Capacitor and Inductor Fundamentals Applications 1 What is Low Voltage DC? Consumer Industrial Computing Telecoms Automotive Medical Mil/Aero © 2019 KEMET Corporation Trends http://magazine.sfpe.org/issue-73-effects-radiant-heat-flux-clean-agent-performance-class-c-fires 1.Mark Owen et al. “Datacom Equipment Power Trends and Cooling Applications”, ASHRAE Datacom Series, ASHRAE, Atlanta, GA, 2012. http://www.futuretimeline.net/subject/computers-internet.htm © 2019 KEMET Corporation Capacitor Fundamentals Parasitics © 2019 KEMET Corporation Ideal Capacitors The value of a capacitor is measured in farads. Dielectric Electrode For 1 farad of capacitance, 1 coulomb of charge is stored on the plates, when 1 volt of force is applied. 1 푐표푢푙표푚푏 1퐹 = 휖 퐾퐴 1푉 + - 퐶 = 표 푄 = 푐ℎ푎푟푔푒 푑 퐶푎푝푎푐푡푎푛푐푒 = 푉 = 푉표푙푡푎푔푒 1 coulomb: ~ 6 x 1019 electrons 휖표: permittivity of free space K: dielectric constant A: surface area of electrodes Distance d: distance between the electrodes © 2019 KEMET Corporation “Pure” Capacitor Impedance vs. Freq. 47 µF Capacitance 1.E+05 C 1.E+04 1.E+03 1 1.E+02 푍 = 푋퐶 = 1.E+01 2휋푓퐶 1.E+00 Impedance (Ohms) Impedance 1.E-01 1.E-02 Z: impedance (Ohms) 1.E-03 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 푓: frequency (Hertz) Frequency (kHz) C: capacitance (Farads) XC: capacitive reactance (Ohms) © 2019 KEMET Corporation Capacitor with Equivalent Series Resistance Impedance vs. Freq. 47 µF Capacitance 1.E+05 0.25 Ohms ESR 1.E+04 0.10 Ohms ESR 1.E+03 0.05 Ohms ESR C ESR 0.01 Ohms ESR 1.E+02 0.001 Ohms ESR 1.E+01 1.E+00 Impedance (Ohms) Impedance 1.E-01 1.E-02 2 2 1.E-03 Z = X C + ESR 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 Frequency (kHz) ESR: Equivalent Series Resistance (Ohms) © 2019 KEMET Corporation Capacitor with Equivalent Series Resistance and Inductance Impedance vs. Freq. 47 µF Capacitance with 2.5 nH ESL 1.E+05 0.25 Ohms ESR 1.E+04 C ESR ESL 0.10 Ohms ESR 1.E+03 0.05 Ohms ESR 1.E+02 0.01 Ohms ESR 0.001 Ohms ESR 1.E+01 1.E+00 1 2 2 Z = ( X C − X L ) + ESR Impedance(Ohms) 1.E-01 f = 1.E-02 2 LC 1.E-03 X L = 2fL 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 Frequency (kHz) self-resonant frequency. L: inductance (Henries) XL: inductive reactance (Ohms) © 2019 KEMET Corporation Capacitor Fundamentals Parasitics and Ripple Voltage © 2019 KEMET Corporation Capacitor Equivalent Circuit Rparallel ESR ESL C © 2019 KEMET Corporation Capacitor Charge ESR Impact Switch Closed Load Current Current ON Charge Capacitor Supply Load Requirements ESR VC = VL(Closed) - VESR © 2019 KEMET Corporation Capacitor Discharge ESR Impact V = V - V Switch Open L(Open) C ESR Load Current Current Stopped Discharge Capacitor Supply Load Requirements ESR VL(Open) = VL(Closed) – 2xVESR © 2019 KEMET Corporation Ripple Voltage Effects Ideal +ESR +L MLCC (X5R) +DC Bias +Cap Roll-Off Polymer © 2019 KEMET Corporation Transient Response (C+ESR+ESL) Voltage recovery from Power Supply Unit (PSU) ESR Voltage drop Capacitance Induced Capacitance: 200 µF Voltage drop 20mv ESR: 33 mΩ ESL: 100 nH ESL Voltage Spikes © 2019 KEMET Corporation Capacitor Fundamentals Ripple Current and ESR © 2019 KEMET Corporation Ripple Current Capability • Ripple current refers to the AC portion of the current signal applied to a device. • Heat is generated by ripple currents. • Several factors contribute to the ripple capability of a capacitor: – Dielectric material and associated DF – Electrodes – Frequency – Package size (surface area) – Package leads – Allowable temperature rise – Heat sink & cooling system © 2019 KEMET Corporation Ripple Current Temperature Rise © 2019 KEMET Corporation Ripple Current ESR Changes with Temperature Impedance and ESR – C1206C106K8RAC @ 25C with 0VDC Bias Impedance and ESR – C1206C106K8RAC @ 85C with 0VDC Bias 푃 = 퐼2푅 © 2019 KEMET Corporation Ripple Current K-SIM Example: C1206C106K8RAC © 2019 KEMET Corporation Why ESR is Important Power Consumption (Heat) 푃 = 퐼2푅 25 2.5 0.25 20 2 0.2 151.5 0.15 101 0.1 Power (Watts) Power Power (Watts) Power Power (Watts) Power 5 0.50.05 00 0 0.01 0.01 0.010.1 0.1 1 ResistanceResistanceResistance (Ohms) (Ohms) (Ohms) 0.25 A 1.0 A 5.0 A Lower ESR ➔ Lower Power Losses ➔ Higher Efficiency © 2019 KEMET Corporation Why ESR is Important • Why ESR is important: – Power Loss = 퐼푅푀푆 ∗ 퐼푅푀푆 ∗ 퐸푆푅 – Simplified to 퐼퐴푉퐺 below (loss is a little higher with 퐼푅푀푆) 푃퐴푉퐺 = 1A x 1A x 0.010Ω = 10mW (using 1A average current) 푃퐴푉퐺 = 5A x 5A x 0.010Ω = 250mW (using 5A average current) Lower ESR ➔ Lower Power Losses ➔ Higher Efficiency © 2019 KEMET Corporation ESR Comparisons Across Dielectrics Minimum ESR in Ohms 0.12 Temperature Dependence 0.1 Red = High Gold = Medium 0.08 Blue = Low 0.06 0.04 0.02 0 Aluminum Polymer Aluminum Ceramic Tantalum Polymer Tantalum MnO2 Film Electrolytic Minimum ESR in Ohms 0.003 0.12 0.001 0.006 0.035 0.001 Aluminum Polymer Aluminum Electrolytic Ceramic Tantalum Polymer Tantalum MnO2 Film © 2019 KEMET Corporation Inductor Fundamentals © 2019 KEMET Corporation What is an Inductor? The inductance is the property of an inductor that tends to oppose any change in the current flowing. Conductor Magnetic flux direction φ according to Lenz's law e: electromotive force dφ/dt: change of magnetic flux over the change in time e i di/dt: change in current over the change in time dφ di e = - = - L x [V] dt dt • The Inductor generates an inductive electromotive force when a DC current varies. • Unit is “H” (henry) • 1H means the inductance value that generates self induction electromotive force of 1 Volt when a DC current varying at a rate of 1 amp per second. © 2019 KEMET Corporation Permeability of Inductor Cores Conductor Magnetic core Magnetic flux direction Magnetic flux direction according to Lenz's law according to Lenz's law lm Permeability for air Magnetic core Permeability Magnetic Resistance µ = μ =4π × 10−7 µ = μ x μ l 0 S 0 m lm : Magnetic path length Rm = μS x μ0 x S S : Effective area L: Inductance [H] µ0: Permeability for Air [H/m] 2 N 2 S µS: Relative permeability L = = μS x µ0 x N x N : Number of turns R lm m R : Magnetic resistance of core [A/Wb] © 2019 KEMET Corporationm Impedance of an Actual Inductor 푉(푛) ൘(푉푛) L RS CP RP 1 1 푍 = f = 1 2 1 2 ( ) +(ω퐶2푃− LC) 푅푃 ω퐿 Impedance [ohm] Impedance RS: Series Resistance CP: Parallel Capacitance RP: Parallel Resistance ω: Angular Frequency Frequency © 2019 KEMET Corporation Factors Affecting Inductance Turns Core Material More turns of wire = greater amount Greater magnetic permeability = greater magnetic field flux. of magnetic field force. Coil Area Coil Length Greater coil area = less opposition to the Longer path for the magnetic field flux = more opposition formation of magnetic field flux. to the flux formation. © 2019 KEMET Corporation Three Types of Losses for an Inductor Copper (Resistive) Loss Core Loss Fringing Loss Heat produced by electrical Loss that occurs in a A phenomenon in which the currents in the conductors of magnetic core due to magnetic flux flowing in a transformer windings, or other alternating magnetization, magnetic core spreads out electrical devices. which is the sum of the (or fringes out) into the hysteresis loss and the eddy surrounding medium, for current loss example in the vicinity of an air gap © 2019 KEMET Corporation Loss Balance in the Hard Switching Topology Core loss[W] Copper loss[W] 0.2 0.2 0.1 0.1 Total loss[W] Total 0.0 1 2 3 4 5 10 20 I0-peak [A] When current is getting higher, Copper loss dominates in hard switching topology But in lower current range, Core loss dominates. And in normal computing (Interactive Architecture), the lower range is dominant in operation. Idling time realizes pretty small current which is close to 0A by current technology. And idling time can be 80% over in operation. © 2019 KEMET Corporation Circuit Efficiency According to the Inductor Core loss affects the loss in lower range 90% 800[w/m3] Low loss material 89% (SENNTIXII) 88% 87% Std material 2500[w/m3] 86% Competitor Pout / Pin ratio Pout 85% 3000[w/m3] 84% MPCG MPC 83% Competitor C 82% 0 2 4 6 8 10 Load Current [A] Vin:12V, Vout:1.5V L:0.56uH Core loss is important to improve total power consumption on IA computing application © 2019 KEMET Corporation Lower Loss Material Development 10000 SENNTIXIILow loss model Std model High μ model 1000 Under NanometNew low lossDevelopment material Pcv(mW/cc) 100 Better 10 10 100 1000 10000 Freq.(kHz) The lowest core loss by Nanomet © 2019 KEMET Corporation Ferrite and Metal Composite Comparison Core Loss Comparison Metal Composite Mn-Zn Ferrite Advantage of Ferrite Very low core loss in dynamic frequency range Low power consumption capability © 2019 KEMET Corporation Fringing Loss Mechanism • When there is a load current, it generates Magnetic flux. • That flux leaks from the gap of the core. • If the flux crosses to the conductor, it generates eddy current on the conductor. • Eddy current makes AC loss worse (it’s Fringing loss).