Here are reminders of Nyquist’s sampling rule and some consequences, with scope images of artifacts that sampling can introduce.

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.

You will need to download, install, and modify the Segger embOS according to the following instructions before beginning Lab 27L.

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.

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.

Setting particular thresholds exactly can be a pain in the neck. The process may put you through tedious algebra. But there are two easy cases.

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.

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.

The principal challenge here is simply to get used to the breadboard and the way to connect instruments to it. We do not expect you to find Ohm’s law surprising. Try to build your circuit on the breadboard, not in the air. Novices often begin by suspending a resistor between the jaws of alligator clips that run to power supply and meters. Try to do better: plug the two leads of the DUT (“Device Under Test”) into the plastic breadboard strip.

This problem is very similar to one done with slightly different numbers in AoE §9.4.1A.

Available at https://LAoE.link/LAoE_Chapter_15O.pdf.

Now things get a little more complicated, and more interesting, as we meet frequency-dependent circuits. We rely on the capacitor (or just “cap”) to implement this new trick, which depends on the capacitor’s ability to “remember” its recent history.

Then the remainder of the lab is given to trying applications for the so-called analog switch or transmission gate: a switch that can pass a signal in either direction, doing a good job of approximating a mechanical switch – or, more precisely, the electromechanical switch called a relay.