AN023 An Useful Model for Charge Pump Converter Analysis Introduction This application note focuses on the analysis of VIN ION VOU T Q1 the charge pump and its equivalent circuit. The AIC1845 is a micro-power charge pump DC/DC C IN RDS-ON Q2 COUT ESR converter that produces a regulated 5V output. This Q3 C1 kind of converter uses capacitors to store and transfer R DS-ON energy. Since the capacitors can not change their voltage level abruptly, the voltage ratio of VOUT over VIN Q4 Fig.2 The on State of Charge Pump Circuit is limited to some range. Capacitive voltage conversion is obtained by switching a capacitor periodically. It first VIN charges the capacitor by connecting it across a voltage source and then connects it to the output. Referring to RDS-ON Q1 CIN Q2 ESR Fig.1, During the on state of internal clock, Q1 and Q4 Q3 are closed, which charges C1 to VIN level. During the off RDS-ON state, Q3 and Q2 are closed. The output voltage is VIN IOFF C1 C OUT VOU T Q4 Fig.3 The OFF State of Charge Pump Circuit plus VC1, that is, 2 VIN. VIN Q1 CIN Q2 C1 Q3 Referring to Fig.2 and Fig.3, here shows the circuit of VOUT COUT Q4 Fig.1 The Circuit of Charge Pump charge pump at different states of operation. RDS-ON is the resistance of the switching element at conduction. ESR is the equivalent series resistance of the flying capacitor C1. ION-AVE and IOFF-AVE are the average current during on state and off state, respectively. D is the duty cycle, which means the proportion the on state takes. Let’s take advantage of conversation of charge for capacitor C1. Assume that the capacitor C1 has reached its steady state. The amount of charge flowing into C1 during on state is equal to that flowing out of C1 at off state. ION− AVE × DT = IOFF− AVE × (1 − D)T (1) ION- AVE × D = IOFF- AVE × (1 − D) (2) February, 2002 1 AN023 2 2 PESR ≅ ION × ESR × D + IOFF × ESR × (1 − D) − AVE − AVE I I = ( IN ) 2 × ESR × D + ( OUT ) 2 × ESR × (1 − D) 2D 1− D 1 2 1 2 = IOUT × ESR × + IOUT × ESR × D 1- D 1 2 = IOUT × ESR × D(1 - D) IIN = ION- AVE × D + IOFF- AVE × (1 − D) = 2 × ION- AVE × D (3) = 2 × IOFF- AVE × (1 - D) IOUT = IOFF- AVE × (1 − D) IIN = 2IOUT (4) When the duty cycle is 0.5, the power loss of switching element is For AIC1845, the controller takes the PSM (Pulse Skipping Modulation) control strategy. When the duty 2 PRDS −ON ≅ IOUT × 2 × RDS -ON 0.5(1 − 0.5) 2 = IOUT × 8RDS −ON cycle is limited to 0.5, there will be: … … … … ..(8) ION- AVE × 0.5 × T = IOFF- AVE × (1 − 0.5) × T ION- AVE = IOFF- AVE … … … … … … … ..(5) 2 PESR ≅ IOUT × ESR × According to the equation (4), we know that as long as 1 0.5(1 − 0.5) 2 = IOUT × 4ESR the flying capacitor C1 is at steady state, the input In fact, no matter the current is at on state or off state, it current is twice the output current. The efficiency of decays exponentially rather than flows steadily. And the charge pump is given below: root mean square value of exponential decay is not ? = VOUT × IOUT V ×I V = OUT OUT = OUT VIN × IIN VIN × 2I OUT 2VIN (6) equal to that of steady flow. That is why the approximation comes from. Let’s consider the power dissipation of RDS-ON and ESR. Let’s treat the charge pump circuit in another approach Assume that the RDS-ON of each switching element is and lay the focus on the flying capacitor C1. Referring to equal. The approximation of the power loss of RDS-ON Fig.2, when the circuit is at the on state, the voltage and ESR are given below: across C1 is: PRDS −ON 2 2 ≅ ION × 2R DS −ON × D + IOFF × 2R DS −ON × (1 − D) - AVE - AVE I IIN 2 ) × 2R DS-ON × D + ( OUT ) 2 × 2R DS-ON × (1 - D) 2D 1- D 2I I = ( OUT ) 2 × 2R DS-ON × D + ( OUT ) 2 × 2R DS-ON × (1 - D) 2D 1- D 2 2 2 2 = IOUT × ( R DS-ON ) + IOUT ×( R DS-ON ) D 1- D 2 2 = IOUT × × R DS-ON D(1 - D) =( … … … … ..(7) 2 AN023 VC-ON (t) = VIN − 2R DS−ON × ION (t) - (ESR × ION (t)) (9) The average of VC1 during the on state is: VC−ON− AVE = VIN − (2R DS −ON × ION− AVE ) − (ESR × ION− AVE ) .… … … ..(10) Similarly, referring to Fig.3, when the circuit is at the off state, the voltage of C1 is: VC-OFF (t) = VOUT − VIN + 2R DS-ON × IOFF (t) + ESR × IOFF (t) (11) The average of VC1 during the off state is: VC−OFF− AVE = VOUT − VIN + 2R DS−ON × IOFF− AVE + ESR × IOFF− AVE (12) The difference of charge stored in C1 between on state and off state is the net charge transferred to the output in one cycle. ∆Q = Q ON - Q OFF = C1 × (VC1−ON− AVE − VC1−OFF− AVE ) = C1 × (2VIN - VOUT - 2R DS-ON × ION- AVE - 2R DS-ON × IOFF- AVE - ESR × ION− AVE - ESR × IOFF- AVE ) … … ..(13) I I I I = C1 × (2VIN − VOUT − 2R DS −ON × OUT − 2R DS −ON × OUT - ESR × OUT - ESR × OUT ) D 1− D D 1- D 1 = C1 × [2VIN − VOUT − (2R DS −ON + ESR) × IOUT × ] D(1 − D) Thus the output current can be written as IOUT = f × ∆Q = f × (Q ON − Q OFF ) = f × C1 × [2VIN − VOUT - (2R DS - ON + ESR ) × IOUT × … … … ..(14) 1 ] D(1 - D) When the duty cycle is 0.5, the output current can be IOUT = f × C1 × [2VIN − VOUT − (2R DS − ON + ESR) × IOUT × 1 ] 0.5(1 − 0.5) … … … (15) = fC1 × [2VIN − VOUT − (8R DS − ON + 4ESR) × IOUT ] And equation (15) can be re-written as: 2VIN − VOUT = 1 × IOUT + (8R DS−ON + 4ESR) × IOUT … … … … … … ..(16) fC1 3 AN023 According the equation (16), when the duty cycle is 0.5, chosen to make the duty cycle of AIC1580 to be 0.5. the equivalent circuit of charge pump is shown in Fig.4. The experiment data and the corresponding RDS-ON The term 8 RDS-ON is the total effect of switching (evaluated from the equivalent circuit in Fig.4) are listed resistance, 1/fC1 is the effect of flying capacitor and in Table.1. The value of RDS-ON is then assigned to all 4ESR is its equivalent resistance. switching resistors of the simulation circuit, Fig.6. For IOUT 2VIN the given loading RLOAD, the output voltage and output VOUT current of experiment results and those from simulation 1/fC1 8RDS-ON 4ESR are shown in Fig.7. From Fig.7, it is easily seen that the LOAD COUT derived equivalent circuit in Fig.4 is quite corresponding to the original charge pump circuit. Fig.4 The Euqivalent Circuit of Charge Pump Experimental and Simulation Results For the reason of simplicity, the output loading is VOUT VIN 1 C1 10µF 2 3 U1 VOUT GND CVIN C+ SHDN AIC1845 C3 6 5 C2 4 1µF 10µF RL Fig. 5 The Test Circuit of AIC1845 4 AN023 Fig.6 The Simulation Circuit of AIC1845 Table. 1 The experiment results and the evaluated RDS-ON. VIN (V) RLOAD (Ω) ESR (mΩ) VOUT (V) IOUT (mA) Frequency(KHz) RDS-ON(Ω) 2.7 99.4 20 4.77 48.20 640 1.43 2.7 109.4 20 4.83 44.30 640 1.40 2.7 121.2 20 4.89 40.32 640 1.38 2.7 131.3 20 4.92 37.49 640 1.40 2.7 141.2 20 4.95 35.07 640 1.40 Table. 2 The simulation results. (RDS-ON is from Table.1) VIN(V) RLOAD(Ω) ESR(mΩ) RDS-ON(Ω) 2.7 99.4 20 1.43 2.7 109.4 20 2.7 121.2 2.7 2.7 Frequency VOUT(V) IOUT(V) 640 4.83 48.62 1.40 640 4.89 44.68 20 1.38 640 4.94 40.77 131.3 20 1.40 640 4.97 37.84 141.2 20 1.40 640 5.00 35.38 (kHz) 5 IOUT(mA) AN023 55 53 51 49 47 45 43 41 39 37 35 33 31 29 4.5 4.6 4.7 4.8 4.9 5 5.1 VOUT(V) 5.2 5.3 5.4 5.5 Experiment results Simulation results-new solution Simulation results-previous solution Fig. 7 The Distribution of Experiment Results and Simulation Results The previous solution means that the equivalent seen that the terms 1/fC1, 4ESR and 8RDS-ON resistance includes only the 1/fC term. should be as small as possible to get large output current. However, for users, since the RDS-ON is fixed and manufactured in IC, what we can do is to lower 1/fC1 and ESR. However even the effect of Summary: 1/fC1 and ESR can be kept as small as possible, 1. For the capacitive switched converter, the function of the term 8RDS-ON still dominates the role that limits the flying capacitor C1 is storing and transferring charge. the maximum output current. Due to the law of conservation of charge for capacitor, we can only obtain the relationship between input From Fig.4, the equivalent circuit shows a one-pole current system. Therefore there is no need to worry about and output current. Contrarily, in the inductor-used application, owing to the voltage-second oscillation problem for charge pump converter. balance of inductor, various voltage conversions are easily obtained. Therefore for the capacitor switched converter, to have an arbitrary voltage conversion is more difficult than inductor-used converter. 2. From the equivalent circuit shown in Fig.4, it is 6