SWITCHING REGULATORS
`
`SECTION 3
`SWITCHING REGULATORS
`Walt Kester, Brian Erisman
`
`INTRODUCTION
`
`Virtually all of today's electronic systems require some form of power conversion.
`The trend toward lower power, portable equipment has driven the technology and
`the requirement for converting power efficiently. Switchmode power converters,
`often referred to simply as "switchers", offer a versatile way of achieving this goal.
`Modern IC switching regulators are small, flexible, and allow either step-up (boost)
`or step-down (buck) operation.
`
`When switcher functions are integrated and include a switch which is part of the
`basic power converter topology, these ICs are called “switching regulators”. When no
`switches are included in the IC, but the signal for driving an external switch is
`provided, it is called a “switching regulator controller”. Sometimes - usually for
`higher power levels - the control is not entirely integrated, but other functions to
`enhance the flexibility of the IC are included instead. In this case the device might
`be called a “controller” of sorts - perhaps a “feedback controller” if it just generates
`the feedback signal to the switch modulator. It is important to know what you are
`getting in your controller, and to know if your switching regulator is really a
`regulator or is it just the controller function.
`
`Also, like switchmode power conversion, linear power conversion and charge pump
`technology offer both regulators and controllers. So within the field of power
`conversion, the terms “regulator” and “controller” can have wide meaning.
`
`The most basic switcher topologies require only one transistor which is essentially
`used as a switch, one diode, one inductor, a capacitor across the output, and for
`practical but not fundamental reasons, another one across the input. A practical
`converter, however, requires several additional elements, such as a voltage
`reference, error amplifier, comparator, oscillator, and switch driver, and may also
`include optional features like current limiting and shutdown capability. Depending
`on the power level, modern IC switching regulators may integrate the entire
`converter except for the main magnetic element(s) (usually a single inductor) and
`the input/output capacitors. Often, a diode, the one which is an essential element of
`basic switcher topologies, cannot be integrated either. In any case, the complete
`power conversion for a switcher cannot be as integrated as a linear regulator, for
`example. The requirement of a magnetic element means that system designers are
`not inclined to think of switching regulators as simply “drop in” solutions. This
`presents the challenge to switching regulator manufacturers to provide careful
`design guidelines, commonly-used application circuits, and plenty of design
`assistance and product support. As the power levels increase, ICs tend to grow in
`complexity because it becomes more critical to optimize the control flexibility and
`precision. Also, since the switches begin to dominate the size of the die, it becomes
`more cost effective to remove them and integrate only the controller.
`
`3.1
`
`Chrimar Systems, Inc.
`Exhibit 2056-1
`IPR2016-00574 USPN 8,902,760
`
`

`
`SWITCHING REGULATORS
`
`The primary limitations of switching regulators as compared to linear regulators are
`their output noise, EMI/RFI emissions, and the proper selection of external support
`components. Although switching regulators do not necessarily require transformers,
`they do use inductors, and magnetic theory is not generally well understood.
`However, manufacturers of switching regulators generally offer applications support
`in this area by offering complete data sheets with recommended parts lists for the
`external inductor as well as capacitors and switching elements.
`
`One unique advantage of switching regulators lies in their ability to convert a given
`supply voltage with a known voltage range to virtually any given desired output
`voltage, with no “first order” limitations on efficiency. This is true regardless of
`whether the output voltage is higher or lower than the input voltage - the same or
`the opposite polarity. Consider the basic components of a switcher, as stated above.
`The inductor and capacitor are, ideally, reactive elements which dissipate no power.
`The transistor is effectively, ideally, a switch in that it is either “on”, thus having no
`voltage dropped across it while current flows through it, or “off”, thus having no
`current flowing through it while there is voltage across it. Since either voltage or
`current are always zero, the power dissipation is zero, thus, ideally, the switch
`dissipates no power. Finally, there is the diode, which has a finite voltage drop while
`current flows through it, and thus dissipates some power. But even that can be
`substituted with a synchronized switch, called a “synchronous rectifier”, so that it
`ideally dissipates no power either.
`
`Switchers also offer the advantage that, since they inherently require a magnetic
`element, it is often a simple matter to “tap” an extra winding onto that element and,
`often with just a diode and capacitor, generate a reasonably well regulated
`additional output. If more outputs are needed, more such taps can be used. Since the
`tap winding requires no electrical connection, it can be isolated from other circuitry,
`or made to “float” atop other voltages.
`
`Of course, nothing is ideal, and everything has a price. Inductors have resistance,
`and their magnetic cores are not ideal either, so they dissipate power. Capacitors
`have resistance, and as current flows in and out of them, they dissipate power, too.
`Transistors, bipolar or field-effect, are not ideal switches, and have a voltage drop
`when they are turned on, plus they cannot be switched instantly, and thus dissipate
`power while they are turning on or off.
`
`As we shall soon see, switchers create ripple currents in their input and output
`capacitors. Those ripple currents create voltage ripple and noise on the converter’s
`input and output due to the resistance, inductance, and finite capacitance of the
`capacitors used. That is the conducted part of the noise. Then there are often ringing
`voltages in the converter, parasitic inductances in components and PCB traces, and
`an inductor which creates a magnetic field which it cannot perfectly contain within
`its core - all contributors to radiated noise. Noise is an inherent by-product of a
`switcher and must be controlled by proper component selection, PCB layout, and, if
`that is not sufficient, additional input or output filtering or shielding.
`
`3.2
`
`Chrimar Systems, Inc.
`Exhibit 2056-2
`IPR2016-00574 USPN 8,902,760
`
`

`
`SWITCHING REGULATORS
`
`INTEGRATED CIRCUIT SWITCHING REGULATORS
`
`n Advantages:
`u High Efficiency
`u Small
`u Flexible - Step-Up (Boost), Step-Down (Buck), etc.
`
`n Disadvantages
`u Noisy (EMI, RFI, Peak-to-Peak Ripple)
`u Require External Components (L’s, C’s)
`u Designs Can Be Tricky
`u Higher Total Cost Than Linear Regulators
`
`n "Regulators" vs. "Controllers"
`
`Figure 3.1
`
`Though switchers can be designed to accommodate a range of input/output
`conditions, it is generally more costly in non-isolated systems to accommodate a
`requirement for both voltage step-up and step-down. So generally it is preferable to
`limit the input/output ranges such that one or the other case can exist, but not both,
`and then a simpler converter design can be chosen.
`
`The concerns of minimizing power dissipation and noise as well as the design
`complexity and power converter versatility set forth the limitations and challenges
`for designing switchers, whether with regulators or controllers.
`
`The ideal switching regulator shown in Figure 3.2 performs a voltage conversion and
`input/output energy transfer without loss of power by the use of purely reactive
`components. Although an actual switching regulator does have internal losses,
`efficiencies can be quite high, generally greater than 80 to 90%. Conservation of
`energy applies, so the input power equals the output power. This says that in step-
`down (buck) designs, the input current is lower than the output current. On the
`other hand, in step-up (boost) designs, the input current is greater than the output
`current. Input currents can therefore be quite high in boost applications, and this
`should be kept in mind, especially when generating high output voltages from
`batteries.
`
`3.3
`
`Chrimar Systems, Inc.
`Exhibit 2056-3
`IPR2016-00574 USPN 8,902,760
`
`

`
`SWITCHING REGULATORS
`
`THE IDEAL SWITCHING REGULATOR
`
`vin
`
`iin
`
`+
`
`Pin
`
`LOSSLESS
`SWITCHING
`REGULATOR
`
`iout
`
`vout
`
`Pout
`
`LOAD
`
`n Pin = Pout
`n Efficiency = Pout / Pin = 100%
`n vin • iin = vout • iout
`vout
`iin
`==
`vin
`iout
`
`Energy Must be Conserved!
`
`Figure 3.2
`
`n n
`
`Design engineers unfamiliar with IC switching regulators are sometimes confused
`by what exactly these devices can do for them. Figure 3.3 summarizes what to
`expect from a typical IC switching regulator. It should be emphasized that these are
`typical specifications, and can vary widely, but serve to illustrate some general
`characteristics.
`
`Input voltages may range from 0.8 to beyond 30V, depending on the breakdown
`voltage of the IC process. Most regulators are available in several output voltage
`options, 12V, 5V, 3.3V, and 3V are the most common, and some regulators allow the
`output voltage to be set using external resistors. Output current varies widely, but
`regulators with internal switches have inherent current handling limitations that
`controllers (with external switches) do not. Output line and load regulation is
`typically about 50mV. The output ripple voltage is highly dependent upon the
`external output capacitor, but with care, can be limited to between 20mV and
`100mV peak-to-peak. This ripple is at the switching frequency, which can range
`from 20kHz to 1MHz. There are also high frequency components in the output
`current of a switching regulator, but these can be minimized with proper external
`filtering, layout, and grounding. Efficiency can also vary widely, with up to 95%
`sometimes being achievable.
`
`3.4
`
`Chrimar Systems, Inc.
`Exhibit 2056-4
`IPR2016-00574 USPN 8,902,760
`
`

`
`WHAT TO EXPECT FROM A SWITCHING REGULATOR IC
`
`SWITCHING REGULATORS
`
`n Input Voltage Range: 0.8V to 30V
`n Output Voltage:
`u “Standard”: 12V, 5V, 3.3V, 3V
`u “Specialized”: VID Programmable for Microprocessors
`u (Some are Adjustable)
`n Output Current
`u Up to 1.5A, Using Internal Switches of a Regulator
`u No Inherent Limitations Using External Switches with a
`Controller
`n Output Line / Load Regulation: 50mV, typical
`n Output Voltage Ripple (peak-peak) :
`20mV - 100mV @ Switching Frequency
`n Switching Frequency: 20kHz - 1MHz
`n Efficiency: Up to 95%
`
`Figure 3.3
`
`POPULAR APPLICATIONS OF SWITCHING REGULATORS
`
`For equipment which is powered by an AC source, the conversion from AC to DC is
`generally accomplished with a switcher, except for low-power applications where size
`and efficiency concerns are outweighed by cost. Then the power conversion may be
`done with just an AC transformer, some diodes, a capacitor, and a linear regulator.
`The size issue quickly brings switchers back into the picture as the preferable
`conversion method as power levels rise up to 10 watts and beyond. Off-line power
`conversion is heavily dominated by switchers in most modern electronic equipment.
`
`Many modern high-power off-line power supply systems use the distributed
`approach by employing a switcher to generate an intermediate DC voltage which is
`then distributed to any number of DC/DC converters which can be located near to
`their respective loads (see Figure 3.4). Although there is the obvious redundancy of
`converting the power twice, distribution offers some advantages. Since such systems
`require isolation from the line voltage, only the first converter requires the isolation;
`all cascaded converters need not be isolated, or at least not to the degree of isolation
`that the first converter requires. The intermediate DC voltage is usually regulated
`to less than 60 volts in order to minimize the isolation requirement for the cascaded
`converters. Its regulation is not critical since it is not a direct output. Since it is
`typically higher than any of the switching regulator output voltages, the distribution
`current is substantially less than the sum of the output currents, thereby reducing
`I2R losses in the system power distribution wiring. This also allows the use of a
`smaller energy storage capacitor on the intermediate DC supply output. (Recall that
`the energy stored in a capacitor is ½CV2).
`
`3.5
`
`Chrimar Systems, Inc.
`Exhibit 2056-5
`IPR2016-00574 USPN 8,902,760
`
`

`
`SWITCHING REGULATORS
`
`Power management can be realized by selectively turning on or off the individual
`DC/DC converters as needed.
`
`POWER DISTRIBUTION USING LINEAR
`AND SWITCHING REGULATORS
`
`TRADITIONAL USING
`LINEAR REGULATORS
`
`DISTRIBUTED USING
`SWITCHING REGULATORS
`
`RECTIFIER
`AND
`FILTER
`
`V1
`
`LINEAR
`REG
`
`AC
`
`AC
`
`OFF LINE
`SW REG
`
`RECTIFIER
`AND
`FILTER
`
`LINEAR
`REG
`
`VN
`
`Figure 3.4
`
`SW REG
`
`VDC < 60V
`
`SW REG
`
`V1
`
`VN
`
`ADVANTAGES OF DISTRIBUTED POWER
`SYSTEMS USING SWITCHING REGULATORS
`
`n Higher Efficiency with Switching Regulators than
`Linear Regulators
`
`n Use of High Intermediate DC Voltage Minimizes
`Power Loss due to Wiring Resistance
`
`n Flexible (Multiple Output Voltages Easily Obtained)
`
`n AC Power Transformer Design Easier (Only One
`Winding Required, Regulation Not Critical)
`
`n Selective Shutdown Techniques Can Be Used for
`Higher Efficiency
`
`n Eliminates Safety Isolation Requirements for DC/DC
`Converters
`
`Figure 3.5
`
`Batteries are the primary power source in much of today's consumer and
`communications equipment. Such systems may require one or several voltages, and
`they may be less or greater than the battery voltage. Since a battery is a self-
`contained power source, power converters seldom require isolation. Often, then, the
`basic switcher topologies are used, and a wide variety of switching regulators are
`
`3.6
`
`Chrimar Systems, Inc.
`Exhibit 2056-6
`IPR2016-00574 USPN 8,902,760
`
`

`
`SWITCHING REGULATORS
`
`available to fill many of the applications. Maximum power levels for these regulators
`typically can range up from as low as tens of milliwatts to several watts.
`
`Efficiency is often of great importance, as it is a factor in determining battery life
`which, in turn, affects practicality and cost of ownership. Often of even greater
`importance, though often confused with efficiency, is quiescent power dissipation
`when operating at a small fraction of the maximum rated load (e.g., standby mode).
`For electronic equipment which must remain under power in order to retain data
`storage or minimal monitoring functions, but is otherwise shut down most of the
`time, the quiescent dissipation is the largest determinant of battery life. Although
`efficiency may indicate power consumption for a specific light load condition, it is not
`the most useful way to address the concern. For example, if there is no load on the
`converter output, the efficiency will be zero no matter how optimal the converter,
`and one could not distinguish a well power-managed converter from a poorly
`managed one by such a specification.
`
`The concern of managing power effectively from no load to full load has driven much
`of the technology which has been and still is emerging from today’s switching
`regulators and controllers. Effective power management, as well as reliable power
`conversion, is often a substantial factor of quality or noteworthy distinction in a
`wide variety of equipment. The limitations and cost of batteries are such that
`consumers place a value on not having to replace them more often than necessary,
`and that is certainly a goal for effective power conversion solutions.
`
`TYPICAL APPLICATION OF A BOOST
`REGULATOR IN BATTERY OPERATED EQUIPMENT
`
`STEP-UP
`(BOOST)
`SWITCHING
`REGULATOR
`
`VOUT > VBATTERY
`
`+
`
`VBATTERY
`
`LOAD
`
`Figure 3.6
`
`3.7
`
`Chrimar Systems, Inc.
`Exhibit 2056-7
`IPR2016-00574 USPN 8,902,760
`
`

`
`SWITCHING REGULATORS
`
`INDUCTOR AND CAPACITOR FUNDAMENTALS
`
`In order to understand switching regulators, the fundamental energy storage
`capabilities of inductors and capacitors must be fully understood. When a voltage is
`applied to an ideal inductor (see Figure 3.7), the current builds up linearly over time
`at a rate equal to V/L, where V is the applied voltage, and L is the value of the
`inductance. This energy is stored in the inductor's magnetic field, and if the switch is
`opened, the magnetic field collapses, and the inductor voltage goes to a large
`instantaneous value until the field has fully collapsed.
`
`INDUCTOR AND CAPACITOR FUNDAMENTALS
`
`C
`
`+v-
`
`I
`
`i
`
`+
`
`V
`
`L
`
`I C
`
`dv
`dt
`
`==
`
`I C
`==
`
`dv
`dt
`
`V L
`
`di
`dt
`
`==
`
`V L
`==
`
`di
`dt
`
`i
`
`v
`
`0
`
`t
`Current Does Not
`Change Instantaneously
`
`0
`
`t
`Voltage Does Not
`Change Instantaneously
`
`Figure 3.7
`
`When a current is applied to an ideal capacitor, the capacitor is gradually charged,
`and the voltage builds up linearly over time at a rate equal to I/C, where I is the
`applied current, and C is the value of the capacitance. Note that the voltage across
`an ideal capacitor cannot change instantaneously.
`
`Of course, there is no such thing as an ideal inductor or capacitor. Real inductors
`have stray winding capacitance, series resistance, and can saturate for large
`currents. Real capacitors have series resistance and inductance and may break down
`under large voltages. Nevertheless, the fundamentals of the ideal inductor and
`capacitor are critical in understanding the operation of switching regulators.
`
`An inductor can be used to transfer energy between two voltage sources as shown in
`Figure 3.8. While energy transfer could occur between two voltage sources with a
`resistor connected between them, the energy transfer would be inefficient due to the
`power loss in the resistor, and the energy could only be transferred from the higher
`to the lower value source. In contrast, an inductor ideally returns all the energy that
`
`3.8
`
`Chrimar Systems, Inc.
`Exhibit 2056-8
`IPR2016-00574 USPN 8,902,760
`
`

`
`SWITCHING REGULATORS
`
`is stored in it, and with the use of properly configured switches, the energy can flow
`from any one source to another, regardless of their respective values and polarities.
`
`ENERGY TRANSFER USING AN INDUCTOR
`
`t
`
`t
`
`t
`
`iL
`
`L
`
`+
`
`i2
`
`V2
`
`(SLOPE)
`
`V L
`
`2
`
`--
`
`t2
`
`L I PEAK
`••
`
`2
`
`1 2
`
`E
`
`==
`
`IPEAK
`
`IPEAK
`
`t1
`
`IPEAK
`
`+
`
`V L
`
`1
`
`i1
`
`V1
`
`iL
`
`i1
`
`i2
`
`0
`
`0
`
`0
`
`Figure 3.8
`
`When the switches are initially placed in the position shown, the voltage V1 is
`applied to the inductor, and the inductor current builds up at a rate equal to V1/L.
`The peak value of the inductor current at the end of the interval t1 is
`
`
`
`t1.
`
`V L
`
`•1
`
`IPEAK
`
`=
`
`The average power transferred to the inductor during the interval t1 is
`
`
`•
`
`IPEAK V1 .
`
`1 2
`
`PAVG
`
`=
`
`The energy transferred during the interval t1 is
`
`
`•
`•
`
`IPEAK V t1 1 .
`
`
`
`1 2
`
`
`=
`•
`
`E PAVG t1
`
`=
`
`3.9
`
`Solving the first equation for t1 and substituting into the last equation yields
`
`L IPEAK
`•
`
`2 .
`
`1 2
`
`E
`
`=
`
`Chrimar Systems, Inc.
`Exhibit 2056-9
`IPR2016-00574 USPN 8,902,760
`
`

`
`SWITCHING REGULATORS
`
`When the switch positions are reversed, the inductor current continues to flow into
`the load voltage V2, and the inductor current decreases at a rate –V2/L. At the end
`of the interval t2, the inductor current has decreased to zero, and the energy has
`been transferred into the load. The figure shows the current waveforms for the
`inductor, the input current i1, and the output current i2. The ideal inductor
`dissipates no power, so there is no power loss in this transfer, assuming ideal circuit
`elements. This fundamental method of energy transfer forms the basis for all
`switching regulators.
`
`IDEAL STEP-DOWN (BUCK) CONVERTER
`
`The fundamental circuit for an ideal step-down (buck) converter is shown in Figure
`3.9. The actual integrated circuit switching regulator contains the switch control
`circuit and may or may not include the switch (depending upon the output current
`requirement). The inductor, diode, and load bypass capacitor are external.
`
`BASIC STEP-DOWN (BUCK) CONVERTER
`
`SW
`
`+
`
`ERROR AMPLIFIER
`AND SWITCH
`CONTROL CIRCUIT
`
`SENSE
`
`L
`
`D
`
`C
`
`LOAD
`
`SW ON
`
`SW OFF
`
`f
`
`==
`
`1
`ton toff
`++
`
`ton
`
`toff
`
`Figure 3.9
`
`The output voltage is sensed and then regulated by the switch control circuit. There
`are several methods for controlling the switch, but for now assume that the switch is
`controlled by a pulse width modulator (PWM) operating at a fixed frequency, f.
`
`The actual waveforms associated with the buck converter are shown in Figure 3.10.
`When the switch is on, the voltage VIN–VOUT appears across the inductor, and the
`inductor current increases with a slope equal to (VIN–VOUT)/L (see Figure 3.10B).
`When the switch turns off, current continues to flow through the inductor and into
`the load (remember that the current cannot change instantaneously in an inductor),
`with the ideal diode providing the return current path. The voltage across the
`inductor is now VOUT, but the polarity has reversed. Therefore, the inductor
`
`3.10
`
`Chrimar Systems, Inc.
`Exhibit 2056-10
`IPR2016-00574 USPN 8,902,760
`
`

`
`SWITCHING REGULATORS
`
`current decreases with a slope equal to – VOUT/L. Note that the inductor current is
`equal to the output current in a buck converter.
`
`The diode and switch currents are shown in Figures 3.10C and 3.10D, respectively,
`and the inductor current is the sum of these waveforms. Also note by inspection that
`the instantaneous input current equals the switch current. Note, however, that the
`average input current is less than the average output current. In a practical
`regulator, both the switch and the diode have voltage drops across them during their
`conduction which creates internal power dissipation and a loss of efficiency, but
`these voltages will be neglected for now. It is also assumed that the output
`capacitor, C, is large enough so that the output voltage does not change significantly
`during the switch on or off times.
`
`BASIC STEP-DOWN (BUCK) CONVERTER WAVEFORMS
`VIN
`
`VIN
`
`+
`
`iIN = iSW
`IIN
`
`vD
`
`iL = iOUT
`IOUT
`
`SW
`
`iD
`
`L
`
`C
`
`D
`
`ton
`
`toff
`
`ton
`
`IOUT
`
`
`VIN VOUT-- -- VOUT
`L
`L
`
`(SLOPES)
`
`IOUT
`
`vD
`
`VOUT
`
`0
`
`LOAD
`
`iL = iOUT
`
`0
`
`0
`
`iD
`
`A
`
`B
`
`C
`
`D
`
`Lower Case = Instantaneous Value
`Upper Case = Average Value
`
`iIN = iSW
`0
`
`Figure 3.10
`
`IOUT
`
`IIN
`
`There are several important things to note about these waveforms. The most
`important is that ideal components have been assumed, i.e., the input voltage source
`has zero impedance, the switch has zero on-resistance and zero turn-on and turn-off
`times. It is also assumed that the inductor does not saturate and that the diode is
`ideal with no forward drop.
`
`Also note that the output current is continuous, while the input current is pulsating.
`Obviously, this has implications regarding input and output filtering. If one is
`concerned about the voltage ripple created on the power source which supplies a
`buck converter, the input filter capacitor (not shown) is generally more critical that
`the output capacitor with respect to ESR/ESL.
`
`3.11
`
`Chrimar Systems, Inc.
`Exhibit 2056-11
`IPR2016-00574 USPN 8,902,760
`
`

`
`SWITCHING REGULATORS
`
`If a steady-state condition exists (see Figure 3.11), the basic relationship between
`the input and output voltage may be derived by inspecting the inductor current
`waveform and writing:
`
`Solving for VOUT:
`
`VIN VOUT
`L
`
`•
`
`ton
`
`=
`
`VOUT
`L
`
`•
`
`toff
`
`.
`
`VOUT VIN
`=
`
`•
`
`ton
`ton toff
`+
`
`=
`
`VIN D
`•
`
`,
`
`where D is the switch duty ratio (more commonly called duty cycle), defined as the
`ratio of the switch on-time (ton) to the total switch cycle time (ton + toff).
`
`This is the classic equation relating input and output voltage in a buck converter
`which is operating with continuous inductor current, defined by the fact that the
`inductor current never goes to zero.
`
`INPUT/OUTPUT RELATIONSHIP
`FOR BUCK CONVERTER
`
`ton
`
`toff
`
`ton
`
`iL = iOUT
`
`-- -- VOUT
`VIN VOUT
`L
`L
`
`0
`
`IOUT
`
`n Write by Inspection from Inductor/Output Current Waveforms:
`
`VIN VOUT
`--
`L
`
`••
`
`ton
`
`==
`
`VOUT
`L
`
`••
`
`toff
`
`Rearrange and Solve for VOUT:
`
`VOUT VIN
`==
`
`••
`
`ton
`ton toff
`++
`
`==
`
`VIN D
`••
`
`n n
`
`n
`
`Figure 3.11
`
`Notice that this relationship is independent of the inductor value L as well as the
`switching frequency 1/(ton + toff) and the load current. Decreasing the inductor
`value, however, will result in a larger peak-to-peak output ripple current, while
`increasing the value results in smaller ripple. There are many other tradeoffs
`involved in selecting the inductor, and these will be discussed in a later section.
`
`3.12
`
`Chrimar Systems, Inc.
`Exhibit 2056-12
`IPR2016-00574 USPN 8,902,760
`
`-
`

`
`SWITCHING REGULATORS
`
`In this simple model, line and load regulation (of the output voltage) is achieved by
`varying the duty cycle using a pulse width modulator (PWM) operating at a fixed
`frequency, f. The PWM is in turn controlled by an error amplifier - an amplifier
`which amplifies the "error" between the measured output voltage and a reference
`voltage. As the input voltage increases, the duty cycle decreases; and as the input
`voltage decreases, the duty cycle increases. Note that while the average inductor
`current changes proportionally to the output current, the duty cycle does not change.
`Only dynamic changes in the duty cycle are required to modulate the inductor
`current to the desired level; then the duty cycle returns to its steady state value. In
`a practical converter, the duty cycle might increase slightly with load current to
`counter the increase in voltage drops in the circuit, but would otherwise follow the
`ideal model.
`
`This discussion so far has assumed the regulator is in the continuous-mode of
`operation, defined by the fact that the inductor current never goes to zero. If,
`however, the output load current is decreased, there comes a point where the
`inductor current will go to zero between cycles, and the inductor current is said to be
`discontinuous. It is necessary to understand this operating mode as well, since many
`switchers must supply a wide dynamic range of output current, where this
`phenomenon is unavoidable. Waveforms for discontinuous operation are shown in
`Figure 3.12.
`
`BUCK CONVERTER WAVEFORMS
`DISCONTINUOUS MODE
`
`iIN = iSW
`IIN
`
`vD
`
`iL = iOUT
`IOUT
`
`VOUT
`
`vD
`
`VIN
`VOUT
`0
`
`iL = iOUT
`
`ton
`
`toff
`
`ton
`
`IOUT
`
`VIN
`
`+
`
`SW
`
`iD
`
`L
`
`C
`
`D
`
`LOAD
`
`iD
`
`0
`
`0
`
`A
`
`B
`
`C
`
`D
`
`Lower Case = Instantaneous Value
`Upper Case = Average Value
`
`iIN = iSW
`0
`
`IIN
`
`Figure 3.12
`
`Behavior during the switch on-time is identical to that of the continuous mode of
`operation. However, during the switch off-time, there are two regions of unique
`behavior. First, the inductor current ramps down at the same rate as it does during
`continuous mode, but then the inductor current goes to zero. When it reaches zero,
`the current tries to reverse but cannot find a path through the diode any longer. So
`the voltage on the input side of the inductor (same as the diode and switch junction)
`
`3.13
`
`Chrimar Systems, Inc.
`Exhibit 2056-13
`IPR2016-00574 USPN 8,902,760
`
`

`
`SWITCHING REGULATORS
`
`jumps up to VOUT such that the inductor has no voltage across it, and the current
`can remain at zero.
`
`Because the impedance at diode node (vD) is high, ringing occurs due to the inductor,
`L, resonating with the stray capacitance which is the sum of the diode capacitance,
`CD, and the switch capacitance, CSW. The oscillation is damped by stray resistances
`in the circuit, and occurs at a frequency given by
`
`fo
`
`=
`
`2 p
`
`1
`
`+
`
`L CD CSW(
`
`)
`
`.
`
`A circuit devoted simply to dampening resonances via power dissipation is called a
`snubber. If the ringing generates EMI/RFI problems, it may be damped with a
`suitable RC snubber. However, this will cause additional power dissipation and
`reduced efficiency.
`
`If the load current of a standard buck converter is low enough, the inductor current
`becomes discontinuous. The current at which this occurs can be calculated by
`observing the waveform shown in Figure 3.13. This waveform is drawn showing the
`inductor current going to exactly zero at the end of the switch off-time. Under these
`conditions, the average output current is
`
`We have already shown that the peak inductor current is
`
`IOUT = IPEAK/2.
`
`IPEAK
`
`=
`
`VIN VOUT
`L
`
`•
`
`ton
`
`.
`
`Thus, discontinuous operation will occur if
`
`IOUT
`
`<
`
`VIN VOUT
`L
`2
`
`•
`
`ton
`
`.
`
`However, VOUT and VIN are related by:
`
`Solving for ton:
`
`VOUT VIN D VIN
`=
`•
`=
`
`•
`
`ton
`ton toff
`+
`
`.
`
`ton
`
`=
`
`VOUT
`VIN
`
`(
`
`•
`
`ton toff
`+
`
`)
`
`=
`
`VOUT
`VIN
`
`•
`
`1
`f
`
`.
`
`3.14
`
`Chrimar Systems, Inc.
`Exhibit 2056-14
`IPR2016-00574 USPN 8,902,760
`
`-
`-
`

`
`Substituting this value for ton into the previous equation for IOUT:
`
`SWITCHING REGULATORS
`
` .
`
`(Criteria for discontinuous operation -
`
`buck converter)
`
`-(cid:230)Ł(cid:231)(cid:231) (cid:246)ł(cid:247)(cid:247)
`VOUT
`V IN
`
`1 2
`
`Lf
`
`VOUT
`
`IOUT
`
`<
`
`BUCK CONVERTER POINT
`OF DISCONTINUOUS OPERATION
`
`INDUCTOR CURRENT AND OUTPUT CURRENT
`IPEAK
`
`VIN VOUT-- -- VOUT
`L
`L
`
`ton
`
`toff
`
`DISCONTINUOUS MODE IF:
`
`VIN VOUT
`--
`
`L2
`
`••
`
`ton
`
`I PEAK
`
`==
`
`1 2
`
`IOUT
`
`<<
`
`IOUT
`
`0
`
`,
`
`f
`
`==
`
`1
`ton toff
`++
`
`VOUT
`--(cid:230)(cid:230) ŁŁ (cid:231)(cid:231) (cid:246)(cid:246) łł (cid:247)(cid:247)
`VOUT
`VIN
`
`1 2
`
`Lf
`
`IOUT
`
`<<
`
`Figure 3.13
`
`IDEAL STEP-UP (BOOST) CONVERTER
`
`The basic step-up (boost) converter circuit is shown in Figure 3.14. During the
`switch on-time, the current builds up in the inductor. When the switch is opened, the
`energy stored in the inductor is transferred to the load through the diode.
`
`The actual waveforms associated with the boost converter are shown in Figure 3.15.
`When the switch is on, the voltage VIN appears across the inductor, and the
`inductor current increases at a rate equal to VIN/L. When the switch is opened, a
`voltage equal to VOUT – VIN appears across the inductor, current is supplied to the
`load, and the current decays at a rate equal to (VOUT – VIN)/L. The inductor
`current waveform is shown in Figure 3.15B.
`
`3.15
`
`Chrimar Systems, Inc.
`Exhibit 2056-15
`IPR2016-00574 USPN 8,902,760
`
`

`
`SWITCHING REGULATORS
`
`BASIC STEP-UP (BOOST) CONVERTER
`
`ERROR AMPLIFIER
`AND SWITCH
`CONTROL CIRCUIT
`
`SENSE
`
`L
`
`+
`
`D
`
`C
`
`SW
`
`LOAD
`
`SW ON
`
`SW OFF
`
`f
`
`==
`
`1
`ton toff
`++
`
`ton
`
`toff
`
`Figure 3.14
`
`BASIC STEP-UP (BOOST) CONVERTER WAVEFORMS
`
`A B
`
`ton
`
`toff
`
`ton
`
`IIN
`
`VIN
`L
`
`VIN VOUT
`--
`L
`
`(SLOPES)
`
`IIN
`
`IIN
`
`IOUT
`
`C
`
`D
`
`VOUT
`vSW
`
`0
`
`0
`
`iIN= iL
`
`iSW
`
`0
`
`0
`
`iD = iOUT
`
`VIN
`
`+
`
`iIN = iL
`IIN
`
`vD
`
`iD = iOUT
`IOUT
`
`L
`
`iSW
`
`D
`
`C
`
`SW
`
`VOUT
`
`LOAD
`
`Lower Case = Instantaneous Value
`Upper Case = Average Value
`
`Figure 3.15
`
`3.16
`
`Chrimar Systems, Inc.
`Exhibit 2056-16
`IPR2016-00574 USPN 8,902,760
`
`

`
`SWITCHING REGULATORS
`
`Note that in the boost converter, the input current is continuous, while the output
`current (Figure 3.15D) is pulsating. This implies that filtering the output of a boost
`converter is more difficult than that of a buck converter. (Refer back to the previous
`discussion of buck converters). Also note that the input current is the sum of the
`switch and diode current.
`
`If a steady-state condition exists (see Figure 3.16), the basic relationship between
`the input and output voltage may be derived by inspecting the inductor current
`waveform and writing:
`
`VIN
`L
`
`•
`
`ton
`
`=
`
`VOUT VIN
`L
`
`•
`
`toff
`
`.
`
`Solving for VOUT:
`
`3.17
`
`VOUT VIN
`=
`
`•
`
`ton toff
`+
`toff
`
`=
`
`VIN
`
`•
`
`1
`
`1
`
`D
`
`.
`
`INPUT/OUTPUT RELATIONSHIP
`FOR BOOST CONVERTER
`
`ton
`
`toff
`
`ton
`
`iL = iIN
`
`0
`
`VIN
`L
`
`VIN VOUT
`--
`L
`
`IOUT
`
`n Write by Inspection from Inductor/Input Current Waveforms:
`
`VIN
`L
`
`••
`
`ton
`
`==
`
`VOUT VIN
`--
`L
`
`••
`
`toff
`
`Rearrange and Solve for VOUT:
`
`VOUT
`
`==
`
`VIN
`
`••
`
`ton toff
`++
`toff
`
`==
`
`VIN
`
`••
`
`1
`
`1
`--
`
`D
`
`n n
`
`n
`
`Figure 3.16
`
`Chrimar Systems, Inc.
`Exhibit 2056-17
`IPR2016-00574 USPN 8,902,760
`
`-
`-
`

`
`SWITCHING REGULATORS
`
`This discussion so far has assumed the boost converter is in the continuous-mode of
`operation, defined by the fact that the inductor current never goes to zero. If,
`however, the output load current is decreased, there comes a point where the
`inductor current will go to zero between cycles, and the inductor current is said to be
`discontinuous. It is necessary to understand this operating mode as well, since many
`switchers must supply a wide dynamic range of output current, where this
`phenomenon is unavoidable.
`
`Discontinuous operation for the boost converter is similar to that of the buck
`converter. Figure 3.17 shows the waveforms. Note that when the inductor current
`goes to zero, ringing occurs at the switch node at a frequency fo given by:
`
`fo
`
`=
`
`2 p
`
`1
`
`+
`
`L CD CSW(
`
`)
`
`.
`
`BOOST CONVERTER WAVEFORMS
`DISCONTINUOUS MODE
`iD = iOUT
`IOUT
`
`VOUT
`
`vSW
`
`VIN
`
`0
`iIN = iL
`
`0
`
`0
`
`iSW
`
`iD = iOUT
`0
`
`ton
`
`ton
`
`toff
`
`IIN
`
`IOUT
`
`A
`
`B
`
`C
`
`D
`
`iIN = iL
`IIN
`
`vSW
`
`VIN
`
`+
`
`VOUT
`
`L
`
`iSW
`
`D
`
`C
`
`SW
`
`LOAD
`
`Lower Case = Instantaneous Value
`Upper Case = Average Value
`
`Figure 3.17
`
`The inductor, L, resonates with the stray switch capacitance a