Control of Boost type Converter in Discontinuous Conduction Mode by Controlling the Product of Inductor oltage-econd Chongming (Michael) Qiao, Jason Zhang International Rectifier 33 Kansas treet, El egundo, CA 945 UA chongmingqiao@hotmail.com; jzhang@irf.com As presented at PEC 5 - Recife, Brazil Abstract: Battery-operated systems such as cell-phone, digital camera become more and more popular. In these applications, a boost-type converter is usually required to convert low battery to higher. In this paper, a variable frequency control of boost converter is discussed. The prototype circuit is built to prove the concept. The extension of this approach in Power Factor-Correction application is discussed. I TRODUCTION Battery-operated systems such as digital camera, TFT-CD bias supplies, require a boost converter to step up the low battery to higher. For these applications, it is very important to extend the battery life. Therefore, efficiency is critical even at light load condition. Fixed frequency PWM control is very popular. Two items related to PWM boost converter is a concern for customers. First, if the boost converter is operated in the continuous conduction mode (CCM), there is a right half plane zero, which is difficult to be stable. The discontinuous conduction mode is desired for low power application. econd, at light load, boost converter is difficult to regulate because PWM controller typical has certain minimum on time and the on time of switch at fixed frequency will keep pumping energy to output and it will cause over at very light load or no load condition. In this paper, another approach is investigated. This approach controls the boost converter always in discontinuous conduction mode by forcing the product of inductor -second to be zero in each switching cycle. By doing so, the stability of system is always guaranteed and no compensation network is required. In addition, the proposed control has natural power limit and will prevent the boost converter from being over stressed by over load. ince it operates in variable frequency, at light load, the frequency is very low and it helps regulate the output as well as offer better efficiency since low switching loss is resulted. The concept can be implemented by sensing inductor or switching with an integrator. One extension of the approach to control of Power Factor Correction is also proposed. The experimental result is provided to prove the concept. II PROPOED CONTROER FOR BOOT CONERTER WITH DUCTOR CURRENT ENG The proposed controller for boost converter with inductor sensing is shown in Figure. Isen m m Rs Reset Dom R Q Q R GND Programmable delay D Q Reset dom R R Figure. Proposed control approach diagram for a boost converter. ref out CC
Inductor inductor across sensing resistor Q comparator output t t t t3 Operation at regulation mode Figure. Operation waveforms at regulation mode. -out A m m This control has two operation mode, regulation mode and power limit mode. At regulation mode, the waveform is shown in Figure. The inductor operates at discontinuous conduction mode and the output is regulated at desired output. Regulation Mode The operation concept is as follows. First, during time t~t, atch R outputs logic High and the switch is on. The inductor linearly increases from zero. When the at sensing resistor Rs reaches the threshold for example m, atch R I _ TH and R are reset to zero. The switch is turned off at t. The inductor is given as ( ~ t ) = The peak inductor is given as i = t --------------() _ peak The peak inductor is limited by the threshold I _ TH and sensing resistor. I _ TH i_ peak = where I_ TH = m ---() R Combination of above two equations results in I _ TH t = --------------------(3) R From t to t, the inductor decreases. Before the across the sensing resistor reaches m, the output of latch R keeps low and switch holds off. At time t, the across sensing resistor reaches m and the inductor decreases to almost zero, the latch r is set to High. This will enable the ET of latch R to be controlled by feedback comparator. If we neglect m, the inductor reduced to zero at t. The across the inductor is ( t ~ t) = OUT. The following equation exists based on inductor second balance. t t t = ( ) ( ) OUT t t = t OUT ------(4) From t to t3, the output is discharged through output load until the output is below reference. At t3, the comparator goes high and ET the latch R. witch is ON again and another cycles starts. The programmable delay is added as an option to ensure the inductor goes to zero. ince the inductor reaches zero in each cycle, the input power will be the energy stored in the inductor divided by switching period. The input power is given as i P _ peak = -----------(5) T where Ts is the switching period. ubstitution of equation () into above equation results in P = -------------(6)) R I _ TH T ince the inductor is discharged to zero in each cycle, the energy stored in the inductor is transferred to the load in each cycle. If assuming the efficiency is %, the input power will be equal to output power. P = P = I -----(7) OUT OUT OUT ubstitution of equation (6) into above equation results in R OUT IOUT F = -------------(8) I _ TH where Fs is the switching frequency and F T =. ince at regulation mode, the output equals nominal output. OUT = OUT _ nom. The equation (8) can be written as R OUT _ nom IOUT F = ---------(9) I _ TH The above equation shows that the switching frequency linearly increases when load goes up.
. Power Regulation Mode inductor inductor across sensing resistor Q tied to CC comparator output t t -out Operation at power limit mode m m High Figure 3. Operation waveform at power limit mode with C_ldy=CC When load keeps going up, eventually the inductor will operate in the boundary of Continuous Conduction Mode (CCM) and Discontinuous Conduction Mode (DCM). The concept of this control is that the switch is turned on only after the inductor reaches to zero. This concept will limit the maximum power that the input can deliver. When load is high enough, the output power will reach the input power limit. The output will be no longer regulated and it will keep decrease as load increase. The operation waveform is shown in Figure 3. At power limit mode, since the output is lower than regulation, the comparator output is always high. The switch is simply controlled by the latch R and sensing comparator. The switch is on when inductor reaches low threshold such as m and turn off when inductor reaches high threshold. The average inductor is given as I _ TH i_ avg= i_ pk= ------() R Input power equals output power, therefore P = I _ avg = POUT = OUT IOUT ubstitution of equation () into above equation results in I _ TH OUT = ---------() R IOUT The above equation shows that the output will be reduced when output goes up. The maximum load with regulated output will be I OUT _ reg I _ TH = -----() R OUT _ nom Where I OUT _ reg is maximum load output with regulated output OUT _ nom. During the power limit mode, the switch period is given as T = t = t ( t t) ubstitution equation (3) and (4) into above equation, we have R F = = ---(3) T I _ TH OUT ubstitution of equation () into above equation results in F R R I OUT = = T I_ TH I_ TH --(4) The above equation shows that the frequency will decrease when load increases. Overall, the relationship between output, frequency and load is shown in Figure 4. The peak frequency occurs at the transition between regulation mode and power limit mode. At = transition time, OUT OUT _ nom ubstitute of above equation to equation (3) results in the maximum operation frequency F _max Average input witching Frequency Output R = = T I _ TH OUT _ nom regulation mode Io(MAX) ----(5) Power limit mode oad Figure 4. Theoretical characteristics for the boost converter with proposed control approach. With this control approach, at each cycle, the second product of inductor is always reset to zero and inductor always goes to zero before another cycle starts. Ideally, the threshold to ensure inductor decreases to zero should be m. However, in reality, since comparator has offset and m is used to
compensate the comparator offset. Additional delay can be generated by putting extra cap at pin. The programmable delay is to ensure inductor fully going to zero before other cycles starts. From equation (3), the switch ON time is fixed if the input is fixed, the operation principle will be similar to constant on-time control and the output is regulated by changing the off time and switching frequency. The characteristics of this control is shown in Figure 4. Before load reaches critical Io(MAX), the output is regulated to desired output. The switching frequency increases as load increases. At light load, the switching frequency can be very low and efficiency is high comparing to fixed PWM control. This feature is usefully for battery-operated application because of energy saving at idle mode. When load keeps increasing and inductor starts to operate at the boundary of Discontinuous and Continuous mode due to the nature of control. The system goes into power limit mode as shown in Figure 3. In this mode, the average inductor is fixed and output starts to goes down as load increases. And the switching frequency also goes down due to longer turn off time. This control approach has natural power limit, which is useful at over load condition as well as soft start. Overall, the following features is summarized as ariable frequency control. At light load, frequency goes down and system efficiency is relatively high. This is beneficial for battery operated systems ystem is self stable, no output loop compensation network required. Natural limit. No soft start is required since the output starts up with limited power. witch turns on at zero results in low switching loss. imple implementation and easy to be integrated into IC. The drawback of the proposed control is that the output and the input do not share a common ground. This can be relieved by putting the inductor sensing resistor in series with inductor as shown in Figure 5. This requires highspeed differential comparator and it is limited to low input application as well. But it will be a good choice for battery operated systems such as white ED driver application. Rs D out Isen CC GND Figure 5. Boost controller with proposed control and differential inductor sensing.
8 9 III EXPERIMENTA ERIFICATION 8 3 3 3 6 J CON R9 C.5 uf coilcraft 5p-3HC uh R6 k Q N394 R7 Q3 N396 D N54 Q4 IRFE/TO R 9.k C4,5uF,8mohmER R.4k J3 CON Q 3 UC 74HC UD 74HC -5 R6 k - U9A M39 5 4 ref C9 J CON T43/TO 5 R3 k ref U4 C uf C4 uf R k U7 M43/TO C3 uf N394 R5 R4 9 Q 5C5 C6 5-5 5 5 5C UA uf U5A R uf k UA 74HC uf -5 4 set J4 5 - JUMPER 3 C7 M39-5 74HC R5 p 5 5 6 6 9-7 U5B M39 R3 k reset 5 6 4 ub Q R4 k D N539 uf R.5k 74HC Figure 6. chematic of a prototype circuit using differential inductor sensing. A small power prototype was built to verify the concept. The schematic is shown in Figure 6. The experiment waveforms for start up and normal operation are shown in Figure 7, Figure 8 and Figure 9. The comparison between experimental results and theoretical prediction for output and frequency versus output is shown in Figure and Figure. ystem specification is as follows: =3.4. out=.5. =5uF with 8mohm ER, Current sensing resistor is Rs=.5ohm and input inductance is =uh. The proposed control offers better efficiency at light load, natural limit and simple implementation. Figure 7. Operation waveforms during the start up.
Frequency versus output 3 5 Frequency (kh 5 5 Figure 8. Operation waveforms at regulation mode. 5 Iout(mA) Fs(KHz) experimental Fs(KHz) theoretical Figure. Comparison between experimental results and theoretical prediction for frequency versus output.. Figure 9. Operation waveform at power limit mode. out() 4 8 6 4 Output versus output 5 5 IOout(mA) I EXTENION I PWM CONTRO WITH WITCHG CURRENT ENG The proposed concept can be applied to use switching as well. The basic concept of this approach is to ensure inductor -second going to zero or inductor going to zero before next cycle starts. This is achieved by using integrator to emulate the inductor as shown in Figure. The operation waveforms are shown in Figure 3. When switch is ON, a capacitor Cint is charged by an internal source that is proportional to CC(=). When switching reaches threshold at m/rs, the switch is turned off. Then the capacitor Cint is discharged by source proportional to (out- ). Until the capacitor is discharged to a preset such as m, the latches are enabled for ET, which is controlled by the feedback comparator. The capacitor will emulate the inductor. If the source coefficients are identical, when the capacitor is discharged to preset, the inductor-second product will go to zero and the theoretical inductor will go to zero. Figure 4 shows a simulated operation waveform for a 5 to application. out(v) experimental out (theoretical) Figure. Comparison of output versus output (theoretical and experimental)
D out -out CC Rs OUT inductor witching A m/rs Cint CC Cint m GND Isen m m Reset Dom Q Q R Programmable delay Q R Reset dom ref Q comparator output Figure 3. Operation waveforms for proposed control with switching sensing. Figure. Proposed controller for boost converter with switching sensing. Comparing with the approach using inductor sensing, this scheme offers same feature such as natural limit and variable frequency control as well as additional features. witching is sensed. It is convenient for small power application with monolithic IC implementation, where switch is integrated inside IC. ensing switching will result in lower losses comparing with inductor sensing. Common ground between input and output. It can be easily extended to buck-boost type converter as shown in Figure 5, with three more features. () Output can be either higher or lower than input. () The output can be short to ground with limit. (3) The output can be shut down. Figure 4. imulation waveforms for 5 to application with proposed control in Figure. out M Rs CC gnd Isen out Proposed controller Cint Figure 5. Buck boost converter with proposed controller and switching sensing.
EXTENION II - PFC CONTRO AT BOUNDARY OF DICONTUOU AND CONTUOU MODE D out Inductor ac - COMP Cint Rs GND ET Isen m 3m Q R Reset Dom gm CC ref Figure 7. Theoretical operation waveforms for proposed PFC controller.. C_int Current imit Comparator COMP Figure 6. Proposed PFC controller operates in boundary of CCM and DCM. The same concept can be applied to control PFC (power factor correction). The diagram is shown in Figure 6 and operation waveforms are shown in Figure 7 and simulation result is shown in Figure 8. Instead of using multiplier and sensing input shown in previous article, the on time of switch is controlled by comparing with output of error amplifier and a ramp generated by a constant source. ince the On time is almost constant during a line cycle if the loop is slow enough, the peak inductor will be linearly proportional to the input and inductance. The switch is turned on again when the inductor reaches almost zero (m/rs). By this operation, the inductor operates in the boundary of Discontinuous Conduction Mode (DCM) and Continuous Conduction Mode (CCM). The average input will be proportion to input and unit-power-factor is achieved. The load regulation is achieved through modifying the switch ON time by compensation loop. An open loop simulation waveform is shown in Figure 8. Comparing with previous approach such as 656 from T, this approach does not require high precision multiplier and no input sensing is required. This is simple and less noise sensitive. Figure 8. imulated waveform for a line cycle. I CONCUION A new approach to control the boost type converter in discontinuous conduction mode is proposed. This approach offers variable frequency control and natural limit. Two extensions are derived. One approach uses switching and an integrator to emulate the inductor. The other extended approach provides simple PFC control. References []. IRU365 datasheet. http://www.irf.com/technicalinfo/refdesigns/irdc365.pdf. []. T 656 datasheet, http://www.st.com/stonline/books/pdf/docs/59.pdf