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The Best of The Nonlinear Distortion

Some of our better articles from previous issues. Also, if you like this sort of thing, see The Neophyte's Guide to Technical Symposia.

Pompous Message from the President

This message comes to you at the start of a very busy year. The fact that The Nonlinear Distortion was scheduled for publication in December, but is just now hitting the streets, is a testament to that fact. We're a company full of busy little elves, trying to keep the customers happy, and to make a buck at the same time. (Of course, being good American industrialists, we like to pretend that are motivated by a sense of mission. We don't mention that our mission is to make a buck.)

NLT is back in operation after three months last fall at the Helsinki University of Technology. Again we are providing expert technical assistance and nontraditional newsletters to the microwave industry. We're completely up to our usual level of work and whimsy, and we look forward to hearing from our current and previous clients and customers.

C/NL2 Ver. 1.2 for Windows 95 & NT: 5X Speed Improvement

NLT has released Version 1.2 of C/NL2, our linear/nonlinear microwave circuit simulator. The new version runs under Windows 95 and Windows NT, as well as Windows 3.1 with Win32s. It is available from Artech House, and will be shipped in early 1996.

We have benchmarked several of our circuits on Version 1.2. They run 2 to 5 times as fast under the 32-bit operating systems as under the old 16-bit Windows 3.1. A nonlinear analysis of a four-FET distributed amplifier, with sixty frequency points, now requires only four seconds on a 66 MHz 486 DX2 with 8 megs of memory. Eat your heart out, harmonic balance!

Other improvements in the new version include improved microstrip models, more versatile graphics, and a simulated sliding load test. The two utilities, Winlin and C/Util, have also been improved.

To order a copy, call Artech House at 800-225-9977.

To download a fully functional demo copy, see the article below.

C/NL2 Demo Now Available On-Line

The C/NL2 demo disk now can be downloaded from America On-Line. To download a copy, use the keyword Quickfind and enter CNL2 at the resulting prompt (leave out the "/"). You can then download it by clicking on the Download Now button.

You can also download a demo disk from this web site or from the Artech House web site.

Download a Demo Copy of C/NL2 (~309K)

Artech House Web Site

OK, So What Else Do You Do?

One of the difficulties of specializing in a narrow technical area like nonlinearity is that people don't realize that you might be able to do something else as well. This is fine for getting out of doing the dishes, but it doesn't help in running a consulting company.

NLT regularly works in the following areas, and does so quite successfully:

* Low-noise amplifiers, RF through millimeter waves;
* Noise analysis of circuits and systems;
* Computer-aided circuit design;
* RF and microwave systems;
* Solid-state device modeling;
* Coupled-line components.

Not all our work involves design and analysis. We also help clients with

* Design reviews and preparations for design and project reviews;
* Resolution of technical differences in the interpretation of specifications;
* Selection the best type of system, component, or design approach from competing trade-offs.

Finally, do you have special projects or problems that don't seem to fit into any established category, but just need an extra problem solver? Call us!

We've Been Busy

Some of last year's more interesting projects:

* Design of about a jillion different mixers for various clients in FET, HEMT, diode, and bipolar (including HBT) technologies;
* Design of broadband diode frequency multipliers;
* Solution of a very perplexing amplifier-distortion problem for a commercial client;
* Further development of specialized software for nonlinear analysis of mixers;
* Solved a problem involving a client's inability to achieve satisfactory performance of Lange couplers;
* Design of large parts of a millimeter-wave radar transmitter and receiver;
* Design of a line of broadband, low-cost, commercial mixers.

FMCW Radar

NLT recently obtained a patent for an FMCW radar transceiver circuit. This circuit is extremely simple and low-cost, and offers adequate performance for a wide range of low-power applications. Although originally conceived as an FMCW radar circuit, it is also useful for sensor, motion-detector, automotive, and wireless LAN applications.

The circuit consists of a half-frequency oscillator and only a few other components. As such, it is much less expensive than transceivers consisting of a collection of mixers, amplifiers, filters, etc. The transceiver provides in-phase and quadrature-phase IF outputs, and can be used in the RF, microwave, and millimeter-wave ranges.

Licensing opportunities are available. Contact NLT (310-426-1639) for details.

Yes, we've all had the experience: after half an hour of diligent number crunching, your favorite harmonic-balance simulator (HB, to those of us in the know) bites the digital dust, leaving only the message, "convergence failure." How do you handle the situation?

With a sense of humor. Coffee and a donut help, too. These usually do about as much good as anything else. Convergence failure is often a consequence of the HB simulator's limitations or the characteristics of the circuit being analyzed. In some cases, however, convergence failure is avoidable. In these cases, what can be done?

To understand why HB simulators sometimes don't converge, you first must understand why they usually do. Virtually all commercial simulators use Newton's method (NM), an iterative process, to solve the nonlinear circuit equations. Even if you're not familiar with the multidimensional form of NM used in HB simulators, you probably have encountered the one-dimensional form, used to find the zero of a function. The zero of a function f(x) is estimated by finding the function's value f(x0) and derivative f'(x0) at some point x0, and using both f(x0) and f'(x0) to estimate the position of the zero by linear extrapolation. If the function is linear, the extrapolation will find the zero exactly. However, if the function is nonlinear, we must repeat the process until it converges to the true zero.

Clearly, the initial estimate must be reasonably close to the zero, and the function f(x) must be smoothly varying in the region between the zero and x=x0, or the extrapolation will not work. Thus, in general Newton's method is not guaranteed to converge. So, the question is this: what kind of situations cause the functional surface (of the multidimensional problem) to be irregular, or the initial estimate performed by the simulator to be poor? Here are some possibilities:

1. If your circuit is unstable, a HB simulation almost certainly won't converge. Stability of nonlinear circuits is difficult to assess, and few simulators give the user any insight in this regard. An unstable circuit has no unique solution, so the simulator cannot converge to it.

2. A discontinuity in the nonlinearity will create two regions where the functional forms of the derivatives in each region, used to perform the extrapolation, are completely unrelated. If your analysis is in one region and the zero is in another, convergence occurs only by accident, if at all.

3. A poor modeling job may create a discontinuity in the I/V or Q/V characteristic or a nonlinear circuit element. The most common problem is a FET model having a pinchoff voltage that is not precisely located at the zero of the gate I/V characteristic, or an I/V characteristic that does not pinch off at all.

4. An attempt to analyze a circuit that is simply too strongly nonlinear. Some switching circuits and digital circuits are just not appropriate for HB simulation.

5. Frequency multiplier analyses, especially resistive diode multipliers, often present convergence difficulties. This is probably because the simulator's initial estimate is designed primarily for fundamental-frequency circuits, and is poor when the main voltage and current components are a harmonic. Of course, the diode's strong, exponential nonlinearity doesn't help.

6. A circuit-file error often causes convergence failure. Well designed circuits always seem to converge better than poor ones. The latter, of course, include circuits with file errors.

7. Strange as it may seem, a simulation may fail to converge at one power level, yet converge successfully at a higher power level. Although in general lower power levels converge better (because the circuit is usually more linear over narrower voltage ranges), this is not always the case.

8. In a power sweep, using small power steps may make convergence successful, and may not take substantially more computer time than fewer, larger steps.

9. To save time, simulators often take "Samanski steps," iterations in which the huge Jacobian matrix is not reformulated and decomposed. Minimizing or eliminating such steps can improve convergence enormously in strongly nonlinear circuits.

HB simulators often use "source stepping" (technically a continuation method) to obtain convergence when problems occur. This is a process in which the excitation level is increased stepwise, with the solution at the previous level used as the initial estimate for the next. In our experience, this process occasionally is successful, but more often is not. Other new technologies, such as norm reduction methods, combined with the use of more appropriate norms, are far more effective. Unfortunately, many of these have not been implemented in commercial HB simulators.

NLT Acts to Quash Comet Imports!

At NLT, we are concerned about the loss of American technological dominance to Pacific-rim countries. Nowhere is this more evident than in the degree to which our comet technology has fallen behind that of Japan.

In the past, the US was the world's premier supplier of comets to the free world. Our comets were unchallenged in brightness, tail length, and longevity. Overall quality was superb. Halley's comet, for example, manufactured in 240 BC and observed by Edmund Halley in 1682, is still flying, having revisited earth most recently in 1986. (OK, we recognize that Halley was an Englishman. So what? England and the US were the same back then, anyway!)

Comet technology took an ominous turn in 1973 when the much-hyped comet Kohoutek, billed as "the comet of the century," became the fizzle of the century and a national embarrassment. At that time comet leadership had already started to seesaw back and forth between Japan and the US. Japan appeared to take an early lead in 1965 with comet Ikeya-Seki, and in 1969 with Tago-Sato-Kosaka (which had a disappointing orbital period of 420,000 years). In the 1970s the US came back strongly with Bennet, Kohoutek, West, and Mercury, and since then has maintained a precarious lead.

This year, however, comet Hyakutake has delivered a knockout blow to the American comet industry. Hyakutake is so bright that it can be observed from Los Angeles, even at night, as it streaks proudly across the sky on its way to the sun, its tail growing longer by the hour. It is an impressive example of Japanese comet technology. There is no more room for complacency; our competition is indeed severe.

What can we do, as concerned citizens, to regain our dominance in comets? We at NLT have some suggestions:

* Lobby Congress for quotas on the importation of foreign comets, and for heavy taxes on those already in our skies;

* Make comets a Federal R&D priority;

* As individuals, we each must vow to buy only American comets. (It's easier to get replacement parts for them, anyway.)

The current Congress is showing great interest in issues of similar importance, so right now there's a good chance for action. Only through concerted effort can we regain our highly elliptical place in solar orbit. This is the time to act! Stamp out imported, foreign comets!

Why Use Nonlinear Technologies?

Again we examine this critical issue: why use Nonlinear Technologies?

* We're cheap: Compared to hiring a new employee, or spinning your wheels dealing with a problem we can solve. Because of our low overhead, our bidding rate is probably about what you charge for a mid-level engineer.

* We offer advanced technical expertise, immediately: Finding and hiring an experienced nonlinear-circuit designer is likely to be a long and frustrating task. Hiring new employees is a lengthy process, requiring high-level approvals. In these situations we can provide expert technical services immediately.

* We solve entrenched problems: Frequently we solve problems that a client wrestled with for months, losing money the entire time.

* We're easy to fire: No long-term commitment (unless you want one). We get in, do the job, and get out.

* We're on your side: We can be very helpful in design reviews and in ironing out technical problems with contractors and customers. Your ability to prevail in such disputes often depends on who is supporting your position.

* No overhead: Your company probably doesn't burden consultant contracts. This is one reason why we're no more expensive than a mid-level employee.

* Your proprietary information is safe: Protecting proprietary information and technology is nothing new to us. We do not accept contracts where a conflict of interest with an existing or former client might result.

Differences Between Southern California and Finland

We spent three months in Finland with the corporate bigwigs. They were awfully busy, and we're not sure they even noticed that they were outside of Los Angeles. At one point, we saw one of them trying to buy tacos for lunch at the local Kioski. (The Kioski actually had them, but they were stuffed with moose and reindeer.) As it happened, however, we had very little to do; after all, how much gardening can you do in Helsinki in midwinter? So, to pass the time, we carefully observed the local culture, and came up with this nonexhaustive list of differences between Finland and Southern California:

* In Finland the teenage kids speak English.

* Finland has beer. (There are unconfirmed rumors that it has been sighted in the US.)

* Finns make their hot tubs out of wood, instead of fiberglass, and leave out the water.

* In Finland snow is white and rain has a pH near 7. (If the weather blows in from Russia, however, the rain clocks in at about 0.2 millirems per hour.)

* Yardsticks in Finland are 39.4 inches long.

* In the northern US, the sun rises. (Of course, when the Congress sees what it costs, that may change.)

* Obnoxious, loudmouthed public drunks in Finland are arrested. In the US, they're elected.

* In Finland a "drive-by" means that you didn't need gas, and "car-jacking" is what you do for a flat tire.

* In Helsinki, busses have curtains for you. If you take the bus in LA, it is curtains for you.

* In Finland, rivers have water in them and national forests have trees in them.

* It costs $3.75 to go by bus from the suburbs to downtown Helsinki. You can get to downtown LA for a lot less, but you wouldn't want to go there.

* In Finland the traffic lights at minor intersections are turned off at night and on weekends. In LA the lights keep operating, but everyone ignores them.

* According to the National Geographic Society, 16% of American teenagers can't find the US on a map of the world. 100% of Finnish teenagers can, but they have no need to.