Editors' Notes—Volume 41, Number 1, 2007
HYSTERESIS AND HISTORY
In the heyday of analog computing, more than half a century ago, special circuits were needed to model nonlinear relationships, such as squaring, rooting, and bounds. Today many such functions can be purchased or assembled rather easily. But a few were really awkward unless their nature could be clearly understood. This little essay is about the tricks used to model linear hysteresis, a function used to simulate such phenomena as backlash in gears or mechanical linkages. In words: Starting from a neutral position, x moves forward; after a short distance, say Δx/2, y starts to follow x and follows linearly. Whenever x reverses, y stays put until x has reversed by Δx, then it follows linearly until x again reverses direction; then y holds until x has again moved forward by Δx.
The figure shows how this was accomplished in the Philbrick K3-H Backlash Component, as described in the Philbrick Catalog and Manual… (1951). The input, via a cathode follower, is split into an adjustable pair of biased voltages, that are then compared with the voltage stored on a capacitor by a pair of diodes. The capacitor voltage can change only when the input either continues its existing course or reverses by more than H. The capacitor voltage is isolated by another follower, then made available at the outputs in ± polarities by a pair of op amps (α). (This description assumes that all elements are ideal—unity-gain followers, zero-drop diode conduction, H<<E, etc., and that if x stops for long periods, the charge on C holds.)
Another way to characterize this function is as a dead-zone in an integrating loop. The integrating capacitor is holding charge while the input is in the dead zone; otherwise the output voltage is tracking the input. A scheme for accomplishing this can be found in the Philbrick Applications Manual… (1966), on page 60.[footnote] http://www.analog.com/library/analogDialogue/archives/philbrick/056-062.pdf
It’s a not-often-thought-about function, but if you ever need it, you can find it in that venerable analog designer’s bag of tricks.
Dan Sheingold [email@example.com]
IN THIS ISSUE
This issue, Volume 41, Number 1, marks the first time that Analog Dialogue has gone to print in Chinese and Japanese, so we would like to take this opportunity to extend a special welcome to our new readers.
Making accurate high-speed time-domain measurements can be challenging, but a few tips and tricks, coupled with some good old-fashioned common-sense engineering, can help yield quick and accurate results. When choosing a scope and probe for high-speed measurement, first consider: signal amplitude, source impedance, rise time, and bandwidth. The type of probe and length of the ground lead are also important.
The circuitry ahead of a high-performance ADC is critical to achieving desired system performance. The optimal design depends on many factors, including the application, system partition, and ADC architecture. Amplifiers consume power and add noise, whereas transformers consume no power and add negligible noise. On the other hand, amplifiers maintain dc levels, provide easily adjustable gain, and have flatter response.
The rapid expansion of the electric power industry has created a worldwide need to reinforce existing transmission and distribution networks and to construct new substations. Advances in microprocessor technology and the increasing cost of support staff are key drivers for power companies to design new automated high-voltage substations using high-accuracy integrated automation systems.
2007 also marks the introduction of the Back Burner, an online column that features design ideas, measurement tips and tricks, tutorials, and teasers. This quarter’s articles, currently available only on the web, include tips on measuring ambient- and PCB temperatures, designs for a pulse oximeter and programmable waveform generator using the ADuC7024, and an algorithm that can enhance performance in an accelerometer-based pedometer. We hope that you enjoy this new column.
As always, your comments are welcome.
Scott Wayne [firstname.lastname@example.org]