In Part 1 andPart 2 I covered a list of itemsthat are not particularly well handled by typical implementations ofSPICE. Now, you'll get the other side. Don't get the idea that nothingworks in circuit solvers at microwave frequencies. A lot does work.
As pointed out earlier, there are things that cannot be handledwithout the aid of field solvers, but the idea is to characterizefeatures with the aid of the field solver, translate thatcharacterization into lumped models thatSPICE can dealwith, and then do the signal integrity work with the SPICE tool.
Any time such a translation is made, there is a frequency rangewherein those models are valid. Any time such a model is generated, itshould also have the frequency range of applicability specified.
Again, I want to emphasize that there are numerous tools – circuitsolvers – which, at heart, are versions of SPICE. The one criticalproperty that such a tool absolutely needs if it is to be useful atmicrowave frequencies, is the ability to work accurately withtransmission lines that have frequency-dependent loss.
Without this capability, it is very difficult to get usefulinformation out of a simulation. That is not to say that without suchcapability you are not going to be able to work with microwavefrequencies; rather, without that capability, reconcile yourself toworking with some tool other than SPICE.
Frequency Dependent Loss
Frequency-dependent loss (FDL) is due primarily to two factors: copperloss and dielectric loss. The word “primarily” is used intentionally.Other sources, such as EMI,are important, even very important, from some perspectives. But, forthe signal integrity modeling of transmission lines, these two are whatwill be covered by the description of frequency-dependent loss.
Numerous of the factors impacting the signal available at thereceiver are functions of frequency. Examples are radiation reflectionsand crosstalk, all of which SPICE can be really good at. But these arenot included in the meaning assigned here. Here, the words”frequency-dependent loss” mean resistive losses in the copper anddielectric losses.
In fact, signal available at the receiver is often described interms of eye opening, a concept that will be described later. In thatsense, even crosstalk can be a major contributor to signal loss. Butall that is yet to come. If you needed something to look forward to,there it is. For now, you need details about copper and dielectriclosses.
Copper has resistive loss as does any conductor. At high frequencies,the internal inductance of conductors pushes the current to the outersurfaces; this effect, shown in Figure7.15 below , is called skin effect.
|Figure7.15. Skin Effect|
This phenomenon decreases the effective area available for currentflow and so increases the effective resistance. It is as if there isonly a thin layer on the surface of the conductor that is involved inhigh-frequency current flow, and the thickness of this layer is calledthe skin depth. As with many physical constants, mathematicaloperators, and similar scientific things, skin depth is designated bythe Greek delta symbol as shown below.
In this equation, pi has its usual meaning, 3.14 and so on, f is thefrequency in Hertz, mu is the magnetic constant—usually that of freespace, except when not—and sigma is the conductivity of the metal. Inthis list, the one that is often overlooked is mu.
In copper, gold, silver, and such metals, the relative magneticconstant is unity so that of free space is correct. In metals such asnickel and iron, the relative magnetic constant can be very high. Ifyou want to generate a low-loss conductor for microwave frequencies,magnetic materials are a poor choice. On the other hand, if you reallywant to have a lot of loss, such as in a chassis, iron might be areally good choice.
The loss due to skin-effect is high at microwave frequencies.Increasing the value of sigma can reduce it. If gold is substituted forcopper, this loss will decrease by a couple percent. On the other hand,the loss is inversely proportional to the circumference of theconductor, so increasing the conductor size by a few percent can do thesame. Decide for yourself which to do – which makes better economicsense for your design.
The current density decreases exponentially with depth in theconductor. The meaning of skin depth is that it is the equivalent depthif the current were evenly distributed in that skin layer. It is usedto calculate the effective resistance of the conductor for a particularfrequency.
As an aside, consider what might happen if the skin depth is largerthan the thickness of the conductor. Consider this in the context of areference plane. Fields will be attenuated, but not blocked, by theconductor.
Can this be a problem? Consider one more situation. Your board has aswitching regulator mounted on it. That regulator is running at 70 or80 kilohertz and switching tens of amps. It is a very bad idea, a verybad idea, to run a signal trace under the switching transistor, eventhough there may be a reference plane between.
In printed circuit boards, conductor thickness is usually a constant,so loss in a trace is strongly dependent on trace width. If theimpedance is to be maintained, increasing trace width requires greaterdielectric thickness. That dependency often means that the totalthickness of the board stackup is strongly related to the trace loss,and so can strongly influence the maximum frequency that can betransported a specified distance on a circuit board.
Although dielectric loss increases at a faster rate than does copperloss and at high enough frequencies becomes the dominant material loss,copper loss never becomes negligible. Dielectric loss is sometimesregarded as the only loss that counts. This is a mistake.
In real circuitry, total loss is made up of numerous contributorsand, while dielectric loss can become a major contributor atfrequencies of one or more gigahertz, it is never the sole contributor.In fact, when package losses, impedance mismatches, connector losses,passives, and copper loss are all accounted for, dielectric loss seldomeven contributes the majority of the loss.
Copper loss comes not only from the bulk resistivity of the copper,it also comes from surface roughness and from other materials used atthe surface of the copper. Sometimes the copper has a solder plating onit—note that solder has a resistivity about five times higher thancopper. Tin plating is often used. Tin has much higher resistivity thancopper.
When a fiberglass core is made, often the copper is roughened andcoated with copper oxide to increase adhesion. That is unfortunate, butneeded. It is always advisable to remove any metal coatings, exceptperhaps gold, that are not absolutely required for reliablemanufacturing of the board. In short, make it as good as you can, butnot better.
In dielectrics, the relative dielectric constant is thought to be dueto such things as the physical distortion of molecules, thereorientation of molecules, the changing of the shape of electronorbits, etc., as shown in Figure 7.16below . Each case has a stimulus and a response.
|Figure7.16. Molecules in an Electric Field|
In such systems, the response always lags the stimulus by someamount. The lag in response shows up in vector representations of thedielectric constant as an imaginary part. When calculating the responseof the system to fields through this dielectric, the imaginary part ofthe dielectric constant shows up as a loss.
It is typical that the delay in field response is somewhat constant.That is, the dielectric response to the imposed field lags by a small,fixed amount of time. In this case, the relationship between the realand imaginary parts of the dielectric response vector is linearlydependent on frequency of the imposed field. Thus, dielectric loss isapproximately linearly dependent on frequency.
The dielectric loss is often specified by the angle of thedielectric vector, illustrated in Figure7.17 below . The tangent of this angle—that is, the tangent equalto the imaginary part divided by the real part of the dielectricconstant—is often published as the loss factor for the dielectric.
|Figure7.17. The Dielectric Constant|
In another feat of scientific innovation, the ratio itself isdesignated by the Greek lower-case delta symbol. This is done,presumably, to maximize the probability of confusing the dielectricloss with the skin depth.
Of course, there is no relationship between the two, but why misssuch a golden opportunity to generate confusion? The dielectric lossfactor is thus designated tan-delta, which delta is symbolicallyidentical to the skin depth, but is physically unrelated in any way asshown below:
At low frequencies and in practical materials, copper loss dominatesand dielectric loss is safely ignored. Depending on geometry, atmoderate frequencies of about one gigahertz in FR4, dielectric losscatches up and becomes about equal to copper loss. At higherfrequencies, dielectric loss dominates.
The dominance of dielectric loss does not mean that copper loss hasgone away. It is still there. It still is increasing as frequencyincreases. You will occasionally encounter the idea that changing theboard material to one of the low-loss materials will reduce signal lossby an amount equal to the improvement in dielectric loss. This ofcourse is far from true. To see for yourself, simulate your total link,silicon to silicon, and vary only the dielectric loss parameter.
When you are looking for a SPICE simulator capable of dealing withfrequency-dependent loss, one choice is the W element available inHSPICE. This is not intended to be an endorsement of HSPICE, but rathera simple statement that it is an option, and it appears to work.
Other options also appear to work; not all include the word “SPICE”in their names. The advantage of tools that include that word in theirnames is that they tend to be fairly standard in the code format thatthey accept. Other tools have other advantages and, as usual, you needto choose the tool that fits the job.
Drivers and Receivers
From the perspectives of circuit simulators, all drivers areessentially the same. Circuitry will vary, but it makes littledifference to the circuit simulator whether that circuit is outputtingmicrowave signals or lower frequencies.
My own bias is to simplify drivers and receivers through use ofideal sources surrounded by appropriate parasitics whenever possible.The advantage of this method is that it typically runs a couple ordersof magnitude faster in SPICE than do transistor-level models. Ofcourse, some refuse to believe that this method could ever generateacceptable accuracy.
To them I point out that even the transistors in thetransistor-level models are themselves parametric models. Useful modelsare sometimes as simple as the one depicted here in Figure 7.18 below , but often need tobe substantially more complex.
|Figure7.18. My Favorite Driver Model|
Certainly there are cases where there is no choice available otherthan running the transistor-level circuitry. But avoid doing so whenpossible. Whether at microwave frequencies or not, these complicatedcircuits cause numerous problems in trying to get a simulation running.Such models are often automatically generated from the layouts of thedriver or receiver circuit.
When so generated, they often are found to include componentarrangements that are physically possible but cannot be handled bySPICE. Most common is the situation where a node joins threecapacitors, and nothing else. The DC solution at this node isindeterminate, so SPICE will fail.
It is my recommendation that a vendor should never release a SPICEmodel that has not been verified functional in a real simulation, and acustomer should never accept such a model. Getting back to the realworld, if you are stuck with such a model, the only choice may be to gothrough it line-by-line and modify it so it will work. Take thatthree-capacitor node and add a ten-meg resistor to ground.
At microwave frequencies, packages cannot be ignored. Nor is it likelyto be adequate to model a package pin as a simple inductor or even acapacitor and inductor. The length and crosstalk of the trace in thepackage coupled, with the tolerance of the termination presumably onthe chip, will result in a frequency-dependent impedance at the pins ofthe connector.
An optimized board interconnect has to, absolutely must, includethese factors. It would not be as bad if the termination could berelied on as being purely resistive, but the pin capacitance at thesilicon will typically, at the very least, be significant, andsometimes even the dominant impedance at the high-frequency end of thespectrum. Also, crosstalk in the package will sometimes be asignificant factor.
Even though signal characteristics may well be specified at the pinat the point where the package meets the board, it is not adequate tospecify impedance as a single number at that point. Optimized boarddesign will require that the impedance either be explicitly defined asa function of frequency, or be implied by specifying a transmissionline model for the package.
Significant problems can occur when generating a model of a package.You might rely solely on simulations, but the real physical entitymight not really hit the mark chosen for the simulation. Simulationsare great tools, but measured values make a better basis for a workingmodel.
Note that there is not exactly universal agreement on that laststatement, but authors get to state their opinion. The design of thepackage will have made good use of simulations, but the finalcharacterization of the physical part should be based on measurement.
Two measurements are available: time domain (TDR) and frequency domain (NA). In eithercase, SPICE models will usually be the translation of these into someform of transmission line model. This can be done by something such asthe application of the peeling algorithm. If you are using such amodel, you have the easy job. If you are the one who must generate thismodel, you probably already know that you have the hard job.
The special mechanical requirements of packages make the use offield solvers unavoidable in many cases. Often the physical sizerequirements force the use of very thin conductors and result in theaccompanying high loss. Mechanical requirements placed on the referenceplanes often result in geometries that cannot be accommodated by the 2Dfield solvers found in many signal integrity tools.
Recall that as shown earlier in this series, a lumped elementtransmission line model, and a single section was deemed adequatebecause the section was physically short. In the case of packages, thetransmission lines are often not short enough to model with a singlesection.
If you try to model a transmission line that is too long as a singlelumped section, you'll get substantial errors at high frequencies. Thiscan easily be seen by SPICE frequency sweeping the model with a singleand with multiple sections.
To model a line with n sections, simply calculate the inductance andcapacitance values for a single section, then divide those values by n;repeat the section n times. Recall that knowledge of the dielectricconstant and impedance of a line is adequate to calculate theinductance and capacitance per unit length. Scale those values to theactual length of the segment that is to be modeled.
I modeled an inch-long segment of transmission line with one, two,and three segments. The frequency response, shown in Figure 7.19 below , of each lookgood up to about a gigahertz. By the time you get to two gigahertz, theone-segment model begins looking inadequate.
By the time you get to five, only the three-segment case looksusable. This illustrates the impact of using too few segments to modela section of transmission line for a particular range of frequency.
|Figure7.19. Three L-C models|
Reference was previously made to a rule sometimes called thetenth-wavelength rule. It says something like, “Always keep segmentsize in your models at most a tenth wavelength of the highest frequencyyou are concerned about.” Examination of Figure 7.19 can show just how mucherror would result from relaxing this rule in this case.
Let me climb onto my soap box: It is no worse to violate a rule ofthumb than it is to use it without understanding what it does for you.Rules of thumb save us a lot of time. If used intelligently, they caneven promote good engineering.
Breakouts, the circuitry that interfaces the package or connector tothe circuit board, are problematic. The realities of snaking a tracethrough a pin field, or attaching a connector to a pad, often forcesignificant deviations from the ideal geometries and impedances desiredfor the traces.
At microwave frequencies, the first half inch or so of trace caneasily account for the majority of the near-end crosstalk. This muchtrace can easily be entirely in the breakout region. The breakoutregion is best treated as a distinct entity when you do your modeling.
|Figure7.20. The Break-Out Under a BGA|
Sometimes the electrical characteristics of the package or connectoritself are significantly influenced by the details of the breakout. Insuch cases, it makes sense to include some or all of the breakout onthe circuit board as part of the package or connector, including it inthe package or connector model.
It makes little sense, for example, to characterize a connector thatmandates use of a through-hole via of some size, without including thatvia in the characterization of the connector. The problem with this isthat the model may then need to include a board-thickness parameter insome way.
For reasons of cost, packages are tending to finer pitches andcloser spacings. At the same time, higher frequencies and the attendantgreater losses call for wider traces. It is often found that traces inbreakout regions simply cannot meet impedance, loss, and crosstalkcharacteristics desired for the rest of the board.
In simulations, it is necessary to optimize the breakouts and thenchoose the remaining interconnect to accommodate what is left of theinterconnect budgets. That is, it is much easier to limit crosstalk inthe long trace run across the board than it is to do so on the breakoutregion. It is much easier to hit the precise desired impedance out inthat open space than it is in the very confined regions of thebreakout.
|Figure7.21. A Typical Interconnect Design|
The interconnect circuit is the entire assembly of features and tracesthat connect a transmitter to a receiver, as seen in Figure 7.21 above. This ofteninvolves numerous discontinuities and variations that are difficult toreliably deal with in hand calculations.
Up to now, the discussion has focused on how to calculate impedanceas a function of distance from a discontinuity, how to calculate thecumulative effect of multiple discontinuities, and how to do all sortsof things by hand. SPICE simulators do an excellent job of dealing withall those things for you.
Having been told that, do not conclude that all the mathematicalderivations have been for nothing. Without understanding themathematics and physics behind what is happening, you would have noidea of how to make improvements when SPICE says that the interconnectlink is broken.
You may have little interest in working with things like hyperbolicfunctions to determine the impedance at a position in the line, whenSPICE can do it easily. But now you know how it works and will haveideas of what to do when SPICE says your link is busted.
In modeling the interconnect, it is important to recognize that,unless you take steps to overcome it, all simulations treat the worldas ideal. The transmission line in the simulator does not randomly varyin width. The transmission line doesn't encounter regions of varieddielectric constant as traces on FR4 really do. In a simulation, unlessyou intentionally model the variations, everything is beautifullyperfect—and not very realistic.
Connectors are a real challenge for measurements and modeling. But thatis starting to sound like a mantra by now. What isn't a real challenge?The dominant thing you need to know about connectors is that they oftenwill be major locations of crosstalk in the link.
Assume you choose a connector that matches your line impedances. Itis typical for the crosstalk of connectors to have a bigger impact onsignal integrity at microwave frequencies than loss in the connectorhas. Never consider using a particular connector if its crosstalk isnot well specified.
Don't settle for statements such as a connector has such-and-suchpercent crosstalk. Drill down and find out what that statement reallymeans. It is fairly easy to get good crosstalk from a single aggressorsignal or a slow rise time. But what is needed is the total sum of thecontributions of all nearby signals at an appropriate rise time orfrequency range.
Take a look at Figure 7.22 below .In some geometries there can be many more than just one or twoaggressors coupling into a particular pin or pin-pair. You can't reallyblame a vendor if all they give you are accurate numbers, but notnecessarily the numbers you need.
|Figure7.22. A Connector with Multiple Crosstalk Aggressors|
If it is necessary to model this connector in a system simulation,who will provide the model and what type of model will it be? Everymodel for any device has a limited range of accuracy.
Questions you need to ask about connector models include over whatfrequency range is the model accurate and what level of accuracy doesit provide in that frequency range? Also understand the conditionsunder which the model is characterized.
There have been cases where board features that were absolutelyrequired for the connector were not included in the model because theymade the connector performance look worse. A useful model is a modelthat accurately represents how the device will perform in a realapplication. Real applications often use board-to-board connectorsactually mounted on boards.
Another aspect of connector selection you need to think about is thephysical length of the path through the connector. Consider modeling anideal lossless connector in SPICE. The only parameter you need to varyin this model is the length of the connector.
As an example, make the impedance of the path through the modelexactly 50 ohms. In a real implementation, the circuits that go to thisconnector may target 50-ohm impedance too, but there will be areal-world tolerance. So model the line in and out of the connector as45 ohms and terminate both ends at 45. Now run frequency sweeps atvarious physical lengths in the connector.
If you do this experiment, what you will see is that the connector,even with ideal lossless lines, acts something like a low-pass filter.And you will see that the knee frequency depends on the length of theconnector.
Cables are not all that different from what has been already covered.Losses in cables tend to be substantially less than in FR4. Some reallygood cables are out there, but even the mediocre ones that arepractical for use in consumer electronics are really good compared toFR4.
Expect losses in cables to be in the range of cable loss-per-meterequal to FR4 loss-per-inch. If microwave cabling is new to you, youshould know some things.
The first goes something like this: if you name a loss figure, acable can be found that can meet it. This fact, that exceedinglywideband and low-loss cables exist, is not really relevant to thedesign of circuitry for consumer applications.
It is not an exaggeration to state cables that cost over $1,000 permeter are readily available. I have some in my lab. For theirapplication, they are the right choice. Their application is definitelynot consumer electronics.
The $600 and the $30 per meter cables also have valid reasons forexistence. In consumer applications, what you need are the cables thatare closer to the dollar-or-less per meter items. These, too, exist. Inthese, the connectors on the ends may cost more than the cable materialitself. The nemesis of the engineer with a cable need is the vendor whoclaims to have a cable that solves all those problems, but the priceisn't stated.
Besides that, one of the major differences between cable and traceis that it is quite difficult to get really good length matching on theindividual conductors in a cable. As the number of pairs in a cableincrease, this problem becomes worse.
In traces on the board, matching lengths is fairly easy and matchingvelocities more difficult. In cables, matching lengths is the moredifficult proposition. It sometimes is also useful to note that thecommon-mode impedance in a cable may be very different than that on thecircuit board. This can be true even though both have precisely thesame differential impedance.
It is significant to note that cables can present very severe ESDproblems. Those center conductors in cables can sometimes supportthousands of volts of charge. The human body ESD model includes a1,500-ohm series resistor. But when that cable plugs in, the seriesresistance is in milli-ohms.
So, at least in the lab, always put a terminator on a cable todischarge it before plugging it into your equipment. It is a good ideato lose sleep at night, figuring out how this will be handled byconsumers if you have a cable that goes outside your chassis.
The same frequency-dependent-loss transmission lines that were usedto model traces are used to model cables in SPICE. Of course, the losstangents are quite different.
An interesting phenomenon has shown up in cable assemblies designedto meet specific interconnect standards. When the maximum loss allowedfor a cable at a specific frequency is specified, all cables,independent of length, tend to have that loss. Consider a cable of somelength and loss, cut it in half, and the measured loss will now also becut in half. That is not what is happening here.
|Figure7.23. Quad and Twin-Ax Cable Constructions|
When all else is the same, the cable loss tends to decrease as thecable diameter is increased; the cable cost increases as the cablediameter increases. If the maximum loss is specified, the manufacturerminimizes cost by decreasing cable diameter, increasing cable loss tothe specified limit. So it is that in this circumstance, cable diametertends to decrease as length decreases, rather than cable lossdecreasing as length decreases.
Crosstalk in differential cables, both quad construction and twin-axconstruction, illustrated in Figure 7.23above, is typically dominated by the connectors. If the cablelength is doubled, the crosstalk does not double, it may even show verylittle increase. Often an important cable parameter is the quality ofthe shielding.
Again, it is possible for the connectors to make major contributionsto EMI. If there was no common-mode signal entering the cable,radiation would not be a significant problem, but since cable lengthsare difficult to match and connectors are not perfect, common mode canbe generated by the cable connectors themselves.
Dennis Miller has worked in electronics since 1963. His earlyengineering interests and education centered on control theory andnumerical analysis. Now his interests are signal integrity andnumerical analysis. Since joining IntelCorp. in 1991, he has been instrumental in the development ofInfiniband technology and similar high speed signaling technologies.
This series of articles is based on material from Designing HighSpeed Interconnect Circuits,” by Dennis Miller, used here with thepermission of Intel Press which holds all copyrights. It can bepurchased on-line.