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.

In this lab you start by building both synchronous and ripple counters out of discrete flip-flops. You then move up from the modest “divide-by-four” to an 8-bit “fully synchronous” counter.

Available at https://LAoE.link/LAoE_Chapter_22O.pdf.

1O.1 Solderless breadboards

All the programs we have created so far follow the Arduino model of a set of initialization functions that execute once (akin to Arduino setup()) followed by a while(1) loop that executes forever (like the Arduino loop() function).

The Digital Project Lab is an open-ended two day lab session that gives you the opportunity to design and build something of moderate complexity using the WebFPGA and any of the components and techniques we have discussed in the course so far.

The PID control loop and the lock-in amplifier are each significant builds and we don’t expect you will be able to complete both of them in a single lab session. Feel free to do one, the other, or both as your time and interest permit.

We have noted elsewhere that all the op-amps we meet in this course use internal “frequency compensation” that makes them stable – at least, if we refrain from putting strange things within their feedback loops. Frequency compensation, surprisingly enough, means deliberate rolling-off of the amplifier’s gain.

Using functions to interface to hardware not only makes your code clearer, it also makes it easier to maintain. Consider the LED and switch connected to the Arduino I/O pins shown in Fig. 23S.1 below.