**From:** Eric Bogatin (*eric@bogent.com*)

**Date:** Mon Nov 15 1999 - 19:33:39 PST

**Next message:**David Instone: "Re: [SI-LIST] : Differential Pair Theory"**Previous message:**sweir: "Re: [SI-LIST] : Differential Pair Theory"**In reply to:**Chris Bobek: "[SI-LIST] : Differential Pair Theory"**Next in thread:**Christian Schuster: "[SI-LIST] : Passivity of a Linear System"**Reply:**Christian Schuster: "[SI-LIST] : Passivity of a Linear System"

Chris-

I'll take a stab at answering some of your diff pair questions below. They

are actually related to a paper that Mike Resso and I have just drafted on

TDR analysis of diff pairs for DesignCon 2000, and also topics I cover in

the classes I teach. You can find out about the public courses on my web

site at http://www.bogatinenterprises.com/. There are two in early Dec that

go into much more detail on diff impedance than I have included below.

I have tried to develop a simple intuitive explanation of diff pair and diff

impedance, that is understandable, but doesn't compromise the underlying

engineering principles. I have added some specific comments below after your

questions. Of course, this is only the quick version- coincidently, I have a

more complete paper I am currently drafting that will be posted on my web

site at the end of this month.

--eric

Eric Bogatin

BOGATIN ENTERPRISES

Training for Signal Integrity and Interconnect Design

26235 W. 110th Terr.

Olathe, KS 66061

v: 913-393-1305

f: 913-393-1306

pager: 888-775-1138

e: eric@bogent.com

web: <http://www.bogatinenterprises.com/>

*> -----Original Message-----
*

*> From: owner-si-list@silab.eng.sun.com
*

*> [mailto:owner-si-list@silab.eng.sun.com]On Behalf Of Chris Bobek
*

*> Sent: Monday, November 15, 1999 3:28 PM
*

*> To: Si-list
*

*> Subject: [SI-LIST] : Differential Pair Theory
*

*>
*

*>
*

*> Hi,
*

*>
*

*> I am trying to understand how differential pairs behave and how you
*

*> terminate them. I've read app notes and books that tell you how to
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*> terminate them, but I don't know how they derived the values and
*

*> methodology. I would just like a general understanding of what's going
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*> on. I understand how and why termination works on normal, single-ended
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*> lines.
*

*>
*

*> As an example, suppose you had a 100ohm, unshielded, twisted pair cable
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*> that ran for 5000 feet between two boards. Once the pair entered the
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*> board, it was routed over several inches to a differential receiver.
*

*> The two boards do not share a ground (suppose they are battery powered).
*

*>
*

*> 1) How did I know to route the traces on the board as two 50 ohm
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*> traces?
*

*> 2) How did I know to terminate the pair by placing a 100ohm resistor
*

*> between the two traces at the receiver?
*

*> 3) Could I terminate each line separately as if they were two,
*

*> single-ended lines (say, using a 50ohm resistor to ground on each line
*

*> at the receiver?)
*

*> 4) Where does the return current flow as the signal is launched down
*

*> the line from the driver, across the twisted pair, across the diff pair
*

*> on the board, and to the receiver?
*

The short answer is, that to first order, the two traces on the PCB are

really a single ended transmission line. The single ended impedance between

the two signal lines, as a coplanar transmission line, is what we also call

its differential impedance. It is strongly affected by the proximity of the

floating metal plane below. Its single ended impedance will be about 100

Ohms, if the plane is in proximity so as to create a characteristic

impedance of one trace to the plane of 50 Ohms. This may not be a very

comfortable answer to some, so here's a bit more detail:

You seem to have a good feel for the impedance environment of the twisted

pair. You recognize that the twisted pair lines represent a single ended

transmission line, with characteristic impedance of 100 Ohms. To connect

them to the two traces on the second board, you would merely solder one

twisted line wire to the signal trace of one of the board traces, and the

other wire to the second signal line trace pair. The transmission line

composed of the two traces on the board is also a single ended transmission

line. However, the presence of the "floating metal plane" below the traces

strongly influences the characteristic impedance of the transmission line

composed of the coplanar printed traces above the plane.

Suppose the plane were not there, and you had the two printed traces on the

FR4 substrate. They would make up a coplanar transmission line. If they were

5 mil line width and separated by 10 mils, let's say, they would have a

single ended characteristic impedance of about 150 Ohms. Now, slowly bring

the floating metal plane up from below. The presence of the plane will

decrease the characteristic impedance of the two printed traces. The

capacitance per length between the traces will increase, since there is now

an additional capacitive coupling path between the two traces through the

floating metal plane, and the loop inductance per length between them will

decrease because of induced eddy currents in the floating metal plane.

First think about the capacitive coupling through the floating plane. When

the plane is far away, the capacitance between the traces is dominated by

the field coupling from one trace to another, call it C21. The series

capacitance between one trace and the floating plane, C11, and then the

other trace and the floating plane, C22, is small. As the plane is brought

closer, C21 will decrease very slightly, but C11 will increase pretty

rapidly. When the separation to the bottom trace is about on the order of

the trace to trace separation, the total capacitance between the traces

begins to be dominated by the trace to plane separation. So, when the plane

is in proximity to the traces, the coupling between traces is not so

critical, it is the trace to plane separation that determines the

capacitance between the traces, and hence the characteristic impedance

between the two traces.

To first order, the characteristic impedance of the two coplanar traces is

going to be related to 1/Ctotal. And Ctotal is 1/2 C11 + C12. When the plane

is close and the traces are far apart from each other, Ctotal is mostly 1/2

C11. If C11 corresponds to a 50 Ohm line, you can see why the single ended

impedance of the coplanar is 100 Ohms, since there are two of these in

series. When the traces are spaced close together, Ctotal gets larger by the

trace to trace coupling capacitance, and the single ended impedance of the

coplanar lines (differential impedance) decreases. That's why diff impedance

is affected by the trace to trace coupling, but is dominated by the trace to

plane impedance. In most situations, C11 is much larger than C12.

In the case of a standard board stack up, with the floating plane positioned

so as to give the two signal lines a line to plane single ended impedance of

50 Ohms, even at a separation = line width, C11 is about 10x C12- so the

single ended impedance of the coplanar lines is really dominated by the

coupling capacitance through the floating plane. The details of this

analysis and the connection to modes, even and odd impedance and

differential impedance is covered in more detail in the classes I teach.

If you had a coplanar transmission line, with a characteristic impedance of

100 Ohms, and you had to terminate it, you would not blink before you said,

just connect a 100 Ohm resistor between the signal and return path. That's

just like the case above, its just that the characteristic impedance of the

coplanar line is reduced by the proximity of the metal plane. A resistor

across the two coplanar lines is all it takes. In this perspective, you can

also see that connecting two, 50 Ohm resistors from the signal paths to the

floating metal plane is the same as connecting the two 50 Ohm resistors

between the signal lines directly. Its still 100 Ohms total between the two

signal lines.

Now let's look at the current distribution. It's all related to the induced

eddy currents in the floating plane. When the plane is in close proximity,

the propagating signal front, which is the voltage between the two coplanar

signal traces (with its associated current based on the impedance the signal

sees), will induce a mirror image propagating current loop in the plane. The

closer the traces are to the floating metal plane, the larger the induced

current is in the plane. This also contributes to decreasing the

characteristic impedance of the two coplanar traces.

But look at the induced currents in the plane. If there is a current, I, in

one trace, there is -I in the other trace. However, there is an induced

current of -I in the floating metal plane directly below the first trace,

and I in the floating plane below the second trace. Even though there is no

DC connection to the floating plane, there will be induced eddy currents in

it, and these will affect the characteristic impedance of the coplanar

traces. Mike Resso and I will be showing a really neat, simple demo of this

at the DesignCon 2000 Conference.

If you were to do something to prevent these eddy currents from flowing,

such as cut gaps transverse to the traces in the floating plane (a common

technique to minimize eddy currents), you will be increasing the

characteristic impedance of the coplanar single ended transmission line. It

will no longer be 100 Ohms, it may go back up to 140 Ohms, for example.

Think about the current distribution in the two traces and the plane. In

cross section, it sure looks like the induced eddy current is a "return

current" for the signal trace above it. But, I don't like using this term

when there are multiple current paths. All the currents contribute to

affecting the characteristic impedance the signal sees. If they all aren't

carefully controlled, the impedance the signal sees will change, and signal

integrity will be affected. Keeping track of the various currents involves a

more complicated analysis that introduces the concept of modes.

Now think about what is going on at the source board. A signal is launched

into the coplanar pair. But, since they have a plane underneath, their

single ended characteristic impedance is only 100 Ohms. While the coplanar

traces have the uniform plane beneath them, they will have this constant

impedance, and the induced eddy current distributions will be distinct under

each trace. If the plane should be suddenly ended, and the 100 Ohm twisted

pair cable now attached to the end of the coplanar lines, the signal will go

from one 100 Ohm environment to another 100 Ohm environment. Of course,

there is also fringe fields and other sources of discontinuity at the

transition. However, it can be kept small. What happened to the induced eddy

currents in the plane below? The loop was closed and the currents blended

together and cancelled out at the edge.

The same thing happens in reverse on the receiver board- the induced eddy

current loop starts when the signal reaches the edge of the board,

propagates down with the signal and comes together under the SMT 100 Ohm

terminating resistor connecting the two signal traces.

I apologize for taking so long in this explanation. If anyone is interested

in the details, I invite you to attend the short courses I have coming up in

San Jose in Dec. Alternatively, I will be posting an article in my December

downloads, "What really is Differential Impedance?" This is along with the

one on "What really is characteristic impedance?" If you sign in on my web

site, you will be automatically notified when they are posted.

as always, I welcome comments.

--eric

*>
*

*> Thank you very much,
*

*>
*

*> Chris
*

*>
*

*>
*

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**Next message:**David Instone: "Re: [SI-LIST] : Differential Pair Theory"**Previous message:**sweir: "Re: [SI-LIST] : Differential Pair Theory"**In reply to:**Chris Bobek: "[SI-LIST] : Differential Pair Theory"**Next in thread:**Christian Schuster: "[SI-LIST] : Passivity of a Linear System"**Reply:**Christian Schuster: "[SI-LIST] : Passivity of a Linear System"

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