Insights from S-parametersInsights from S-parameters

Stephen MuellerStephen Mueller

Field Applications EngineerField Applications Engineer

Agenda

What are s-parameters?What are s-parameters?

Connection between return and insertion lossConnection between return and insertion loss

4 patterns4 patterns

RippleRipple

Monotonic drop-offMonotonic drop-off

Wide dipsWide dips

Narrow dipsNarrow dips

ConclusionConclusion

12/15/14 2

Characterize an Interconnect by How “Precision” Reference Signals Scatter Off a DUT

S11 S21

Incident Wave

Reflected Wave

Transmitted wave

TDR TDT

tTime Domain

tFrequency Domain

waveform out from a port

waveform in to a portparameter =

Measured in time and frequency domains

Displayed in frequency domain

Displayed in time domain

Dec 2013Company Confidential 3

S-Parameters From Many Sources: Measurement, Circuit Simulation, EM Simulation

Electromagnetic simulation

Measurement

Circuit simulation

Teledyne LeCroy SPARQ

Polar Instruments 2D field solver Simbeor 3D Field Solver

Dec 2013Company Confidential 4

The “Ends” as “Ports”

incident

reflected~50Ω Z0 = 50Ω

50 Ω source impedance

Port as a coax cable

11

reflected sine waveS

incident sine wave= =

Phase(S11) = Phase(Vreflected) - Phase(Vincident)

( ) ( )( )incident

reflected11 VAmplitude

VAmplitudeSMag =

• Has magnitude and phase• Can be described as a complex number: real and imaginary

parts

Dec 2013Company Confidential 5

2 Port S-Parameters

S11: Return loss It is the reflected signal Impedance mismatch from 50 Ohms

throughout the interconnect A little about losses

S21: Insertion loss is |S21 in dB| It is the transmitted signal Sensitive to losses Sometimes sensitive to impedance

mismatches throughout the interconnect

~50Ω Z0 = 50Ω

Vsource

Magnitude and phase Detector

DUTmagnitude/

phase detector

50Ω

Z0= 50Ω

Transparent interconnect:S11: large, negative dBS21: small, negative dB

1 S11VSWR

1 S11

+=

−

Dec 2013Company Confidential 6

Connection Between Insertion and Return Loss

lossesSS1 221

211 ++=

Vincident

VtransmittedVreflected How is Vtransmitted related to Vincident and Vreflected?

There is no such thing as conservation of voltageThere is conservation of energy

Energy in a wave ~ V2

21121 S1S −=In a lossless interconnect

Sources of loss:- conductor- dielectric- coupling (cross talk)- radiation

S11 + S21 = 1

How large does S11 have to be to affect S21? What ∆Z is this?Dec 2013Company Confidential 7

-45-40-35-30-25-20-15-10 -5-50 0

-4.5-4.0-3.5-3.0-2.5-2.0-1.5-1.0-0.5

-5.0

0.0

dB(S11_sim)

dB(S

21_s

im)

For Lossless Interconnect:Insertion Loss from Return Loss

21121 S1S −=

S11 of < -10 dB yields S21 > -0.5 dB

When plotted in dB, relationship between When plotted in dB, relationship between S11 and S21 looks unusualS11 and S21 looks unusual

Dec 2013Company Confidential 8

Four Important Patterns in S11, S21(also applies to differential S-parameters)

Ripples in S11, sometimes in S21: reflections

Monotonic drop in S21: losses

Broad dips: ¼ wave stub resonances

Sharp dips (hi Q), coupling to resonances

Insertion loss

return lossInsertion loss

Dec 2013Company Confidential 9

How Return, Insertion Loss Gets its Ripples

When Len << ¼ λ Reflections from front and back, 180 deg out

of phase No net reflection, all transmitted waves in

phase and add S11 large negative dB, S21 nearly 0 db Extrapolating to DC: phase S21 = 0

Z0 < 50 Ohms

When Len << ¼ λ

min S11 max S21

½

0

000

0

50 Ω 50 Ω

S21

S11

At low frequency ALL interconnects

are transparent

Dec 2013Company Confidential 10

When Len = ¼ λ, S21 Lowest, S11 Highest

When Len = (½ x n + ¼ ) λ Max S11, min S21

Z0 < 50 Ohms

min S21

When Len << ¼ λ

When Len = 1/4 λ

½ ¼ ¼ + 0

½ max S11

½ + 0 ¾

min S11 max S21

½

0

000

0

S21

S11

Dec 2013Company Confidential 11

When Z0 ≠ 50 Ohms, Multiple Reflections From The Terminations Cause Ripples

When Len = n x ½ λ Reflected waves from front and back subtract

Minimum reflected signal

Transmitted waves all in phase, S21 max

As frequency increases, insertion, return loss increase, decrease

Longer distance between reflections, shorter the frequency between high and low

Larger the impedance difference, the larger the modulation

Z0 < 50 Ohms

min S21

When Len << ¼ λ

When Len = 1/4 λ

½ ¼ ¼ + 0

½ max S11

½ + 0 ¾

min S11 max S21

½

0

000

0

When Len = ½ λ

min S11 max S21

½

1

½ ½ + 0

1 + 0 1½

S21

S11

Dec 2013Company Confidential 12

Impact of Other Features

Uniform 46 Ohm lossless line

Uniform 46 Ohm lossy line

Uniform 46 Ohm lossy line with connectorsTDR response with

connectors

Connector discontinuities at the ends generally

increase S11 with frequency

Simulated examples

Dec 2013Company Confidential 13

Measured Examples: What do you See?

Dec 2013Company Confidential 14

50 ohm 4 inch MS with capacitive launches

Measured Examples: De-embedding

Dec 2013Company Confidential 15

50 ohm 4 inch MS with capacitive launches de-embedded

Measured Examples: What do you See?

S11

S21

40 dB full scale, 20 GHz full scale

90 ohm 4 inch MS

50 ohm 0.5 inch MS

50 ohm 6 inch MS

50 ohm 3 inch PTFE MS

Dec 2013Company Confidential 16

Attenuation and Insertion LossIn real interconnects, amplitude drops off exponentially with distance

( )dB/len

nepers/lendd 20

out in inV d V e V 10α

−−α= =

d

S21 is attenuation when terminations are matched and there is no S21 is attenuation when terminations are matched and there is no coupling out of the transmission linecoupling out of the transmission line

out

in

VS21

V=

[ ] [ ]out

in

VS21 in dB 20 x log dB / in x d attenuation

V

= = −α = ÷

Dec 2013Company Confidential 17

Estimating Attenuation per Length in 50 Ohm Interconnects

dB/inch

w = line width in milsf in GHzDk = dielectric constantDf = dissipation factor

[ ][ ] [ ]21

21 Len

S dB 1S per Length atten dB / in f 2.3 x f x Df x Dk

Len in w = = = − + ÷

w = 5 milsDk = 4Df = 0.02

Measured attenuation from two different transmission lines

Simple estimate matches measured behavior ok

( )Len GHzatten ~ 2.3 x Df x Dk ~ 0.1dB / inch / GHz− −

Dec 2013Company Confidential 18

The ¼ Wave Stub Resonance

TD, Lenstub 2 x TD

When 2 x TD = ½ cycle, minimum received signalTD = ¼ cycle: the quarter wave resonance

res

1 1TD

4 f=

innsec

LenTD

6=

1.5

Len=res

1 1f

4 TD=

f in GHz Len in inches

Dec 2013Company Confidential 19

¼ Wave Resonance in the Frequency Domain

Lenstub

1.5

Len=

res

1 1f

4 TD=

Stub 0.5 inches longfres = 3 GHz

What is worst case Bit Rate (BR) for this stub?

If Nyquist = 3 GHz, no eye at BR = 6 Gbps

Stub length = 0.5 inches

S21 S11

Where does the energy go?

Dec 2013Company Confidential 20

Measured Example: ~3/8” Stub

Dec 2013Company Confidential 21

1.5

Len=

res

1 1f

4 TD=

fres = 3.9 GHz

Stub 0.385 inches long

Measured Insertion Loss with and without Via Stub in a ¼ inch Thick Backplane

No via stub in the channel

0.2 inch via stub

res

1.5 1.5f 7.5 GHz

Len 0.20= = =

SDD21

SDD11

Dec 2013Company Confidential 22

Coupling to Hi-Q Resonances

What are hi-Q resonators? Any floating metal Plane cavities

Voltage between the two planes

Dec 2013Company Confidential 23

Via to Cavity Coupling in 4 Layer Board

Len

GHz3

Lenx2Dk

GHz12fres ==

3.25 inches

1.187 inches

0.8 inches

Plane resonances expected:Len = 3.25 in fres = 0.92 GHzLen = 1.187 in fres = 2.5 GHzLen = 0.8 in fres = 3.75 GHz

0.8 inches

S21 no return vias

Dec 2013Company Confidential 24

Introducing the SPARQ (“S-Parameters Quick”)

40 GHz frequency range on up to 4 ports, 30GHz to 12 Low cost for performance Single-button-press operation Built-in automatic OSLT calibration Fast calibration and measurement time Small footprint and Portable (4 port: 13” x 13” x 7”, 17 lbs)