Passive Component Analysis

Passive Component Analysis

OMICRON Lab Webinar Nov. 2015

Page 2Smart Measurement Solutions®

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Agenda

• Why do we analyze passive components

• How to measure component impedance

• A detailed look at a capacitor

• Inductor and transformer

• Filter simulation vs. real world

• Summary


Passive Components

• Essential parts in analog circuits

• Inductor and capacitor used e.g. to store energy or to

create filter circuits

Inductor: 𝑣 𝑡 = 𝐿𝑑𝑖 𝑡

𝑑𝑡𝑋𝐿 = 𝜔𝐿

𝑉

𝐼= 𝑍𝐿 = 𝑗𝜔𝐿

Capacitor: 𝑖 𝑡 = 𝐶𝑑𝑣 𝑡

𝑑𝑡𝑋𝐶 =

−1

𝜔𝐶

𝑉

𝐼= 𝑍𝐶 =

1

𝑗𝜔𝐶


Capacitor:• Plates are resistive

• Rolling of foils creates inductance

• Insulator not lossless

Theory and Reality

• Theoretically inductor and capacitor are purely reactive

elements No resistive behavior and therefore lossless

• In reality parasitics can strongly influence the real

behavior especially at higher frequencies

Examples:

Inductor:• Wire has resistance

• Windings form electric field

• Core is not lossless


Equivalent Circuits

• Are used to model the real behavior of the components

• Different complexity of models

− 1st order models are valid for one frequency

Single Frequency Mode in BAS calculates R, L and C

Frequency Sweep Mode calculates R, L and C over frequency

0

2

4

6

8

10

0

2n

4n

6n

8n

10n

5M 10M 15M 20M 25M 30M 35M 40M

TR

1/O

hm T

R2

/H

f/HzTR1: Rs(Impedance) TR2: Ls(Impedance)


Equivalent Circuits

• Higher complexity models are valid for a frequency range

− 2nd Order equivalent circuits for inductor and capacitor

− 3rd Order models (e.g. quartz crystal or piezo element)

• Parameter identification requires manual

work or e.g. curve-fitting procedure

≙ ≙

see Application Note:

Equivalent Circuit Analysis of Quartz Crystals

https://www.omicron-lab.com/application-notes/


Bode 100 Impedance Measurement Methods

• Direct Measurements

− One-Port Reflection

− Impedance Adapter (3-port technique)

− External bridge (e.g. high impedance bridge)

• Indirect Measurements (via Gain)

− Shunt-Thru (2-port technique)

− Series-Thru (2-port technique)

− Voltage-Current Gain (3-port technique)


Direct Measurement MethodsOne-Port

Recommended for 0.5 Ω - 10 kΩ

Impedance Adapter

Recommended for 20 mΩ - 600 kΩ

External Bridge / Coupler

Range depends on bridge


Indirect Measurement MethodsSeries-Thru

Recommended for 1 kΩ < 10 MΩ

𝑍𝐷𝑈𝑇 = 100 Ω ⋅1 − 𝑆21𝑆21

Shunt-Thru

Recommended for 1 mΩ - 10 Ω

𝑍𝐷𝑈𝑇 = 25Ω ⋅𝑆21

1 − 𝑆21

𝐺𝑎𝑖𝑛 =𝑉𝐶𝐻2𝑉𝐶𝐻1

=𝑉

𝐼= 𝑍𝐷𝑈𝑇

Voltage Current Gain


Impedance Range Overview


Why is it important to measure capacitors?

• A capacitor is NEVER just a capacitor

• Capacitor ESR influences the phase margin of power supplies

• Capacitor ESR influences the output ripple at the switching

frequency of a SMPS

• ESR can change over Frequency

• Capacitors are inductors above

their resonance frequency


What does the data sheet tell us?

220 µF aluminum capacitor

C = 220µF (± 20%)

𝐸𝑆𝑅 =tan 𝛿

𝜔𝐶=

0.12

2𝜋 ⋅ 120𝐻𝑧 ⋅ 220µF= 0.72 Ω@ 120 𝐻𝑧


This is what the measurement tells us

-100

-50

0

50

100

102 103 104 105 106 107

TR

2/°

f/HzTR2: Phase(Impedance)

Phase

-210

-110

010

110

102 103 104 105 106 107

TR

1/O

hm

f/HzTR1: Mag(Impedance)

Impedance

Capacity

f/Hz TR1/Ohm

Cursor 1 120,000 233,077m

1

-210

-110

010

102 103 104 105 106 107

TR

1/O

hm

f/HzTR1: Rs(Impedance)

ESR


Calibration

Open

Short Load


User Calibration / Probe Calibration

• User Calibration (User Range Calibration)

Calibrates at exactly the frequencies that are currently measured

+ No interpolation, suitable for narrowband probes

• Probe Calibration (Full Range Calibration)

calibrates at pre-defined frequencies and interpolates in-between

+ Calibration does not get lost when frequency range is changed


Detailed Example available

-5m

-4m

-3m

-2m

-1m

0

1m

2m

3m

4m

5m

101 102 103 104 105 106

TR

2/F

f/HzTR2: Cs(Impedance)

-210

-110

010

101 102 103 104 105 106

TR

1/O

hm



Capacitor ESR Measurement with Bode 100 and B-WIC



Fitting Model to Measured Impedance

• Various methods

available

• We use curve-fitting

• A Preview tool is

available on

request


Simulation vs. Measurement

-210

-110

010

110

210

310

-90

-60

-30

0

30

60

90

101 102 103 104 105 106 107

TR

1/O

hm T

R2

/°

f/HzTR1: Mag(Impedance) TR2: Phase(Impedance)


Voltage sensitivity of capacitors


DC Biased Impedance Measurements



Why should we measure inductors?

• An inductor is NEVER just an inductor

• AC resistance <> DC resistance

− skin effects

− “Eddie Currents”

• Inductors have resonance frequencies

• Inductors with magnetic cores can have core losses


What does the data sheet tell us?

33 µH shielded power inductor

H = 33µH (± 20%) @ 1 kHz𝑅𝐷𝐶=0,049 𝛺 (𝑡𝑦𝑝.)𝑅𝐷𝐶=0,057 𝛺 (𝑚𝑎𝑥.)fres = 11 MHz


f/Hz TR2/H

Cursor 1 292,486 33,019µCursor 2 101,789k 30,551µ

C2-C1 101,496k -2,468µ

1 2

-200u

-100u

0

100u

200u

300u

102 103 104 105 106 107

TR

2/H

f/HzTR2: Ls(Impedance)

f/Hz TR1/Ohm

Cursor 1 292,486 40,049mCursor 2 101,789k 759,543m

C2-C1 101,496k 719,494m

1 2

-110

010

110

210

310

410

102 103 104 105 106 107

TR

1/O

hm


f/Hz TR2/°

Cursor 1 13,362M -5,879

1

-200

-150

-100

-50

0

50

100

150

200

102 103 104 105 106 107

TR

2/°

f/HzTR2: Phase(Impedance)

f/Hz TR1/Ohm

Cursor 1 13,362M 40,673k

1

-110

010

110

210

310

410

102 103 104 105 106 107

TR

1/O

hm

f/HzTR1: Mag(Impedance)

This is what the measurement tells us

Impedance

Inductance

ESR

Phase


Flyback Transformer Leakage Inductance

• Not all flux generated by the primary winding is coupled to the secondary winding

− some flux leaks

− some contributes to core losses

• Represented by a series inductance in the circuit

• Leakage inductance creates a voltage spike when turning off current through primary side (flyback converter)


Measuring Leakage Inductance

Leakage inductance is measured by shorting all other

windings except the primary winding

-110

010

110

210

310

410

510

103 104 105 106 107

TR

1/O

hm

f/HzTR1: Mag(Impedance) Memory 1 : Mag(Impedance)

0

2u

4u

6u

8u

10u

12u

103 104 105 106 107

TR

2/H

f/HzTR2: Ls(Impedance)

Leakage inductance is not constant over frequency

Secondary open Secondary shorted Leakage inductance


LC Filter Bode Diagram

Passband

Resonance

(Double-pole)

Stopband

-40dB/Decade

-180° Phase

Simulation in LTSpice:


LC Filter Test board

Measuring the voltage transfer function 𝐻 𝑗𝜔 =𝑉𝑜𝑢𝑡

𝑉𝑖𝑛


Measurement vs. Simulation

Measurement

Simulation

• Stopband is

different

• Phase does not

reach -180°

• Second resonance

at 30 MHz

parasitic effects


-140

-120

-100

-80

-60

-40

-20

0

20

-180

-150

-120-90-60

-300

30

60

90120

150

180

101 102 103 104 105 106 107

TR

1/d

B TR

2/°

f/HzTR1: Mag(Gain) TR2: Phase(Gain)

LC Filter Including Parasitics

• much better fit

between

simulation and

measurement

• Could be further

improved by better

component

models


Reducing Output Ripple

2 x 10µF ceramics adds 20dB attenuation at 300 kHz

f/Hz TR1/dB

Cursor 1 290,070k -62,575

1

-80

-60

-40

-20

0

101 102 103 104 105 106 107

TR

1/d

B

f/HzTR1: Mag(Gain) Memory 1 : Mag(Gain)

Imroved stop

band

performance

at 300 kHz

(e.g. switching

frequency)


Summary

• Component parasitics are

important to understand real life

circuit behavior

• Models considering parasitics

allow better simulation

• Measuring components can tell us more

than the data sheet says

Thank you for your attention!

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Passive Component Analysis