capacitor and inductor fundamentals...saturation current in an inductor is the current at which the...

1

Capacitor and Inductor Fundamentals

Applications

© 2019 KEMET Corporation

What is Low Voltage DC?

Consumer Industrial Computing Telecoms Automotive Medical Mil/Aero


Trends

http://www.futuretimeline.net/subject/computers-internet.htm

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.


Capacitor Fundamentals

Parasitics


Ideal Capacitors

Dielectric

Electrode

Distance

𝐶 =𝜖𝑜𝐾𝐴

𝑑 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑎𝑛𝑐𝑒 =𝑄 = 𝑐ℎ𝑎𝑟𝑔𝑒

𝑉 = 𝑉𝑜𝑙𝑡𝑎𝑔𝑒

+ -1𝐹 =

1 𝑐𝑜𝑢𝑙𝑜𝑚𝑏

1𝑉

The value of a capacitor is measured in farads.

For 1 farad of capacitance, 1 coulomb of charge is

stored on the plates, when 1 volt of force is

applied.

1 coulomb: ~ 6 x 1019 electrons

𝜖𝑜: permittivity of free space

K: dielectric constant

A: surface area of electrodes

d: distance between the electrodes


𝑍 = 𝑋𝐶 =1

2𝜋𝑓𝐶

“Pure” Capacitor

Z: impedance (Ohms)

𝑓: frequency (Hertz)

C: capacitance (Farads)

XC: capacitive reactance (Ohms)

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

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

Imp

ed

an

ce

(O

hm

s)

Frequency (kHz)

Impedance vs. Freq. 47 µF Capacitance

C


Capacitor with Equivalent Series Resistance

C ESR

22ESRXZ

C+=1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

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

Imp

ed

an

ce

(O

hm

s)

Frequency (kHz)

Impedance vs. Freq. 47 µF Capacitance

0.25 Ohms ESR

0.10 Ohms ESR

0.05 Ohms ESR

0.01 Ohms ESR

0.001 Ohms ESR

ESR: Equivalent Series Resistance (Ohms)


Capacitor with Equivalent Series Resistance and Inductance

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

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

Imp

ed

an

ce

(O

hm

s)

Frequency (kHz)

Impedance vs. Freq. 47 µF Capacitance with 2.5 nH ESL

0.25 Ohms ESR

0.10 Ohms ESR

0.05 Ohms ESR

0.01 Ohms ESR

0.001 Ohms ESR

C ESR ESL

( ) 22ESRXXZ LC +−=

fLX L 2=

L: inductance (Henries)

XL: inductive reactance (Ohms)

self-resonant frequency.

LCf

=

2

1



Parasitics and Ripple Voltage


Capacitor Equivalent Circuit

ESR ESL

C

Rparallel


Switch Closed

Current

ON Charge

Capacitor

Supply

Load

Requirements

LoadCurrent

ESR

VC = VL(Closed) - VESR

Capacitor ChargeESR Impact


Switch Open

Current

Stopped

DischargeCapacitor

SupplyLoad

Requirements

Load

Current

ESR

VL(Open) = VC - VESR

VL(Open) = VL(Closed) – 2xVESR

Capacitor DischargeESR Impact


Ripple Voltage Effects

Ideal

MLCC (X5R)

Polymer

+ESR

+L

+DC Bias

+Cap Roll-Off


Capacitance: 200 µF

ESR: 33 mΩ

ESL: 100 nH

20

mv

ESL Voltage Spikes

Capacitance Induced

Voltage drop

ESR Voltage drop

Voltage recovery from

Power Supply Unit

(PSU)

Transient Response (C+ESR+ESL)



Ripple Current and ESR


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


Ripple CurrentTemperature Rise


Ripple CurrentESR Changes with Temperature

𝑃 = 𝐼2𝑅

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


Ripple CurrentK-SIM Example: C1206C106K8RAC


Why ESR is ImportantPower Consumption (Heat)

𝑃 = 𝐼2𝑅

Lower ESR Lower Power Losses Higher Efficiency

0

0.05

0.1

0.15

0.2

0.25

0.01

Pow

er

(Watt

s)

Resistance (Ohms)

0.25 A 1.0 A 5.0 A

0

0.5

1

1.5

2

2.5

0.01 0.1

Pow

er

(Watt

s)

Resistance (Ohms)

0.25 A 1.0 A 5.0 A

0

5

10

15

20

25

0.01 0.1 1

Pow

er

(Watt

s)

Resistance (Ohms)

0.25 A 1.0 A 5.0 A


Why ESR is Important

• Why ESR is important:

– Power Loss = 𝐼𝑅𝑀𝑆 ∗ 𝐼𝑅𝑀𝑆 ∗ 𝐸𝑆𝑅

– Simplified to 𝐼𝐴𝑉𝐺 below (loss is a little higher with 𝐼𝑅𝑀𝑆)

𝑃𝐴𝑉𝐺 = 1A x 1A x 0.010Ω = 10mW (using 1A average current)

𝑃𝐴𝑉𝐺 = 5A x 5A x 0.010Ω = 250mW (using 5A average current)

Lower ESR Lower Power Losses Higher Efficiency


ESR Comparisons Across Dielectrics

0

0.02

0.04

0.06

0.08

0.1

0.12

Aluminum Polymer AluminumElectrolytic

Ceramic Tantalum Polymer Tantalum MnO2 Film

Minimum ESR in Ohms 0.003 0.12 0.001 0.006 0.035 0.001

Minimum ESR in Ohms

Aluminum Polymer Aluminum Electrolytic Ceramic Tantalum Polymer Tantalum MnO2 Film

Temperature DependenceRed = High

Gold = Medium

Blue = Low


Inductor Fundamentals


What is an Inductor?

• 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.

Magnetic flux direction

according to Lenz's law

i

φ

e

dφdt

e = - = - L x [V]didt

Conductor

The inductance is the property of an inductor that tends to oppose any change in the current flowing.

e: electromotive force

dφ/dt: change of magnetic flux over the change in time

di/dt: change in current over the change in time


Permeability of Inductor Cores

Conductor Magnetic core

L: Inductance [H]

µ0: Permeability for Air [H/m]

µS: Relative permeability

N : Number of turns

Rm: Magnetic resistance of core [A/Wb]

Permeability for airµ = μ0 =4π × 10−7

Magnetic core Permeabilityµ = μS x μ0

L = N2

Rm

= μS x µ0 x N2 xSlm

Conductor Magnetic core

lm

Magnetic Resistancelm

μS x μ0 x SRm = lm : Magnetic path lengthS : Effective area






Impedance of an Actual Inductor

Frequency

Impedance [

ohm

]

RS: Series Resistance

CP: Parallel Capacitance

RP: Parallel Resistance

ω: Angular Frequency

LCf

=

2

1

൘𝑉(𝑖𝑛)

𝑖(𝑉𝑖𝑛)RS

RP

CP

L

𝑍 =1

(1𝑅𝑃)2+(ω𝐶𝑃 −

1ω𝐿)

2


Factors Affecting Inductance

More turns of wire = greater amount

of magnetic field force.

Greater coil area = less opposition to the

formation of magnetic field flux.

Greater magnetic permeability = greater magnetic field flux.

Longer path for the magnetic field flux = more opposition

to the flux formation.

Turns

Coil Area Coil Length

Core Material


Three Types of Losses for an Inductor

Fringing LossCore LossCopper (Resistive) Loss

A phenomenon in which the

magnetic flux flowing in a

magnetic core spreads out

(or fringes out) into the

surrounding medium, for

example in the vicinity of an

air gap

Loss that occurs in a

magnetic core due to

alternating magnetization,

which is the sum of the

hysteresis loss and the eddy

current loss

Heat produced by electrical

currents in the conductors of

transformer windings, or other

electrical devices.


Loss Balance in the Hard Switching Topology

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.

0.0

0.1

0.1

0.2

0.2

1 2 3 4 5 10 20

Tota

l lo

ss [W

]

I0-peak [A]

Core loss[W] Copper loss[W]


Circuit Efficiency According to the Inductor

82%

83%

84%

85%

86%

87%

88%

89%

90%

0 2 4 6 8 10

Pou

t /

Pin

rat

io

Load Current [A]

MPCG

MPC

Competitor C

Low loss material(SENNTIXII)

Std material

Competitor

Vin:12V, Vout:1.5V L:0.56uH

Core loss affects the loss in lower range

800[w/m3]

2500[w/m3]

3000[w/m3]

Core loss is important to improve total power consumption on IA computing application


Lower Loss Material Development

10

100

1000

10000

10 100 1000 10000

Pcv(m

W/c

c)

Freq.(kHz)

Low loss model

Std model

High μ model

New low loss material

The lowest core loss by Nanomet

SENNTIXII

Nanomet Under Development

Bett

er


Ferrite and Metal Composite ComparisonCore Loss Comparison

Metal Composite

Mn-Zn Ferrite

Very low core loss in dynamic frequency range

Advantage of Ferrite

Low power consumption capability


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).

Gap

Core

Conductor

Magnetic Flux

Fringing loss(Eddy current loss)

It is necessary to take enough distance between the gap and conductor to avoid crossing magnetic flux to the conductor.

Measurement


Ferrite and Metal Composite ComparisonSaturation Characteristics

1. Higher inductance with high permeability

2. Stable inductance below saturation

Advantages of Ferrite

1. Very slow saturation

2. Very stable saturation across temperature range

Advantages of Metal Composite

High L and Low DCR capability Good for Auto app especially

Mn-Zn Ferrite

Metal Composite


Saturation Current

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.


Type of Magnetic Core

Material Type Ferrite Core Metal Composite Core

Permeability GoodNot Good

Magnetic Saturation Not Good Good

Thermal PropertyNot Good

Good

Efficiency Good Not Good


Thank You!

capacitor and inductor fundamentals...saturation current in an inductor is the current at which the...

Documents