What to do when SPICE models run out of gas: Part 1 - Embedded.com

What to do when SPICE models run out of gas: Part 1

As embedded systems developers move from designs that operate in thehundreds of megahertz to systems that transport data at microwavegigahertz frequencies, SPICE will still be the workhorse of signalintegrity analysis.

But it will be necessary to answer three questions in relation toany design in this realm: (1) When are SPICE (Simulation Program with ICEmphasis) simulationsvalid? (2) What does asimulation tool need to yield good results? (3) What do you do with problemsthat are outside the capabilities of SPICE simulators?

This series of articles explores modeling alternatives and issuesthat cannot be directly resolved by a SPICE simulator, even though itis not yet time to abandon SPICE.

Enhance your ability with SPICE tools by learning how to castproblems in terms that SPICE can simulate. The slow field solvers maybe correct for some structures, but they can also be used to generatemodels that are useful in SPICE simulations.

The underlying reality is that a simple problem, such as 10 inchesof differential trace with a connector in the middle, can be modeled inseconds with SPICE, and can take hours in a 3D full-wave field solver.Real engineers need to be productive; you cannot afford slow tools incases that don't mandate such.

Time Domain Analysis
Signal integrity engineers have good reasons for preferring to work inthe time domain. There is no reasonto abandon the time domain now, but there is good reason to add the frequency domain to your areasof competence. 

When functions are expressed as a function of time, they are said tobe in the time domain. Examples are such things as voltage, v(t), orcurrent, i(t). Similarly, an oscilloscope waveform is almost always atime-domain presentation.

In SPICE, time-domain analysis is performed by the .tran statement.This statement tells the simulator to observe the circuit for somespecified amount of time. The simulator is usually initialized at thebeginning of this time period with a voltage step or a pulse.

SPICE
Whether recognized or not, SPICE simulators are at the heart of many ormost circuit simulators. So the material that is about to be describedcan be of use to you if you use numerous other circuit simulators inaddition to SPICE.

A critical requirement of any simulator that qualifies it for use atmicrowave frequencies is that the simulator absolutely must have thecapability of modeling transmission lines with frequency-dependentloss. Frequency-dependent loss (Figure7.1 below )  is so pervasive at microwave frequencies thatany tool without this capability will be of little use.

Figure7.1. A Plot of Frequency-Dependent Loss

Unmodelable Features
Real interconnect circuits have numerous features that circuitsimulators simply don't know how to deal with. The presence of suchfeatures does not render the simulator useless; rather, it usuallymeans some other tool is needed to translate the feature into languagethe circuit simulator understands. Such an approach applies to thingssuch as corners (Figure 7.2 below ),end effects, bends in edge-coupled pairs, and vias (Figure 7.3 below ).

Figure7.2. A Corner in an Edge-Coupled Pair
Figure7.3. A Via

Other features are random in nature and deviate from the idealcharacteristics that SPICE presumes. These features, such as roughnessand etching variations, are modeled in SPICE only when the simulationdeck is intentionally designed to include such characteristics.

In some instances, the major loss mechanism is radiation. SPICEsimulators do not know about radiation. Finally, there are solutions toMaxwell's equations that do not conform to circuit theory, and, ininstances where these higher order modes become significant, theaccuracy of circuit simulators decreases. Following in this article areseveral examples of such features and how they can be accommodated.

Differential and Common Modes
SPICE doesn't inherently understand the differences between and impactsofdifferential and common modes.If a pair of edge-coupled traces turns a corner (Figure 7.4, below ), the trace on theoutside edge will travel farther than the one on the inside edge.

This causes a conversion of some of the differential energy intocommon-mode energy. This can be partially modeled by adding a sectionto the transmission line at the point in the model where the bend takesplace, but this is only an approximation. In the real physical world,the subsequent trace will radiate energy much worse than did thesection where the signals were matched. SPICE will not model thiseffect.

On the other hand, the procedure of adding a section of transmissionline for the corner is valid in that the SPICE simulation will likelyaccurately model the increased crosstalk caused by the added commonmode. So it is recommended that this procedure is used.

Recall that a short segment of transmission line often has adisproportionate impact on simulation time. Where segments are short,as this would be, it is much preferable to model the segment as anequivalent L C section. The equations to do this were presented earlierand will be again later. In this short segment, you can ignore loss.

With any instance where an edge-coupled differential pair is to makea bend, add a small segment of trace to the inside trace to account forthe phase shift caused by the bend. It is true that inbroadside-coupled traces this would not be necessary, butlayer-to-layer registration is typically too poorly controlled to makebroadside practical in commercial printed circuit boards.

Figure7.4. Detail of a Corner

At lower frequencies, it was acceptable to equalize line lengths bymatching the total length of the net to the required value. Atmicrowave frequencies with differential signaling, this procedure is nolonger adequate. A definition is needed to describe the requirements.

Define a feature as anything in the signal path that is not asimple, straight, isolated, plain old differential pair of traces. Lookat Figure 7.5 below forexamples of features in a typical layout. In traversing a link betweentwo pieces of silicon, there will usually be numerous features, such aspackages, corners, vias, perhaps a connector, maybe a passive componentlike a capacitor.

For purposes of this discussion, all these are features. The tracesbetween features are defined as segments. So an interconnect consistsof segments separated by features.

With these definitions, the following statement is made: Within adifferential pair, trace lengths are to be adjusted or equalized tomaintain precisely complementary phase alignment, also calledbalancing, of the signals on a segment-by-segment basis.

It is not adequate simply to match physical lengths at the end ofthe link; it is best done segment by segment. This ideal is not alwayspractical in real layouts. Yet, even such a thing as a 90-degree bendin the traces followed a half- inch later by a complementary bendproduces significant and easily measurable impact on the signal.

Figure7.5. Examples of Features

The reason that this careful matching at the segment level isdesirable is that now segment lengths are significant compared towavelengths. The more significant portion of a wavelength means thatthese segments can become much better antennas radiating thecommon-mode signal.

Similarly, the higher frequency produces much better coupling of thecommon mode into the planar waveguides produced by the reference planesand results in both additional radiation and coupling to the resonantmodes of that waveguide.

As will be detailed later, the common-mode portion of the signalproduces crosstalk typically an order-of-magnitude worse than does thedifferential portion. The simplest way of viewing all this is thatcommon mode is “bad” and differential mode is “good.” Avoid making ortransporting common mode.

Again, if a small section of transmission line is added to accountfor each corner, there is an impact on simulation time. Simulation goesmuch faster if you use an LC equivalent rather than anactual transmission-lineequivalent.

The error will be small as long as the length of a segment that isrepresented by a single L-C segment is less than “one- tenth thewavelength of the highest frequency of interest in the circuit. Thisfrequency will usually be about 1.5 times the data rate.

If the data rate is 2.5 gigabits per second, this frequency shouldbe at least 3.75 gigahertz. Wavelength in FR4 at this frequency will beabout 1.6 inches, so no segment greater than .16 inch in length shouldbe modeled as a single L-C section for that data rate.

In most cases, a simple bend in a differential pair will not addthis much trace, so there is no problem. The appropriate values for theelements of the L-C segment are easy to calculate. They derive simplyfrom the two equations:

Note that stripline fields aretotally immersed in the board material, so their effective dielectricconstant equals the dielectric constant of the board material. This isnot true with microstrip. Theeffective dielectric constant for microstrip will typically be somewhatless than the dielectric constant of the board because some of thefield lines are in air.

That final equation presumes a non-magnetic material—usually a safepresumption in circuit boards. The trick is in selection of the unitsfor the speed of light. The inductance and capacitance in the aboveformulae are always in terms of per unit length.

The unit length is established by the units used for the speed oflight (c) in the above equation. Light travels at about 186,000 milesper second. If you use that value in these equations, the capacitanceand inductance will be per mile. A more reasonable light-speed valuemight be 3*10^10 cm per second.

With a typical dielectric constant for FR4 of about four, thesignal velocity would be about half the speed of light. In that case,for a specified characteristic impedance:

Recall the capacitance in these equations is capacitance percentimeter of trace. Substitute the capacitance back into theimpedance equation to get the inductance . To get theinductance and capacitance values that are used in the SPICE model ofthe segment, multiply each by the length in centimeters of the desiredsegment.

It is usual to model such a transmission line segment either as twohalf-inductances with a capacitor to ground in the middle, or twohalf-capacitances with an inductor between. Three ways that a segmentof transmission line can be implemented are shown in Figure 7.6 below .

Though the three act essentially identically at middle frequencies,they act very differently at very high frequencies. If you care whetherthe circuit presents an open or short at very high frequency, youchoose which of the three on that basis. In a SPICE simulation, thesemodels run a lot faster than a short transmission line segment runs.

Figure7.6. Three Ways for an L-C Section

One final comment on this procedure. Although it is simple enoughthat it could be easily programmed into a spreadsheet, the procedureisn't always quite as simple as has been shown here.

In the case of stripline, the dielectric constant is that of thecircuit board material, so the procedure is simple. It is simplebecause the signal velocity can be derived from the relative dielectricconstant. Namely, the velocity equals the speed of light divided by thesquare root of the relative dielectric constant.

In the case of microstrip, it isn't that easy. There, the dielectricconstant that you need to use is the effective dielectric constant madeup partly of air and partly of board.

In this case, the method might not work exactly as shown because theeffective dielectric constant might not be known. One solution would beto let the simulator calculate the velocity for you and use thatcalculation with the two fundamental equations. Or, you can find one ofthe analytic approximation formulae for the values of L and C.

The point of all this is that SPICE simulations often go faster ifdiscreet equivalents are substituted where there are very shortsections of transmission line, particularly in the case of lossytransmission lines. Calculating the values of capacitance andinductance that simultaneously yield the right impedance and velocityis easy to do.

Return Paths and Image Currents
SPICE does not know about return paths and image currents. When thefrequency of interest was a few megahertz, this was no big deal. Whenfrequencies got up to a few hundred megahertz, it became a big deal. Toget good correlation between simulations and measurements, it becamenecessary to explicitly model the return paths.

SPICE provides a node, zero, that is ground. At low frequencies,this is fine. It makes little difference that node zero at this end ofthe board is at precisely the same potential as node zero at that endof the board. It makes little difference that the signal into node zeroat this end of the board sees absolutely no time delay in getting tothat end of the board, as shown in Figure7.7 below.

At low frequencies, the distance from this end to that end of aboard were small enough that the timing differences were imperceptible.They were inconsequential. It takes about two nanoseconds, maybe alittle less, for a signal to cross a typical baseboard in a personalcomputer.

The original personal computers had clock cycles that were over 100times longer than this. Now cycle times are approaching an order ofmagnitude smaller than this, and the time required to cross a board isvery significant. Even the time required for the signal to traverse apackage and pin can be significant.

Figure7.7. SPICE's Ideal World

To accommodate the reality that return paths are a part of theinterconnect circuit, the return paths must be modeled in SPICE just asthe signal path must be modeled. Unfortunately, the return path isoften less conspicuous than is the signal path.

As an example of this dilemma, consider an integrated circuit housedin a package with multiple ground pins. The ground pins may bedistributed throughout the pin field. Some may be much nearer thesignal pin than others.

Some may connect through paths inside the silicon or the packagethat are not made public to the board designer. It has never been easyto generate a really good SPICE model of the return paths for many realcircuits.

And now things are going to get even more complicated. Microwavesignals respond to capacitances and inductances that are small enoughto be nearly immeasurable. At microwave frequencies, components thatwere intended to be capacitors can look like inductors. Short stubs canlook inductive at some frequencies and capacitive at others. SPICEprograms can directly handle some effects, others it cannot.

Features such as plane-splits and vias cannot be directly modeled inSPICE and so must be simulated in field solvers and then converted intoSPICE-compatible formats—usually L-C equivalents.

That is not to say that you have to throw your SPICE simulator awaywhen you encounter these features. No, what it means is that you mayneed another tool to help you generate L-C equivalent models for thesefeatures.

Next in Part 2: Differentialtransmission lines and receivers

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.

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