Capacitor and Inductor Fundamentals

Applications

1 What is Low Voltage DC?

Consumer Industrial Computing Telecoms Automotive Medical Mil/Aero

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

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 퐶푎푝푎푐𝑖푡푎푛푐푒 = 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)

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)

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 = 2fL 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)

Rparallel

ESR ESL

Switch Closed

Load Current

Current ON Charge Capacitor Supply Load Requirements

ESR

VC = VL(Closed) - VESR

V = V - V Switch Open L(Open) C ESR

Load Current Current Stopped Discharge Capacitor Supply Load Requirements

ESR

VL(Open) = VL(Closed) – 2xVESR

Ideal +ESR

+L MLCC (X5R)

+DC Bias

+Cap Roll-Off Polymer

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

• 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

Impedance and ESR – C1206C106K8RAC @ 25C with 0VDC Bias Impedance and ESR – C1206C106K8RAC @ 85C with 0VDC Bias

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

• 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

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

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.

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(𝑖푛) ൘𝑖(푉𝑖푛) L RS

1 푍 = 1 2 1 2 ( ) +(ω퐶푃 − ) 푅푃 ω퐿 1 Impedance [ohm] Impedance f = 2 LC RS: Series Resistance CP: Parallel Capacitance RP: Parallel Resistance ω: Angular Frequency Frequency

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.

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

Core loss[W] Copper loss[W] 0.2

0.2

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.

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 / / Pinratio 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

Metal Composite Mn-Zn Ferrite

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). Core

Conductor Fringing loss Gap (Eddy current loss) Measurement Magnetic Flux It is necessary to take enough distance between the gap and conductor to avoid crossing magnetic flux to the conductor.

Mn-Zn Ferrite

Metal Composite

Advantages of Ferrite Advantages of Metal Composite 1. Higher inductance with high permeability 1. Very slow saturation 2. Stable inductance below saturation 2. Very stable saturation across temperature range High L and Low DCR capability Good for Auto app especially

Saturation current in an inductor is the current at which the core is completely filled with magnetic flux and it can't take any more. It is the current at which all the magnetic domains in the core are aligned and there are no more available. You cannot saturate an inductor that doesn't have a core. Saturation is related to the quantity of material in the core - if saturation is a problem in a circuit, the usual solution is to use a physically larger inductor.

Material Type Ferrite Core Metal Composite Core

Not Good Permeability Good

Magnetic Saturation Not Good Good

Not Good Thermal Property Good

Efficiency Good Not Good