1

Bu

s D

esig

n B

oo

t C

amp

Chapter 8

Differential Signaling

Instructor: Howard Heck

2

Bu

s D

esig

n B

oo

t C

amp

Day 1 Introduction – Bus design Overview          Falconer      0.25 Transmission Line Fundamentals            Leddige       2.0 Digital Timing Analysis                           Heck           2.0 Crosstalk                                              Falconer      2.0 Non-ideal Interconnect     Hall   2.0       

Day 2 Connectors, Packages and Vias             Mix               2.0 NIRPS, SSO, Power Delivery                  Hall               2.0 Differential Signaling                               Heck             2.0 Buffer Modeling                                      Nelson          2.0

Day 3 Introduction to network analysis              Hall               2.0 Equalization Overview                             Heck             2.0 Design Methodology (DOE & PD)            Shykind         2.0 High Speed Meas & Validation                McCall           2.0 

Schedule

3

Bu

s D

esig

n B

oo

t C

amp

Contents

IntroductionCommon and Differential ModesCommon Mode Noise RejectionTerminationTransmitters & ReceiversDifferential Printed Circuit Boards

StructuresLossesCommon Mode Conversion in PCBs

Differential S-ParametersSummaryReferences

4

Bu

s D

esig

n B

oo

t C

amp

Introduction

Differential signaling uses two conductors per signal. The transmitter translates the single input signal into a pair

of outputs that are driven 180° out of phase. The receiver, a differential amplifier, recovers the signal as

the difference in the voltages on the two lines.

The cost of differential signaling seems clear – 2x the # of signal pins (die, package) and PCB traces.

So, why do this? What’s the benefit?

+

-

V(t)

V+(t)

V-(t)

V(t-l/p)

l

Differential PairDifferentialTransmitter

DifferentialReceiver

5

Bu

s D

esig

n B

oo

t C

amp

Differential Signaling Description

Recall from the crosstalk chapter that for a system with 2 signal conductors (& 1 reference conductor) there are 2 modes (even and odd mode).

Treating them as completely isolated, all signals on the lines propagation as a combination of the two modes.

Since the two lines are driven 180° out of phase, the waves will propagate in the odd mode.

HE E

H

Even ModeEven Mode Odd ModeOdd Mode

6

Bu

s D

esig

n B

oo

t C

amp

Differential Signaling Description If the pair is not isolated, signals on the other conductors

will affect the propagation. More modes will exist, and signals will be a combination of all of

those modes.

Noise from those conductors, and from any other sources, can be decomposed into two “modes” – common and differential.

These aren’t actual modes, but they provide a convenient and useful way of looking at the components of the signal.

HE E

H

Even ModeEven Mode Odd ModeOdd Mode

7

Bu

s D

esig

n B

oo

t C

amp

Common and Differential Modes Differential mode signals propagate 180° out of phase. Common mode signals propagate in phase. The receiver is essentially a differential sense amplifier.

The output depends on the difference between the inputs. Since common mode signals are in phase, a purely common

mode signal tends to put the receiver into an unstable state.

The answer to “why differential” lies in understanding how injection of a common mode noise signal on top of a differential signal affects the operation of the receiver.

+

-

+

-

8

Bu

s D

esig

n B

oo

t C

amp

Common Mode Noise Rejection

The signal to be transmitted is represented by voltage, V(t). The two out-of-phase waveforms are defined as:

201

tVVtV

202

tVVtV

[8.1]

[8.2]

where V0 is a constant

Modal decomposition of the the signal pair (see Young, chapters 10 & 11) allows us to analyze coupled lines without explicitly using mutual circuit elements.

odd

evenVV

VV

V

V

V

VV

2

2

2

1

21

21

21

21

12

12

[8.3]

9

Bu

s D

esig

n B

oo

t C

amp

Common Mode Noise Rejection #2

Combing the first three equations:

0

0012 22

222

VtVVtVVtVtV

tVeven

22

222

0012 tVtVVtVVtVtV

tVodd

[8.4]

[8.5]

Veven carries only a DC component, so it generates no noise due to reactive parasitics, or SSO.

Vodd carries a scaled version of the signal.

If lines are tightly coupled (not always the case), then noise from external sources affects both lines as common mode noise.

Transients on the two conductors tend to be self canceling, greatly reducing power supply noise.

Benefit #1Benefit #1

Benefit #2Benefit #2

Benefit #3Benefit #3

10

Bu

s D

esig

n B

oo

t C

amp

Common Mode Noise Rejection #3 In summary, differential signaling offers excellent immunity

to SSO & crosstalk. i.e. the receiver rejects the common mode noise. Even mode picks up the common mode noise. Odd mode remains noise free.

To prove it, we can superimpose common mode noise, Vnoise(t), in the mode voltages at the receiver:

[8.5]

[8.4] tVVttV noiseeven 02

2

p

odd

vltV

ttV

11

Bu

s D

esig

n B

oo

t C

amp

Common Mode Noise Rejection #4 Now translate the voltages back to back to V+ and V-:

[8.6]

[8.7]

22

2

2

0pv

l

noiseoddeven

tVtVVttVttV

ttV

22

0

pnoisev

ltVtV

VttV

22

2

2

0pv

l

noiseoddeven

tVtVVttVttV

ttV

22

0

pnoisev

ltVtV

VttV

12

Bu

s D

esig

n B

oo

t C

amp

Common Mode Noise Rejection #3

The differential receiver detects the signal as the difference between V+ and V- :

[8.8] ttVttVrcv

Vóila! The common mode noise has been removed. In practice, receivers aren’t perfect and some common

mode noise gets through. Differential receivers typically spec a common mode rejection ratio

(CMRR).

22

2

22

2 00pp v

l

noisev

l

noise

rcv

tVtVV

tVtVV

ttVttVttV

13

Bu

s D

esig

n B

oo

t C

amp

Final Thoughts on CM Rejection Breaks in symmetry cause mode conversion between

even and odd modes, which will inject common mode noise onto the signal. Examples: serpentines reference plane changes crosstalk electrical length mismatch

Note that while differential signaling requires 2x the pins, the immunity to SSO noise allows us to reduce the number of power and ground pins in packages, sockets, and connectors. It may also allow us to remove some decoupling.

Finally, realize that the common mode rejection ratio (CMRR) of the receiver will affect performance, too.

14

Bu

s D

esig

n B

oo

t C

amp

Benefit of Differential Signaling

A differential pair shares a common return path, but the common mode noise introduced by the return path is rejected by the differential receiver.

This makes differential signaling much quieter than single ended signaling. Remember Shannon’s theorem: SNR limits performance.

So, differential signaling can operate at much Higher data rates. Must be at >2x to make it worthwhile.

High speed links operating in excess of ~1 Gb/s use differential signaling (e.g. Infiniband, PCI-Express).

In fact, differential signals are already used for high speed clocks in desktop PCs.

15

Bu

s D

esig

n B

oo

t C

amp

Termination of Differential Signals

The goal is to terminate the signals in a resistor network that terminates each mode.

We can use a pi network to terminate both the even and odd modes.

We can again use modal decomposition.

[8.9]

oddeven

oddodd

even

even

odd

even

ZyZy

ZyZyZy

Zy

,02,01

,02,01

,01

,01

21

210

01

1

0

0

The optimum termination will give us even = odd = 0.

01

1

,01

,01

even

even

Zy

Zy

evenZy,0

11

1/y1

1/y1

1/y2

021

21

,02,01

,02,01

oddeven

oddodd

ZyZy

ZyZy

oddeven

oddeven

ZZ

ZZy

,0,0

,0,02 2

[8.10]

[8.11]

16

Bu

s D

esig

n B

oo

t C

amp

Differential Transmitters

Differential signaling typically uses current-mode transmitters. One example is shown here (a source coupled pair).

Features: provides an extremely sharp transient response

because the current switches from 0 to k·Iref over a half volt input swing.

Draws constant current from the supply, which reduces the AC component of power supply noise.

The source voltage, VS, is stable, reducing the turn-on transient that results with a switched current-source configuration.

Other options include using a cascode current mirror to reduce the output capacitance.

Irefin in

lineline

Vs

17

Bu

s D

esig

n B

oo

t C

amp

Differential Receivers

Source coupled FET receivers are often used with differential signaling.

An example is shown here (self-biasing Chappell Amplifier).

Dally provides a good reference on differential transmitter and receiver circuits.

in in

out

18

Bu

s D

esig

n B

oo

t C

amp

Differential PCBs It is possible to implement tightly

coupled differential interconnects, e.g. using twisted pair wires. Coupling is 99.9%

It is not practical to do so in a PCB: Typical coupling for differential

traces is 20-50%. This is OK, as long as the traces

are symmetrical. Routing with minimum spacing

is OK, but must be maintainedor we’ll get an impedance discontinuity.

Trace lengths must be matched, or common mode current will be generated. The amount of current imbalance can be expressed as:

0.010"

0.038"

r=2.5

AWG 24 Wire

5

5

52

4.5

2.5

r=4.2

r=4.2

56,0 quietZ 872 ,0,0 odddiff ZZ

diffr

d It

l

Imbalance [8.12]

19

Bu

s D

esig

n B

oo

t C

amp

Differential PCBs #2 Differential impedance is defined as:

Differential impedance control in HVM PCBs is typically 15-20%. Versus single ended impedance (10-15%). Strongly influenced by the etch profile (W1, W2).

Skin effect will show up differently than with single ended lines.

odddiff ZZ ,0,0 2 [8.13]

w1

st

h1

h2

r1

r2

w2

20

Bu

s D

esig

n B

oo

t C

amp

Current Distribution & Differential Losses For coupled differential

lines, the virtual ground will pull the current to the edges.

Current flows in a smaller area, which increases resistance.

t

W E

Virtual Ground

For very narrow spacing, the current area will asymptote to t·skin .

For very wide spacing, the current area will asymptote to W·skin .

Narrow Spacing Intermediate Spacing Wide Spacing

21

Bu

s D

esig

n B

oo

t C

amp

Current Distribution and Differential Losses

Ports are matched to Zdiff.

Current distributions effect the loss.

Evidence of a minimum loss “sweet spot”.

2

5

4.5

Vary

Zdiff variesZdiffZodd

1 2

Differential Single LineTransitional

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

1 10 100 1000Spacing [mils]

Lo

ss (

1-|S

21|)

5 GHz

10 GHz

22

Bu

s D

esig

n B

oo

t C

amp

Phenomenon:Phenomenon: Differential pairs see variation in effective dielectric constant due to local non-uniformity.

D+D+

D-D-r = 3.5

FR4 Glass Cloth w/ FR4 Glass Cloth w/ Differential SignalsDifferential Signals

r = 3.3

D+D+ D-D-

Glass Epoxy

10 mils10 mils

16.7 mils16.7 mils

Glass

Root CauseRoot Cause: Different dielectric constants (r): glass ~ 6, epoxy ~ 3A line routed over a glass

bundle travels more slowly due to the higher r (& vice versa).

Converts differential signals to common mode thru electrical length mismatch caused by the r difference.

Common Mode Conversion in PCBs

23

Bu

s D

esig

n B

oo

t C

amp

Transmitter ReceiverD+

D-

Vdiff = D+D-

V

-V

0

V

-V

0Vcomm = D+ + D

2

V

-V

0

V

-V

0

MechanismMechanism

Differential phase skew degrades voltage & Differential phase skew degrades voltage & timing margins.timing margins.

Common Mode Conversion in PCBs #2

24

Bu

s D

esig

n B

oo

t C

amp

Impact:Impact: Max data rate degradation.Noise , SNR .

0.00

0.05

0.10

0.15

0.20

0.25

0 5 10 15Length [in]

% V

olt

age

No

ise 5 Gb/s

10 Gb/s

0

40

80

120

160

200

0 5 10 15Length [in]

Tim

ing

No

ise

[ps]

5 Gb/s

10 Gb/s

In the plots, In the plots, r1,effr1,eff = 3.3 and = 3.3 and r2,effr2,eff = 3.5. = 3.5.

Mode Conversion in PCBs #3

DDjzjzz

DM

CMnoise

eee

zV

lzVzV

2

1

0,%

0

,

ceffr where

bitcellnoisenoise tzVzt ,%,

= 1 dB/inr,effr,eff (D+) = 3.3(D+) = 3.3

r,eff r,eff (D-) = 3.5(D-) = 3.5

~15 ps/inPhase skew

1st order model:

25

Bu

s D

esig

n B

oo

t C

amp

Example 1:Balanced Ckt/Length Skew Ckt

Circuit: 3 differential pairs. 12” traces with 5 mil space

between all traces. Terminated in Zodd at both

ends. 16.67 mA current source

transmitter. Only the middle pairs driven. Results are plotted for D2 &

D2. In the skewed case, D2 is

0.1” longer than D2.

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.0 0.5 1.0 1.5 2.0 2.5 3.0

time [ns]

vo

lta

ge

[V

] V(Tx)

V(Rx)

Vbar(Tx)

Vbar(Rx)

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.0 0.5 1.0 1.5 2.0 2.5 3.0

time [ns]

vo

lta

ge

[V

] V(Tx)V(Rx)Vbar(Tx)Vbar(Rx)

Balanced

Skewed

55

55

55

55

55

5

D1 D1 D2 D2 D3 D3

26

Bu

s D

esig

n B

oo

t C

amp

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1.4 1.5 1.6 1.7 1.8

time [ns]

Vco

mm

[V

]

Balanced - RxSkewed Rx

-0.50

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

1.4 1.5 1.6 1.7 1.8

time [ns]

Vdi

ff [

V]

Balanced - RxSkewed - Rx

Example 1:Balanced Ckt/Length Skew CktHere are the common mode and differential mode waveforms at the receiver.

Common Mode

Differential Mode

27

Bu

s D

esig

n B

oo

t C

amp 0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

1.4 1.5 1.6 1.7 1.8

time [ns]

Vco

mm

[V

]

Balanced - RxCase1 - RxCase 2 - Rx

Example 2: CrosstalkSame 3 differential pairs

Trace Case 1 Case 2

D1 Quiet Quiet

D1bar Quiet Quiet

D2 LH LH

D2bar HL HL

D3 HL LH

D3bar LH HL

Common Mode

Differential Mode

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.0 0.5 1.0 1.5 2.0 2.5 3.0

time [ns]

vo

lta

ge

[V

] V(Tx)V(Rx)Vbar(Tx)Vbar(Rx)

Case 1

-0.50

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

1.4 1.5 1.6 1.7 1.8

time [ns]

Vdi

ff [

V]

Balanced - RxXtalk1 RxXtalk2 Rx

28

Bu

s D

esig

n B

oo

t C

amp

Differential S-Parameters

Differential S-Parameters are derived from a 4-port measurement.

Traditional 4-port measurements are taken by driving each port, and recording the response at all other ports while terminated in 50.

Although, it is perfectly adequate to describe a differential pair with 4-port single ended s-parameters, it is more useful to convert to a multi-mode port.

4 Port

1

3

b1a3

b3

b2a4

b4

4

3

2

1

44434241

34333231

24232221

14131211

4

3

2

1

a

a

a

a

SSSS

SSSS

SSSS

SSSS

b

b

b

b

29

Bu

s D

esig

n B

oo

t C

amp

Multi-Mode S-Parameters

Matrix assumes differential and common mode stimulus.

Specify the differential S-parameters in terms of differential and common mode responses.Differential stimulus, differential responseCommon mode stimulus, common mode responseDifferential stimulus, common mode response (aka ACCM Noise)Common mode stimulus, differential response

This can be done either by driving the network with differential and common mode stimulus, or by converting the traditional 4-port s-matrix.Converting the s-matrix alLs the use of the 4-port VNA.

2

1

2

1

44434241

34333231

24232221

14131211

2

1

2

1

cm

cm

dm

dm

cccccdcd

cccccdcd

dcdcdddd

dcdcdddd

cm

cm

dm

dm

a

a

a

a

SSSS

SSSS

SSSS

SSSS

b

b

b

b

4 Port

1

3

bdm1acm1

bcm1

bdm2acm2

bcm2

adm1adm2

30

Bu

s D

esig

n B

oo

t C

amp

Conversion to Multi-Mode S-Parameters Converting the S-parameters into the

multi-mode is a matter of performing some algebra.

Example: Differential return loss, Sdd11:

The stimulus is equal, but opposite: 13 aa 24 aa

2 Port

1

3

b1a3

b3

b2a4

b4

031

31

0;01

111

422

aaaadm

dmdd aa

bb

a

bS

cmdm

4143132121111 aSaSaSaSb

4343332321313 aSaSaSaSb

)()()()( 3414433133321223111131 SSaSSaSSaSSabb

For a symmetrical network: 3412 SS 1432 SS &

1

3414233131321223111111 2

)()()()(

a

SSaSSaSSaSSaSdd

1

3414233131321223111111 2

)()()()(

a

SSaSSaSSaSSaSdd

Also use: 13 aa

24 aa

)(2

13313311111 SSSSSdd

&

[8.15]

[8.16]

31

Bu

s D

esig

n B

oo

t C

amp

Advantages/Disadvantages of Multi-Mode Matrix

Advantages: Describes 4-port network in terms of 4 two port matrices.

Differential Common mode Differential to common mode Common mode to differential

Easier to relate to system specifications. ACCM noise, differential impedance

Disadvantages: Must convert from measured 4-port scattering matrix.

32

Bu

s D

esig

n B

oo

t C

amp

Summary

Differential signaling offers much higher performance by minimizing common mode noise.

Differential transmitters and receivers typically operate in current mode.

Differential PCB traces must be symmetric to minimize the generation of common mode current.Ditto for packages, connectors, and sockets.

33

Bu

s D

esig

n B

oo

t C

amp

References

S. Hall, G. Hall, and J. McCall, High Speed Digital System Design, John Wiley & Sons, Inc. (Wiley Interscience), 2000, 1st edition.

W. Dally and J. Poulton, Digital Systems Engineering, Cambridge University Press, 1998.

B. Young, Digital Signal Integrity, Prentice-Hall PTR, 2001, 1st edition.

Tektronix, Inc., “Differential Oscilloscope Measurements,” Application Note 51W-10540-1, July 1996.

E. Bogatin, M. Resso, “Differential Impedance Measurement With Time Domain Reflectometry,” Agilent Technologies Application Note 1382-5, May 9, 2002

34

Bu

s D

esig

n B

oo

t C

amp

Appendix: Low & High Frequency Losses Some additional details

35

Bu

s D

esig

n B

oo

t C

amp

Differential Microstrip Losses

y = -1E-09x - 1.1925

R2 = 0.9992

y = -5E-10x - 1.2079R2 = 0.9953

-25

-20

-15

-10

-5

0

0 5 10 15 20 25Frequency, GHz

Lo

ss,

dB

tan=0.01

tan=0.03

The plot shows strip losses as a function of frequency and loss tangent assuming smooth conductor (5/5/5).

This indicates that dielectric losses dominate beyond 2.5 GHz to 4 GHz. (i.e. scale linearly with frequency)

36

Bu

s D

esig

n B

oo

t C

amp

-1.8

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Frequency [GHz]

Lo

ss [

dB

]

Low Frequency Loss in Differential strips

Low frequency losses are greater for narrowly spaced differential microstrips.

Model predicts that loss curves for wide and narrow spaces intersect at: 700MHz when tan=0.03, 3 GHz when tan=0.01

W 5 mils

r 4.2

h 4.5 mils

tan 0.03

Zodd 50± 5

W/S/W=5/15/5

W/S/W=5/5/5 Curves Intersect

37

Bu

s D

esig

n B

oo

t C

amp

High Frequency Loss in Differential strips

Model predicts losses that high frequencies increase with for wide spacing. Worse high values of tan. Why?

W 5 mils

r 4.2

h 4.5 mils

tan 0.03

Zodd 50± 5

-30

-25

-20

-15

-10

-5

0

0 5 10 15 20 25Frequency

loss

[d

B]

w=5, s=5w=5, s=10w=5, s=15w=5, s=20

38

Bu

s D

esig

n B

oo

t C

amp

Differential Microstrip Loss Mechanism Conductor losses increase due to skin effect & proximity effect. In absence of dielectric losses, narrow spacing will produce higher

losses due to proximity effect – area of current flow determines losses (approx. f0.5 behavior).

Dielectric losses increase due to damped response of electric dipoles as a function of the frequency of applied oscillating electric field. Dielectric loss increases linearly w/ freq. (assuming homogeneous media).

Why does narrow spacing have the highest losses at low frequencies but the lowest loss at high frequencies? At low frequencies, tan losses are small and losses are dominated by skin and proximity effects.

• Narrow spacing = smaller area for current = high loss At high frequencies, tan losses dominate.

• Smaller spacing leads to more E-fields fringing through the air and less through the lossy dielectric.

Narrow Spacing Wide SpacingCurrent Distribution

E-Fields

39

Bu

s D

esig

n B

oo

t C

amp

High Frequency Loss in Differential Striplines

Narrow spacing remains the highest loss configuration in a stripline at all frequencies.

Since the dielectric media is homogeneous, all the fields are contained within the lossy material.

With no fields fringing into a loss-free dielectric (air), the only conductor losses are affected by spacing.

W 5 mils

r 4.2

B 18 mils

tan 0.03

Zodd 50± 5

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

0 5 10 15 20frequency

loss

, dB

5-5strip,.035-10strip,.035-15strip,.035-20strip,.03