the Series-Pass Transistor
A major limitation of a linear regulator is the inevitable and large dissipation in the series-pass element. It is clear that all the load current must pass through the pass transistor Q1, and its dissipation will be (Vdc - Vo )( Io ). The minimum differential (Vdc - Vo ), the headroom, is typically 2.5 V for NPN pass transistors. Assume for now that the filter capacitor is large enough to yield insignificant ripple. Typically the raw DC input comes from the rectified secondary of a 60-Hz trans former. In this case the secondary turns can always be chosen so that the rectified secondary voltage is near Vo + 2.5 V when the input AC is at its low tolerance limit. At this point the dissipation in Q1 will be quite low.
However, when the input AC voltage is at its high tolerance limit, the voltage across Q1 will be much greater, and its dissipation will be larger, reducing the power supply efficiency. Due to the minimum 2.5-volt headroom requirement, this effect is much more pronounced at lower output voltages.
This effect is dramatically demonstrated in the following examples.
We will assume an AC input voltage range of ±15%. Consider three examples as follows:
• Output of 5V at 10A
• Output of 15 V at 10 A
• Output of 30 V at 10 A
Assume for now that a large secondary filter capacitor is used such that ripple voltage to the regulator is negligible. The rectified secondary voltage range (Vdc) will be identical to the AC input voltage range of ±15%. The transformer secondary voltages will be chosen to yield (Vo + 2.5 V) when the AC input is at its low tolerance limit of -15%. Hence, the maximum DC input is 35% higher when the AC input is at its maximum tolerance limit of +15%. This yields the following:
It is clear from this example that at lower DC output voltages the efficiency will be very low. In fact, as shown next, when realistic input line ripple voltages are included, the efficiency for a 5-volt output with a line voltage range of ±15% will be only 32 to 35%.
2.4 Linear Regulator Efficiency vs. Output Voltage
We will consider in general the range of efficiency expected for a range of output voltages from 5 V to 100 V with line inputs ranging from ±5 to ±15% when a realistic ripple value is included.
Assume the minimum headroom is to be 2.5 V, and this must be guaranteed at the bottom of the input ripple waveform at the lower limit of the input AC voltages range, as shown in FIG. 1b. Regulator efficiency can be calculated as follows for various assumed input AC tolerances and output voltages.
Let the input voltage range be ±T% about its nominal. The trans former secondary turns will be selected so that the voltage at the bottom of the ripple waveform will be 2.5 V above the desired output voltage when the AC input is at its lower limit.
Let the peak-to-peak ripple voltage be Vr volts. When the input AC is at its low tolerance limit, the average or DC voltage at the input to the pass transistor will be
Vdc = (Vo + 2.5 + Vr /2) volts
When the AC input is at its high tolerance limit, the DC voltage at the input to the series-pass element is
FIG. 2 Linear regulator efficiency versus output voltage. Efficiency shown for maximum Vac input, assuming a 2.5-V headroom is maintained at the bottom of the ripple waveform at minimum Vac input. Eight volts peak-to-peak ripple is assumed at the top of the filter capacitor. (From Eqn. 2)
The maximum achievable worst-case efficiency (which occurs at maximum input voltage and hence maximum input power) is
This is plotted in FIG. 2 for an assumed peak-to-peak (p/p) ripple voltage of 8 V. It will be shown that in a 60-Hz full-wave rectifier, the p/p ripple voltage is8Vifthe filter capacitor is chosen to be of the order of 1000 microfarads (µF) per ampere of DC load current, an industry standard value.
It can be seen in FIG. 2 that even for 10-V outputs, the efficiency is less than 50% for a typical AC line range of ±10%. In general it is the poor efficiency, the weight, the size, and the cost of the 60-Hz input transformer that was the driving force behind the development of switching power supplies.
However, the linear regulator with its lower electrical noise still has applications and may not have excessive power loss. For example, if a reasonably pre-regulated input is available (frequently the case in some of the switching configurations to be shown later), a liner regulator is a reasonable choice where lower noise is required. Complete integrated-circuit linear regulators are available up to 3-Aoutput in single plastic packages and up to 5 A in metal-case integrated circuit packages. However, the dissipation across the internal series pass transistor can still become a problem at the higher currents. We now show some methods of reducing the dissipation.
2.5 Linear Regulators with PNP Series-Pass Transistors for Reduced Dissipation
Linear regulators using PNP transistors as the series-pass element can operate with a minimum headroom down to less than 0.5 V. Hence they can achieve better efficiency. Typical arrangements are shown in FIG. 3.
With an NPN series-pass element configured as shown in FIG. 3a, the base current (Ib ) must come from some point at a potential higher than Vo + Vbe, typically Vo + 1 volts. If the base drive comes through a resistor as shown, the input end of that resistor must come from a voltage even higher than Vo +1. The typical choice is to supply the base current from the raw DC input as shown.
A conflict now exists because the raw DC input at the bottom of the ripple waveform at the low end of the input range cannot be per mitted to come too close to the required minimum base input voltage (say, Vo + 1). Further, the base resistor Rb would need to have a very low value to provide sufficient base current at the maximum output current. Under these conditions, at the high end of the input range (when Vdc - Vo is much greater), Rb would deliver an excessive drive current; a significant amount would have to be diverted away into the current amplifier, adding to its dissipation. Hence a compromise is required. This is why the minimum header voltage is selected to be typically 2.5 V in this arrangement. It maintains a more constant current through Rb over the range of input voltage.
However, with a PNP series-pass transistor (as in FIG. 3b), this problem does not exist. The drive current is derived from the common negative line via the current amplifier. The minimum header voltage is defined only by the knee of the Ic versus Vce characteristic of the pass transistor. This may be less than 0.5V, providing higher efficiency particularly for low-voltage, high-current applications.
Although integrated-circuit linear regulators with PNP pass transistors are now available, they are intrinsically more expensive because the fabrication is more difficult.
FIG. 3 (a) A linear regulator with an NPN series-pass transistor.
In this example, the base drive is taken from Vdc via a resistor Rb .
A typical minimum voltage of 1.5 V is required across Rb to supply the
base current, which when added to the base-emitter drop makes a minimum
header voltage of 2.5 V. (b) Linear regulator with a PNP series-pass
transistor. In this case the base drive (Ib ) is derived from the negative
common line via the drive circuit. The header voltage is no longer restricted
to a minimum of 2.5 V, and much lower values are possible.
Similar results can be obtained with NPN transistors by fitting the transistor in the negative return line. This requires the positive line to be the common line. (Normally this would not be a problem in single output supply.)
This completes our overview of linear regulators and serves to demonstrate some of the reasons for moving to the more complicated switching methods for modern, low-weight, small, and efficient power systems.
3. Switching Regulator Topologies
3.1 The Buck Switching Regulator
The high dissipation across the series-pass transistor in a linear regulator and the large 60-Hz transformer required for line operation made linear regulators unattractive for modern electronic applications.
Further, the high power loss in the series device requires a large heat sink and large storage capacitors and makes the linear power supply disproportionately large.
As electronics advanced, integrated circuits made the electronic systems smaller. Typically, linear regulators could achieve output power densities of 0.2 to 0.3 W/in^3, and this was not good enough for the ever smaller modern electronic systems. Further, linear power sup plies could not provide the extended hold-up time required for the controlled shutdown of digital storage systems.
Although the technology was previously well known, switching regulators started being widely used as alternatives to linear regulators only in the early 1960s when suitable semiconductors with reasonable performance and cost became available. Typically these new switching supplies used a transistor switch to generate a square waveform from a non-regulated DC input voltage. This square wave, with adjustable duty cycle, was applied to a low pass output power filter so as to provide a regulated DC output.
Usually the filter would be an inductor (or more correctly a choke, since it had to support some DC) and an output capacitor. By varying the duty cycle, the average DC voltage developed across the output capacitor could be controlled. The low pass filter ensured that the DC output voltage would be the average value of the rectangular voltage pulses (of adjustable duty cycle) as applied to the input of the lowpass filter. A typical topology and waveforms are shown later in FIG. 4.
With appropriately chosen low pass inductor/capacitor (LC)filters, the square-wave modulation could be effectively minimized, and near-ripple-free DC output voltages, equal to the average value of the duty-cycle-modulated raw DC input, could be provided. By sensing the DC output voltage and controlling the switch duty cycle in a negative-feedback loop, the DC output could be regulated against input line voltage changes and output load changes.
Modern very high frequency switching supplies are currently achieving up to 20W/in^3 compared with 0.3W/in^3 for the older linear power supplies. Further, they are capable of generating a multiplicity of isolated output voltages from a single input. They do not require a 50/60-Hz isolation power transformer, and they have efficiencies from 70% up to 95%. Some DC/DC converter designers are claiming load power densities of up to 50 W/in3 for the actual switching elements.
3.1.1 Basic Elements and Waveforms of a Typical Buck Regulator
In the interest of simplicity, we describe fixed-frequency operation for the following switching regulator examples. In such regulators the on period of the power device (Ton) is adjusted to maintain regulation, while the total cycle period (T) is fixed, and the frequency is thus fixed at 1/T.
FIG. 4 Buck switching regulator and typical waveforms.
The ratio Ton/T is normally referred to as the duty ratio or duty cycle (D) in many modern treatises. In other guides on the subject, you may find this shown as Ton/(Ton+ Toff), where Toff is the off period of the power device so that Ton +Toff =T. Operators D and M are also used in various combinations but essentially refer to the same quantity.
Bear in mind that other modes of operation can be and are used. For example, the on period can be fixed and the frequency changed, or a combination of both may be employed.
The terms dI, di, dV, dv, dT and dt are used somewhat loosely in this guide and normally refer to the changes _I, _V, and _t, where, for example, in the limit,_I/_t goes to the derivative di/dt, giving the rate of change of current with time or the slope of the waveform. Since in most cases the waveform slopes are linear the result is the same so this becomes a moot point.
3.1.2 Buck Regulator Basic Operation
The basic elements of the buck regulator are shown in FIG. 4.
Transistor Q1 is switched hard "on" and hard "off" in series with the DC input Vdc to produce a rectangular voltage at point V1. For fixed frequency duty-cycle control, Q1 conducts for a time Ton (a small part of the total switching period T).When Q1 is "on," the voltage at V1is Vdc, assuming for the moment the "on" voltage drop across Q1 is zero.
A current builds up in the series inductor Lo flowing toward the output. When Q1 turns "off," the voltage at V1 is driven rapidly toward ground by the current flowing in inductor Lo and will go negative until it is caught and clamped at about -0.8 V by diode D1 (the so-called free-wheeling diode).
Assume for the moment that the "on" drop of diode D1 is zero. The square voltage shown in FIG. 4b would be rectangular, ranging between Vdc and ground, (0V)with a "high" period of Ton. The average value of this rectangular waveform is VdcTon/T. The low pass LoCo filter in series betweenV1 and the output tV extracts the DC component and yields a clean, near-ripple-free DC voltage at the output with a magnitude Vo of VdcTon/T.
To control the voltage, Vo is sensed by sampling resistors R1 and R2 and compared with a reference voltage Vref in the error amplifier (EA).
The amplified DC error voltage Vea is fed to a pulse-width-modulator (PWM). In this example the PWM is essentially a voltage comparator with a sawtooth waveform as the other input (see FIG. 4a).
This sawtooth waveform has a period T and amplitude typically in the order of 3 V. The high-gain PWM voltage comparator generates a rectangular output waveform (Vwm, see FIG. 4c) that goes high at the start of the sawtooth ramp, and goes low the instant the ramp volt age crosses the DC voltage level from the error-amplifier output. The PWM output pulse width (Ton) is thus controlled by the EA amplifier output voltage.
The PWM output pulse is fed to a driver circuit and used to control the "on" time of transistor switch Q1 inside the negative-feedback loop. The phasing is such that if Vdc goes slightly higher, the EA DC level goes closer to the bottom of the ramp, the ramp crosses the EA output level earlier, and the Q1 "on" time decreases, maintaining the output voltage constant. Similarly, if Vdc is reduced, the "on" time of Q1 increases to maintain Vo constant. In general, for all changes, the "on" time of Q1 is controlled so as to make the sampled DC output voltage Vo R2/(R1 + R2) closely track the reference voltage Vref.
3.2 Typical Waveforms in the Buck Regulator
In general, the major advantage of the switching regulator technique over its linear counterpart is the elimination of the power loss intrinsic in the linear regulator pass element.
In the switching regulator the pass element is either fully "on" (with very little power loss) or fully "off" (with negligible power loss). The buck regulator is a good example of this-it has low internal losses and hence high power conversion efficiency.
However, to fully appreciate the subtleties of its operation, it is necessary to understand the waveforms and the magnitude and timing of the currents and voltages throughout the circuit. To this end we will look in more detail at a full cycle of events starting when Q1 turns fully "on." For convenience we will assume ideal components and steady-state conditions, with the amplitude of the input voltage Vdc constant, exceeding the output voltage Vo , which is also constant.
When Q1 turns fully "on," the supply voltage Vdc will appear across the diode D1 at point V1. Since the output voltage Vo is less than Vdc, the inductor Lo will have a voltage impressed across it of (Vdc - Vo ).
With a constant voltage across the inductor, its current rises linearly at a rate given by di/dt = (Vdc -Vo )/Lo . (This is shown in FIG. 4d as a ramp that sits on top of the step current waveform.) When Q1 turns "off," the voltage at point V1 is driven toward zero because it is not possible to change the previously established inductor current instantaneously. Hence the voltage polarity across Lo immediately reverses, trying to maintain the previous current.
(This polarity reversal is often referred to as the flyback or inductive kickback effect of the inductor.) Without diode D1, V1 would have gone very far negative, but with D1 fitted as shown, as the V1 volt age passes through zero, D1 conducts and clamps the left side of Lo at one diode drop below ground. The voltage across the inductor has now reversed, and the current in the inductor and D1 will ramp down, returning to its original starting value, during the "off" period of Q1.
More precisely, when Q1 turns "off," the current I2 (which had been flowing in Q1, Lo and the output capacitor Co and the load just prior to turning "off") is diverted and now flows through diode D1, Lo and the output capacitor and load, as shown in FIG. 4e. The voltage polarity across Lo has reversed with a magnitude of (Vo + 1).
The current in Lo now ramps down linearly at a rate defined by the equation di/dt =(Vo +1)/Lo . This is the downward ramp that sits on a step in FIG. 4e.Under steady-state conditions, at the end of the Q1 "off" time, the current in Lo will have fallen to I1 and is still flowing through D1, Lo and the output capacitor and load.
Note:
Notice the input current is discontinuous with a pulse-like characteristic, whereas the output current remains nearly continuous with some relatively small ripple component depending on the value of Lo and Co.
Now when Q1 turns "on" again, it initially supplies current into the cathode of D1, displacing its previous forward current. While the current in Q1 rises toward the previous value of I1, the forward D1 current will be displaced, and V1 rises to near Vdc, back-biasing D1.
Because Q1 is switched "on" hard, this recovery process is very rapid, typically less than 1 µs.
Notice that the current in Lo is the sum of the Q1 current when it is "on" (see FIG. 4d) plus the D1 current when Q1 is "off." This is shown in FIG. 4 f as IL,o . It has a DC component and a triangular waveform ripple component (I2 - I1) centered on the mean DC out put current Io . Thus the value of the current at the center of the ramp in Figure 1.4d and 1.4e is simply the DC mean output current Io . As the load resistance and hence load current is changed, the center of the ramp (the mean value) in either FIG. 4d or 1.4e moves, but the slopes of the ramps remain constant, because during the Q1 "on" time, the ramp rate in Lo remains the same at (Vdc -Vo )/Lo , and during the Q1 "off" time, it remains the same at (Vo + 1)/L as the load current changes, because the input and output voltages remain constant.
Because the p-p ripple current remains constant regardless of the mean output current, it will be seen shortly that when the DC current Io is reduced to the point where the lower value of the ripple current in Figure 4d and 4e just reaches zero (the critical load current), there will be a drastic change in performance. (This will be discussed in more detail later.)
3.3 Buck Regulator Efficiency
To get a general feel for the intrinsic power loss in the buck regulator compared with a linear regulator, we will start by assuming ideal components for transistor Q1 and diode D1 in both topologies. Using the currents shown in FIG. 4d and 1.4e, the typical conduction losses in Q1 and free-wheeling diode D1 can be calculated and the efficiency obtained. Notice that when Q1 is "off," it operates at a maximum volt age of Vdc but at zero current. When Q1 is "on," current flows, but the voltage across Q1 is zero. At the same time, D1 is reverse-biased at a voltage of Vdc but has zero current. (Clearly, if Q1 and D1 were ideal components, the currents would flow through Q1 and D1 with zero voltage drop, and the loss would be zero.) Hence unlike the linear regulator, which has an intrinsic loss even with ideal components, the intrinsic loss in a switching regulator with ideal components is zero, and the efficiency is 100%. Thus in the buck regulator, the real efficiency depends on the actual performance of the components. Since improvements are continually being made in semiconductors, we will see ever higher efficiencies.
To consider more realistic components, the losses in the buck circuit are the conduction losses in Q1 and D1 and the resistive winding loss in the choke. The conduction losses, being related to the mean DC currents, are relatively easy to calculate. To this we must add the AC switching losses in Q1 and D1, and the AC induced core loss in the inductor, so the switching loss is more difficult to establish.
The switching loss in Q1 during the turn "on" and turn "off" transitions is a result of the momentary overlap of current and voltage during the switching transitions. Diode D1 also has switching loss associated with the reverse recovery action of the diode, where again there is a condition of voltage and current stress during the transitions.
The ripple wave for min the inductor Lo results in hysteretic and eddy current loss in the core material. We will now calculate some typical losses.
3.3.1 Calculating Conduction Loss and Conduction-Related Efficiency
By neglecting second-order effects and AC switching losses, the conduction loss can be quite easily calculated. It can be seen from FIG. 4d and 4e that the average currents in Q1 and D1 during their conduction times of Ton and Toff are the values at the center of the ramps or Io , the mean DC output current. These currents flow at a forward voltage of about 1 V over a wide range of currents. Thus conduction losses will be approximately
Therefore, by neglecting AC switching losses, the conduction-related efficiency would be
3.4 Buck Regulator Efficiency Including AC Switching Losses
The switching loss is much more difficult to establish, because it depends on many variables relating to the performance of the semiconductors and to the methods of driving the switching devices. Other variables, related to the actual power circuit designs, include the action of any snubbers, load line shaping, and energy recovery arrangements. It depends on what the designer may choose to use in a particular design. Unless all these things are considered, any calculations are at best only a very rough approximation and can be far from the real values found in the actual design, particularly at high frequencies with the very fast switching devices now available.
Many semiconductor manufacturers now provide switching loss equations for their switching devices when recommended drive conditions are used, particularly the modern fast IGBTs (Insulated Gate Bipolar Transistors). Some fast digital oscilloscopes claim that they will actually measure switching loss, providing the real-time device current and voltage is accurately provided to the oscilloscope. (Doing this can also be problematical at very high frequency.) The method I prefer, which is unquestionably accurate, is to measure the temperature rise of the device in question in a working model. The model must include all the intended snubbers and load line shaping circuits, etc.
Replacing the AC current in the device with a DC current to obtain the same temperature rise will provide a direct indication of power loss by simple DC power measurements. This method also allows easy optimization of the drive and load line shaping, which can be dynamically adjusted during operation for minimum temperature rise and hence minimum switching loss.
Alternating-current switching loss (or voltage/current overlap loss) calculation depends on the shape and timing of the rising and falling voltage and current waveforms. An idealized linear example-which is unlikely to exist in practice-is shown in FIG. 5a and serves to illustrate the principle.
FIG. 5a shows the best-case scenario. At the turn "on" of the switching device, the voltage and current start changing simultaneously and reach their final values simultaneously. The current waveform goes from 0 to Io , and voltage across Q1 goes from a maximum of Vdc down to zero. The average power during this switching transition is
P(Ton) = _ Ton
0 IV dt = IoVdc/6, and the power averaged over one complete period is (IoVdc/6)(Ton/T).
Assuming the same scenario of simultaneous starting and ending points for the current fall and voltage rise wave forms at the turn "off" transition, the voltage/current overlap dissipation at this transition is given by
P(Toff) = _ Toff
0 IV dt = IoVdc/6 and this power averaged over one complete cycle is (IoVdc/6)(Toff/T).
FIG. 5 Idealized transistor switching waveforms. (a) Waveforms show
the voltage and current transitions starting and ending simultaneously.
(b) Waveforms show the worst-case scenario, where at turn "on" voltage
remains constant at Vdc(max) until current reaches its maximum. At turn "off," the
current remains constant at Io until Q1 voltage reaches its maximum of
Vdc.
Assuming Ton = Toff = Ts , the total switching losses (the sum of turn "off" and turn "on" losses) are Pac = (Vdc Io Ts )/3T, and efficiency is calculated as shown next in Eqn. 4.
It would make an interesting comparison to calculate the efficiency of the buck regulator and compare it with that of a linear regulator.
Assume the buck regulator provides 5 V from a 48-V DC input at 50-kHz switching frequency (T =20 µs).
If there were no AC switching losses and a switching transition period Ts of 0.3 µs were assumed, Eqn. 3 would give a conduction loss efficiency of
If switching losses for the best-case scenario as shown in FIG. 5a were assumed, for Ts = 0.3 µs and T = 20 µs, Eqn. 4 would give a switching-related efficiency of
If a worst-case scenario were assumed (which is closer to reality), as shown in FIG. 5b, efficiencies would lower. In FIG. 5b it is assumed that at turn "on" the voltage across the transistor remains at its maximum value (Vdc) until the on-turning current reaches its maximum value of Io . Then the voltage starts falling. To a close approximation, the current rise time Tcr will equal voltage fall time. Then the turn "on" switching losses will be
also for Tcr = Tvf = Ts , P(Ton) = Vdc Io (Ts/T).
At turn "off" (as seen in FIG. 5b), we may assume that current hangs on at this maximum value Io until the voltage has risen to its maximum value of Vdc in a time Tvr. Then current starts falling and reaches zero in a time Tcf. The total turn "off" dissipation will be
With Tvr = Tcf = Ts , P(Toff) = Vdc Io (Ts/T). The total AC losses (the sum of the turn "on" plus the turn "off" losses) will be:
...and the total losses (the sum of DC plus AC losses) will be ...
...and the efficiency will be ...
Hence in the worst-case scenario, for the same buck regulator with Ts = 0.3 µs, the efficiency from Eqn. 7 will be ...
Comparing this with a linear regulator doing the same job (bringing 48 V down to 5 V), its efficiency (from Eqn. 1) would be Vo /Vdc(max) , or 5/48; this is only 10.4% and is clearly unacceptable.
3.5 Selecting the Optimum Switching Frequency
We have seen that the output voltage of the buck regulator is given by the equation Vo = VdcTon/T. We must now decide on a value for this period and hence the operating frequency.
The initial reaction may be to minimize the size of the filter components Lo , Co by using as high a frequency as possible. However, using higher frequencies does not necessarily minimize the overall size of the regulator when all factors are considered.
We can see this better by examining the expression for the AC losses shown in Eqn. 5, Pac = 2Vdc Io Ts T . We see that the AC losses are inversely proportional to the switching period T. Further, this equation only shows the losses in the switching transistor; it neglects losses in the free-wheeling diode D1 due to its finite reverse recovery time (the time required for the diode to cease conducting reverse current, measured from the instant it has been subjected to a reverse bias volt age). The free-wheeling diode can dissipate significant power and should be of the ultrafast soft recovery type with minimum recovered charge. The reverse recovery time will typically be 35 ns or less.
In simple terms, the more switching transitions there are in a particular period, the more switching loss there will be. As a result there is a trade-off-decreasing the switching period T (increasing the switching frequency) may well decrease the size of the filter elements, but it will also add to the total losses and may require a larger heat sink.
In general, although the overall volume of the buck regulator will be lower at a higher frequency, the increase in the switching loss and the more stringent high-frequency layout and component-selection requirements make the final choice a compromise among all the op posing elements.
Note:
The picture is constantly changing as better, lower cost, and faster transistors and diodes are developed. My choice at the present stage of the technology is to design below100 kHz, as this is less demanding on component selection, layout, and transformer/inductor designs. As a result it is probably lower cost. Generally speaking, higher frequencies absorb more development time and require more experience. However, efficient commercial designs are on the market operating well into the MHz range. The final choice is up to the designer, and I hesitate to recommend a limit because technology is constantly changing toward higher frequency operation.
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