AN015 The effect of ESR on DC/DC power converter Introduction The capacitors, inductors, and resistors in circuit C= εA … … … … … … … … … … … .(equ.1) d analysis have ideal properties. Capacitors and inductors follow precise derivative relationships. In the real world, components do not follow such simple models. The non-ideal behavior of energy storage components is very important in the context of power electronics. This article is to discuss the effect of capacitor’s ESR (Equivalent series Resistor) characteristics on DC/DC power converter. And now, capacitors shall be presenting first. where εis the electrical permittivity of the insulating layer, A is the surface area, and d is the distance between 2 plates. By definition, the magnitude of the charge Q stored on either plates of the capacitor is directly proportional to the potential difference V between the plates. Therefore, we may write Q = CV … … … … … … … … … … … . (equ.2) where V is the applied voltage. In the arrangement of parallel plates, the electric field is given by Capacitors- Principles and Equivalent Circuits E= V … … … … … … … … … … … . .(equ.3) d The time derivative of Q=CV gives the standard property i =C dv … … … … … … … … … … … . ..(equ.4) dt The parallel plate arrangement has provided some challenges for years. Picture that two plates with measurements of one square meter for both plates, Figure 1. The Basic Parallel-Plate Capacitor Geometry[1] Capacitor devices come in many forms, but nearly all of them are composed of conducting plates or films, also separated by an insulating layer such as air or paper. A common parallel arrangement, shown in figure 1, gives equation 1 as follows. which are separated by 1um air space, form a capacitor of less than 10µF. Nevertheless, typical capacitors used in power converter are usually on the order of 100µF or more. However, the permittivity of free space or air is small, withε0 = 8.854pF/m and very large plates are required to give significant values of C. But the effect of inserting the dielectric is Dec 2000 1 AN015 to increase the capacitance by a factor of dielectric numbers of important properties. constant k. Ø The current is not exactly consistent with i=Cdv/dt e K= … … … … … … … … … … … . (equ.5) e0 Ø Current flows even when dc voltage is applied Ø Resonance occurred due to the combination of L Typical values of k are shown in table 1 as below. Table1. Dielectric Constant and Strength Material Air Paper Glass Paraffin Rubber Mica Water Dielectric Constant 1.00059 3.7 4~6 2.3 2~3.5 6 80 Dielectric 6 Strength(10 V/m) 3 16 9 11 30 150 - and C. The device behaves as an inductor when operated at a frequency which is over the resonant frequency. Ø Extra power loss The properties are out of consideration in general applications. However, they play as a decisive role in some of the applications for high operating frequency or low voltage with high current, e.g. VRMx.x. The inductance is expected to be in the nano-henry Although the term “dielectric” is nearly invariable applied to insulating materials, which is somewhat a misleading. Water, which has a high dielectric ( 10 −9 H ) range, since it represents wire inductance and geometric effect. The leakage resistance should be very high, and the time constant of the insulation, constant, is not an insulator. τ = R LEAK C … … … … … … … … … … … . (equ.6) In a capacitor device, the wires and plates have should be very long. resistance and inductance. The insulation is not perfect and has a leakage resistance. These direct In many power electronics applications, a capacitor is properties can be summarized in a circuit model, to be used at a specific frequency. Given a radian shown in figure 2.[2] frequency ω, the circuit model can be evaluated as a set of impedance, then simplified. The simplified one is shown in figure 3, the derivation starts with a capacitor C in parallel with the leakage resistance RLEAK. Figure 2. General Circuit Model for a Real Capacitor The properties of the model can be minimized, but not be avoided altogether. This equivalent exhibits Figure 3. 2 AN015 widely used by manufacturers as the basis of Fig. 3 can be turned into an equivalent series, as figure 4, after some certain mathematical transform. specifications. Since the ESR is obtained through a transformation, therefore, it is a non-linear frequency-dependent resistance. The value is given at a specific frequency (120Hz or 100KHz is common) on data sheets. Figure 4. 2 2 2 Since RLEAKC is high, ω RLEAK C >>1 is true as the frequency goes above about reactance portion simplifies to resistance portion simplifies to 1Hz. Then the −j . The series ωC 1 ω 2RLEAKC 2 Figure 6. The standard model of a capacitor . It gets Besides, the parameter, dissipation factor df, is often much “lovelier” for the exhibition in figure 5, used to indicate the quality of a capacitor. It shows comparing with figure 4. the ratio of resistance to reactance. For the frequency 1 below , the standard model’s reactance is ESL C approximately df = 1 , which gives ?C R = (ESR)? E … … … … … … … … … … … . (equ.8) X Figure 5. The ratio is also called loss tangent, df, coming with Till now, the equivalent circuit has been simplified to a series R-L-C combination. The inductor in the circuit is termed as an equivalent series inductance or ESL. The capacitor represents the internal ideal capacitance effect. The resistor, termed as an X an impedance angle f = tan −1( ) . If the wire R resistance is small, the ESR becomes the second term in equation 7 and the dissipation factor can be written as equivalent series resistance or ESR, has the value of ESR = Rw + 1 2 ω R LEAK C 2 … … … … … … … . (equ.7) The combination, shown in figure 6, is sometimes df = tan δ = ESRωC ≒ ωC 2 ω RLEAKC 2 = 1 ωRLEAKC … .. (equ.9)。 called as a standard model of a capacitor. It has been 3 AN015 The leakage resistance can be calculated from the process. Even when LDO used, the ESR effect resistivity of insulation, ρ ,since the geometry is appears as the variation loading current applied. known. We substitute εA ρd and for C and RLEAK d A and derive the result tan δ = 1 from equation 9. ωερ Tutorial example Switching mode power supply part Thus the loss tangent is independent of geometry and can be considered a material property As the IT market grows rapidly, the device power associated with the insulator. That is, the ESR value requirement is getting more and more complicated. strongly depends on the choice of insulation Obvouusly, one trend is to use the switching mode material. power supply instead of conventional linear regulator, which betters the efficiency. The effect of ESR This design example, as showm in figure 8, provides Unfortunately, the effect of ESR will never disappear. Below the resonant frequency, a real capacitor will show a resistance in series with a capacitive reactance. The capacitor becomes a simple RC series combination. In some applications such as a an output voltage of 1.3V to 3.5V, which meets the VRM8.4 specification. It can deliver high current to a CPU VCORE load. According to the tight VRM transicent demand, the effect of ESR plays a significant role in the application. DC/DC converter, a capacitor is often exposed to a square wave of current. Ideally, this produces a triangular voltage across the part shown in figure 7. Figure 7. But to lead to some unusual result, the ESR will exhibit an ESR voltage drop. With the ESR, a small square wave adds in series with the triangle, the abrupt voltage change called an ESR jump. In some case, it can dominate over ripple during the design 4 AN015 AIC1570- Advanced PWM Switching and Dual Linear Controller IC!!! The AIC1570 combines a synchronous voltage mode controller with a low dropout linear regulator and a linear controller as well as the monitoring and protection functions in this chip. The PWM controller regulates the microprocessor core voltage with a synchronous rectified buck converter. The linear controller regulates power for the GTL bus and the linear regulator provides power for the clock driver circuit. An integrated 5 bit D/A converter that adjusts the core PWM output voltage from 2.1V to 3.5V in 0.1V increments and from 1.3V to 2.05V in 0.05V increments. The linear regulator uses an internal driver device to provide 2.5V±2.5%. The linear controller drives with an external N-channel MOSEFET to provide 1.5V±2.5%. Features l Provides 3 Regulated Voltages for Microprocessor Core, Clock and GTL Power. l Simple Voltage-Mode PWM Control. l Dual N-Channel MOSFET Synchronous Driver. l Operates from +3.3V, +5V and +12V Inputs l Fast Transient Response. l Full 0% to 100% Duty Ratios. l ±1.0% Output Voltage for VCORE and ±2.0% Output Voltage Reference for VCLK and VGTL. l TTL Compatible 5-bit Digital-to-Analog Core Output Voltage Selection. Range from 1.3V to 3.5V. l 0.1V Steps from 2.1V to 3.5V.,0.05V Steps from 1.3V to 2.05V. l Adjustable Current Limit without External Sense Resistor. l Microprocessor Core Voltage Protection against Shorted MOSFET. l Power Good Output Voltage Monitor. l Over-Voltage and Over-Current Fault Monitors. l 200KHz Free-Running Oscillator Programmable up to 350KHz 5 AN015 C18 +12VIN R15 VCC 10 1000pF R2 1 20 C16 1µF 24 23 L1 OCSET 2.2K C15 Q1 UGATE + 1µH C1-C7 6 x 1000µF 1uF PHASE +5VIN GND VOUT1 L2 +3.3VIN VIN2 + C19 1000µF 12 22 Q3 GATE3 VOUT3 R11 FB3 21 + C24-36 15 16 2.5V 3.5µH Q2 LGATE D5820 PGND R4 4.99K 7 x 1000µF 10K + R12 10K C43-46 4 x 1000µF 19 VSEN C40 VOUT1 waveform shown in figure 9 0.68µF VOUT2 VOUT2 R8 2.21K FB1 13 18 1.5V VOUT3 waveform shown in figure 13 + C47 R13 1.87 K FB2 270uF R10 160K C41 10pF R9 732K 11 C42 R14 10K 2.2nF 17 7 PGOOD FAULT VID0 6 8 VID1 5 10 VID2 4 VID3 3 VID4 2 9 14 COMP1 RT SS C48 40nF Figure 8. AIC1570 3 in 1 Power Solution for Motherboard[3] Figure 9.VOUT1 of AIC1570 6 AN015 Generally, we place several single capacitors in The circuit is initiated at t=t0, during the rising or parallel, which reduce the total ESR. And figure 9 falling edge of the CPU supply current transient. A shows the real output voltage waveform when voltage drop is produced at t=t1 due to influence of constant current pulled. It still dominates a certain ESR and ESL, which gives percentage of the output variation although the effect of ESR jump is slight. Also, the waveform would be VDROP@t1= ESR × ∆IOUT + ESL ∆IOUT … … (equ.10) ∆t worse if neither the measurement is taken skillfully enough nor appropriately layout applied. After the initial transient, the ESL term in equation 10 drops off as in equation below Figure 10 shows a 35A load current occurred in about VDROP@t2= ESR × ∆IOUT … … … … … … … . (equ.11) 8A/us current slew rate. And figure 11 is a redraw waveform from figure 10, which presents clearer Within a clock cycle of the output current transient, the current feedback loop detects change of output transient response. current and increases power-switch duty cycle to maximum. Figure 12 shows the transient step and is followed by the description. IL IOUT IL (0) IOUT↑ (1) IOUT↑-IL IL↑ Figure 10. IOUT↑ (2) IL↑ (3) IOUT↑-IL↑ IL↑ IOUT IOUT↑ IL↑-IOUT↑ IOUT↑ (4) VOUT Figure 12.Transient Current Flow Sequence t0 t1 t2 t3 t4 Figure 11. 7 AN015 Figure 13 illustrates the output drop due to the (0) Circuit is initiated at t=t0 unavoidable ESR and ESL effect, which follows the (1) Capacitor provides most of transient current while output current transient occurs equation 11 and 12. And we can see the difference from the implementation of the larger and smaller (2) The output inductor current starts to ramp up output capacitors at the same test condition. (3) Inductor current goes up to cover both of the output current and the current charge back to Conclusion capacitor (4) Output current is provided by inductor current The following tips should be noticed to prevent your applications from ESR and ESL effects. l Linear output part Care must be taken for the different placement as shown in figure 14. l An appropriate layout applied. l Sufficient grounding implemented. l Suitable measurement taken as in figure 15. [4] Figure 13. Output Transient in LDO Controller Output 8 AN015 figure 14. The Placement of Capacitors[5] Figure 15. Correct Measurement for Transient Response Reference [1] Harris Benson, University Physics, John Wiley & Sons, 1995, Chapter 26 [2] Philips T. Krein, Elements of Power Electronics, Oxford Univ Press, 1998, pp384-385, 392 [3] Analog integrations Corporation, AIC1570 Data Sheet, AIC, 2000 http://www.analog.com.tw/products.htm [4] Gloria, The best source of Electrolytic Capacitors, GAE Radial low ESR, [5] http://www.glorai-cap.com.tw [6] Gloria, The best source of Electrolytic Capacitors, General Information for Application, http://www.glorai-cap.com.tw 9