Charge Pump Converter Operation PrinciplesAje Tu 19/08/2005AbstractThis paper analyzes the charge pump circuit operation principles. Useful formulas are derived based practical approximations. Some characteristics of charge pump converter are well explained by the derived formulas.IntroductionCharge pump converters have been widely used in modern electronic products. Comparing to conventional boost converters, charge pump converters feature several advantages including: 1.) less EMI emission due to inductorless design, 2.) less PCB area since only small MLCC capacitors are used, 3.) less expensive. Charge pump converters will keep dominating in industry for low power applications like white LED backlight in hand held devices.However, charge pump converter is not well understood today. Aimtron and AIC analyze operation principles of charge pump converter in [1, 2]. The analysis is based on some impractical assumptions, and some errors occur during the derivation procedures. This paper analyzes the charge pump circuit operation principles. Useful formulas are derived based practical assumptions. Some characteristics of charge pump converter are well explained by the derived formulas.Charge Pump ConvertersFigure 1 shows a 2X charge pump converter. Q1/Q2 and Q3/Q4 turn on and off alternatively.V I NV I ND S(O N)V CD S(O N)O U TV I ND S(O N)(a) (b) (c)Figure 1. Charge pump converter circuitry on different operation stages.When Q1/Q2 turn on, the flying capacitor C F is charging through V IN , R DS(ON) of Q1/Q2, and its ownequivalent series resistance ESR. Figure 1a shows charging state equivalent circuit. When Q3/Q4 turn on, the flying capacitor C F is discharging through V IN , R DS(ON) of Q3/Q4 and its own equivalent series resistance ESR to V OUT . Figure 1b shows charging state equivalent circuit.Long Charging and Discharging Time ConstantAssumptions that approximate real applications are made for the following derivation.1.) Charging and discharging time constants (2R DS(ON)+ESR)C F are far large than switching period T. Thisleads to piecewise linear current and voltage waveforms as shown in Figure 2. 2.) C IN and C OUT are large enough so that V IN and V OUT could be regarded as DC values. 3.) R DS(ON) of Q1~Q4 are identical for simplicity.V CI O FFD T(1-D )TI O FF-A V GV C-A V GV YV XFigure 2. Current and voltage waveforms of charge pump converters.According to capacitor charge balance principle in steady state, integrations of I ON and I OFF over charging and discharging period respectively are identical.DT)-(1I DT I A VG -OFF A VG -ON ⨯=⨯(1)where I ON-AVG is the averaged charging current when Q1/Q2 turn on; I OFF-AVG is the averaged charging current when Q1/Q2 turn on; T is the switching period of the converter, D is the duty cycle of the Q1/Q2.The averaged input current I IN is expressed asDT)-(1I DT I T I A VG -OFF A VG -ON IN ⨯+⨯=⨯(2)The averaged output current I OUT is expressed asDT I D)T -(1I T I A VG -ON A VG -OFF OU T ⨯=⨯=⨯ (3)OU T IN 2I I =(4)Referring to Figure 1a and Figure 1b respectively, the averaged charging current I ON-AVG and I OFF-AVG could be written as:ESR 2R V -V I DS(ON)AVG-C IN AVG -ON +=(5)ESR2R V -V V I DS(ON)OUTAVG -C IN AVG -OFF ++=(6)(5) + (6) results inESR2R V -2V I I DS(ON)OUTIN AVG -OFF AVG -ON +=+(7)Taking Equation (3) into (7) results in:D)-D(11ESR)I (2R -2V V OUTDS(ON)IN OUT +=(8)AVG -OFF COUT OUTOUTRipple -OUT I ESR DT C I V ⨯+= (9)whereDT C I OUTOUTand A VG -OFF C OU T I ESR ⨯ correspond to capacitance and equivalent series resistance of the output capacitor respectively.Considering the flying capacitor, the charge difference during a switching period is expressed as:T I V C Q OU T VF F ⨯=⨯=∆∆(10)FOUT VF C TI V ⨯=∆ (11)The difference between maximum and minimum I ON is:ESR)(2R C T I ESR 2R V I DS(ON)F OUT DS(ON)VFON +⨯=+=∆∆ (12)Several characteristics of charge pump converters are observed according to the above equations. 1.) From Equation (8), output capability is limited by R DS(ON) of MOSFET and ESR of flying capacitors. 2.) From Equation (3) and (9), small duty cycle operation results small output ripple voltage and lowers output capability.3.) From Equation (3) and (8), if the R DS(ON) of MOSFET are identical, D = 0.5 leads to maximum output capability.4.) From Equations (11) and (12), small C F results in higher ΔV F , ΔI ON , and input voltage ripple.Figure 3 shows the simulation waveforms of a 2X charge pump converter, where charging and discharging time constant is 4 times of switching period. It is observed that the current and voltage waveforms could be approximate by piecewise linear waveforms.Figure 3. Simulation waveforms of a 2X charge pump converter with long charging time constant.Short Charging and Discharging Time ConstantIn applications where charging and discharging time constant is compatible to switching period, current and voltage waveforms are no longer piecewise linear. Formulas in above section are no longer applicable. Assumptions that approximate real applications are made for the following derivation. 1.) CIN and C OUT are large enough so that V IN and V OUT could be regarded as DC values. 2.) R DS(ON) of Q1~Q4 are identical for simplicity. 3.) D = 0.5 for simplicity.According to capacitor charge balance principle in steady state,T I dt e RV -V V dt e RV -V OUT TT/2RC T/2-t -OUT Y IN T/2RC t-X IN FF⨯=+=⎰⎰(21)where R = 2R DS(ON) + ESR is the equivalent total resistance in the charging and discharging loops, V X andV CV INV OUTI CI OUTI INV Y are valley and peak C F voltage respectively.Rearranging Equation (21) results inT I )e-)(1V -V (V C )e -)(1V -(V C OU T 2R C T -OU T Y IN F 2R C T -X IN F FF⨯=+=(22)By deleting C F and )e -(1F2RC T -terms, (22) results inOU T Y X V V V =+(23)T I V C Q OU T C F F ⨯=⨯=∆∆(24)FOUT X Y C TI V -V ⨯=(25)(23) - (25) results inFOUTOUT X 2C TI -2V V ⨯= (26)Take (26) into (22) results inT I )e -)(12C TI 2V -(V C OUT 2RC T-FOUT OUT IN F F ⨯=⨯+ (27)FOUT2RC T-F OUT OUTIN C T2I )e -)(1C T I V -2V F ⨯=⨯+ (28)Rearranging Equation (28) results in)e-(1C T 2I C TI V -2V F2RC T -F OUT FOUT OUT IN ⨯=⨯+ (29)FFF2RC T-2RC T -FOUT IN 2RC T -F OUT FOUT IN OUT e -1e1C T I -2V )e-(1C T 2I -C TI 2V V +⨯⨯=⨯⨯+= (30)A--AOUTIN OUT e -1e 1A R 2I -2V V +⨯⨯⨯=(31)where A = T/2RC FSeveral characteristics of charge pump converters are observed according to the above equations. 1.) From Equation (23), V OUT is the summation of the peak and valley voltages of flying capacitor. 2.) From Equations (23) and (25), small C F results in higher ΔV F , ΔI ON , and input voltage ripple. 3.) From Equation (31), R = 2R DS(ON) +ESR primarily limits the output capability of charge pumpconverter. However, parameter A = T/2RC F also induces a factors onto the output capability that will be analyzed later.Figure 4 shows the simulation waveforms of a 2X charge pump converter, where charging and discharging time constant is 0.4 times of switching period.Figure 3. Simulation waveforms of a 2X charge pump converter with short charging time constant.Figure 5 shows the T/2RC F effect on the output capability. When T/2RC F < 0.5, the A--Ae-1e 1A +⨯ term approaches to 2 and its limitation could be neglected. Equation (31) is simplified as Equation (32) that isidentical to Equation (8).OU T D S(ON )IN OU T 4ESR)I (8R -2V V +=(32)T/2RC F > 1.0 is not recommended since significant reduce in output capability is predicted. If R DS(ON) is 1.0m Ω, switching frequency is 1MHz, T/2RC F = 0.5 results in C F = 0.5uF . Flying capacitor larger than 0.5uF is strongly recommended.V CV INV OUTI CI OUTI INFigure 5. Effect of A = T/2RC F on output capability.From Equation (25)OUT DS(ON)F OUT DS(ON)XY ON I A ESR)(2R C T I ESR 2R V -V I ⨯=+⨯=+=∆Again A = T/2RC F < 0.5 is recommended, otherwise large input voltage ripple will be result in.ConclusionA = T/2RC F is an important parameter for 2X charge pump converter. It affects not only output capability but also the input ripple voltage. A = T/2RC F < 0.5 is strongly suggested according to the analysis results. In practical application, switching period and R DS(ON) is constant once the charge pump IC is decided. Therefore the flying capacitor should be carefully selected to 1.) minimize R = 2R DS(ON) +ESR and 2.) make sure A = T/2RC F < 0.5 for maximum output capability and minimum input voltage ripple.Reference[1] “Principle of Charge Pump ”, Application Note, Aimtron Technology. [2] “AIC1845”, Datasheet, Analog Integrations Corporation.A。