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Figure 13L.1 gives a preview of what’s coming in the form of waveforms at several points. Before you have built the circuits, these waveforms may be a bit cryptic; but trying to understand these plots may help you to get a grip on the whole project. Then we’ll finish these lab notes with some suggestions on how to test your circuits.
In this chapter we meet an amplifier sensitive to a difference between two inputs rather than to a difference from ground. This novelty permits implementation of the hugely important operational amplifier, which from the next class onward will be our principal analog building block.
Surface gravity waves induce a drift on objects floating on the water’s surface. This study presents laboratory experiments investigating the drift of large two-dimensional floating objects on deep-water, unidirectional, regular waves, with wave steepness ranging from 0.04 to 0.31 (0.04 $\lt k{a_w}\lt$ 0.31, where $k$ is the wavenumber and $a_w$ the wave amplitude). The objects were carefully designed to have a rectangular cross-section with a constant aspect ratio; their size varied from 2.6 $\%$ to 27 $\%$ of the incident wavelength. We observed Lagrangian behaviour for small objects. Small and large objects exhibited fundamentally different drift behaviour at high compared with low wave steepness, with a regime shift observed at a certain size and wave steepness. The scaling of object drift with steepness depends on the relative size of the object. For small objects, drift scales with steepness squared, whereas drift becomes a linear function of steepness as the object size increases. For objects that are relatively large but smaller than 13–16% of a wavelength (low to high steepness), we provide experimental evidence supporting the mechanisms of drift enhancement recently identified by Xiao et al. (J. Fluid Mech., vol. 980, 2024, p. A27) and termed the ‘diffraction-modified Stokes drift’. This enhanced drift behaviour, compared with the theoretical Stokes drift for infinitely small fluid parcels, is attributed to changes in the objects’ oscillatory motion and local wave amplitude distribution (standing wave pattern) due to the presence of the object. In the case of larger objects, similar to Harms (J. Waterw. Port Coast. Ocean Eng., vol. 113(6), 1987, pp. 606–622), we relate the critical size at which drift is maximised to their vertical bobbing motion. We determine the domain of validity for both Stokes drift and the diffraction-modified Stokes drift model of Xiao et al. (J. Fluid Mech., vol. 980, 2024, A27) in terms of relative size and wave steepness and propose an empirical parametrisation based on our experimental data.
You now have a working DAC available in your microcontroller. We are going to use the built-in ADC to allow us to digitize analog signals as well. Once you’ve got these peripherals available, it’s fun to try altering waveforms, fun to see the result on a scope and fun to hear the result.
This chapter concerns the vast family of large neighborhood search primal heuristics. These are local search heuristics that generally assume the knowledge of one or more feasible MIP solutions and explore "large" neighborhoods in the attempt to improve the incumbent, i.e., the best feasible solution computed so far by the MIP algorithm. A neighborhood is large if, in general, it cannot be explored by complete enumeration, so the various techniques developed for defining those neighborhoods and exploring them are discussed.
The skeleton code below initializes the DAC, sets up the SysTick timer to provide a 1ms interrupt for the Delay() function and then outputs a sawtooth waveform on Arduino pin A0.
How do high-gain amplifiers, see Fig. 5W.1, compare with respect to “linearity” or constancy of gain over the output swing? Explain your conclusion, briefly. Assume that each amplifier is fed by a properly-biased input.
This chapter discusses the extension of many primal heuristics developed for MIP to mixed integer nonlinear programming, a larger and even more challenging class of mathematical optimization problems that contains MIP. The importance of primal heuristics for this area is highlighted and some novel ideas originated from specifically considering mixed integer nonlinear programs are also reviewed.
We use the Golden Rules to calculate gain if, say, we feed back one part in 100. The Golden Rules rely on an assumption that op-amp gain is very high (because, in Black’s words, “… improvements are attained in proportion to the sacrifice that is made in amplifier gain…”).
Construct the parallel resonant circuit shown in Fig. 3L.1. Drive it with a sinewave, varying the frequency through a range that includes what you calculate to be the circuit’s resonant frequency. Compare the resonant frequency that you observe with the one you calculated.
In the previous chapters we used several of the built-in peripherals in the SparkFun SAMD21 Mini including the DAC, the Timer/Counter and the EIC (in a worked example). While modern microcontrollers like the SAMD21 have an impressive selection of internal devices, many systems incorporating a microcontroller require peripherals not available internally or may need to communicate with some external computer or system. To handle access to external devices and systems, most microcontrollers support some form of external communications.