The Classroom

# We look at sine waves, and several ways to generate them.

Daniel Koch

Issue 59, June 2022

Most makers are familiar with sine waves at least in concept. They are the basis for natural sound that we hear, and the majority of electronic sound as well (a speaker fed with a square wave does not output quite a sine wave, but it's close). They are also the shape of electromagnetic waves as well. However, sometimes we want to generate a sine wave. We will take a look at what a sine wave is, some examples found in nature, and then look at how we can electronically generate a sine wave using several different circuits and pieces of equipment.

# WHAT IS A SINE WAVE?

The sine wave, also called a sinusoidal wave, is a mathematical concept that originates from the trigonometric function 'sine'. The representations we see of it are actually the graph thereof, but physical manifestations exist as well. In its simplest form, the sine wave can be defined as y = sin x, so that the value on the vertical y axis is the sine function of the horizontal x value.

As soon as time is introduced, it gets a whole lot more complicated. The formula for that involves phase, angular frequency, and ordinary frequency. It's far past the level we need to proceed with Classroom, and unless you're studying physics or working as a physicist, you're not likely to need to know. For curiosity value, however, here it is:

where:

• A is the amplitude of the wave;
• ƒ is the frequency. This is ordinary frequency, the basic one we measure in Hertz and use commonly.
• ω is the angular frequency, expressed in radians per second and found by 2πƒ. This is a rate-of-change expression. It is represented by the Greek letter Omega in its capital form, although we are used to Ω, its lower case form.
• sin is the sine function, an entire topic on its own.
• φ is the phase, which means how far from t (time) = 0 the wave crosses 0 amplitude. Measured in Radians, and represented by the mathematical version of the Greek lower case letter Phi.

By the way, the concept of phase becomes important later on. A wave has a total of 360° contained in it, and while this is most obvious with sine waves, any wave can be thought of this way. So, if a wave is 60° out of phase with another (or a theoretical point when there is only one wave, then one wave is occurring behind or in front of another. Out of phase waves can lead or trail a wave, they do not always have to be behind in terms of time. The most extreme example (and the easiest to draw, to be honest) is two sine waves 180° out of phase. Because 180° is half of 360°, this means the positive peak of one wave is directly opposite the negative peak of the other.

While we tend to think of trigonometry as the maths of triangles, it is in fact the maths of a circle. A sine wave is also related to the circle. It cannot be drawn by simply tracing one, but it can be drawn by rolling one. However, the circle needs to be operated as a cam, and the paper moved under it at a constant speed. We have linked to a video at the end in the Reading and Resources section showing a bunch of different LEGO cams used with a plotter. Watch what happens when a circle is used as a cam.

It is important to note that the exact shape does not define a sine wave. It is the relationship between x and y. You could double the scale of the x-axis, the waveform would look like far sharper peaks, but still be a sine wave because the relationship between x and y has not changed. In the image, the same sine wave was used (from a signal generator), but the horizontal scale on the oscilloscope was changed.

# SINE WAVES IN NATURE

The waves we see in nature are generally sine waves. They may not always look like sine waves, either because of our perspective, or because of influencing factors. The clearest is when an object is dropped into still water. The water surface first falls with the object, then under inertia, moves back up past its original zero point, up to a peak, and back down again. It is not a perfect sine wave because of resistance from air, the rest of the water, and so on: Each cycle is slightly lower in amplitude than the one before it. Without friction taking energy from the wave, it would be a perfect sine wave.

Waves in the ocean are sinusoidal, as are sound waves, and electromagnetic waves. A simple experiment is a weight on a spring, suspended vertically. If the weight is lifted, then released, the weight bounces up and down. If its vertical position was graphed against time, a sine wave would result. In a future project, we plan to do some experiments with sound, water, and strobe lights to enable visualisation of sound waves in a fixed wave.

# ELECTROMAGNETIC WAVES

All waves on the electromagnetic spectrum travel as sine waves, too. What makes them different is the frequency they travel at, and their wavelength. The frequency matters a lot: A gamma ray of a given amplitude might kill you, while a Very low Frequency (VLF) radio wave of identical amplitude will have no effect. Gamma rays are one of the highest frequencies known, and have the ability to destroy living organisms, and at low doses, can still damage DNA. There is a bit more to what gives an EM wave of a given frequency its properties, determines how much energy it has, and what it can do, but frequency is the main one. Amplitude in each case is the intensity of that wave.

Whether it be a sound wave; Electromagnetic wave, which includes visible light; or audio wave, waves have four main characteristics we define even in basic discussions. Frequency is how many full cycles of the wave happen per second. This is measured from two identical points on the wave. That may be the peaks, it may be where a wave crosses zero, or it may be a point on the slope.

It is always the same point, so if the rising edge is the first point, the falling point following it is not counted; the next rising edge is the end of that period. The period is the time that cycle takes, usually in some fraction of a second. Wavelength is the physical distance between those identical points, and can range from picometres for the highest frequencies, to kilometres for some of the lowest.

Finally, amplitude is the height of the wave in whatever system it is being measured in. For Alternating Current power, that is volts. Electromagnetic waves may be measured in volts for amplitude, or one of several other units for field strength, energy, and so on. The graph always looks the same. For physical waves like ocean waves, the amplitude is a physical distance in metres.

# WHY DO WE NEED TO GENERATE SINE WAVES?

Sine waves are used quite a lot in electronics. A lot of the time, they are generated not so much deliberately, but because that's how many oscillators work naturally. The current surging between a capacitor and inductor in an LC tank circuit, for example, behaves sinusoidally.

Audio waves are also sinusoidal, and while a square wave fed to a speaker will generate sound, it is rarely clean-sounding. Incidentally, the speaker still moves somewhat sinusoidally, because of the mass of the speaker and its inertia shaping the square wave.

Sine waves are useful in testing audio systems and radio systems, and others besides. So, the two most common reasons to deliberately generate a sine wave are as a specific sound generator, or as a test signal.

Next month, we are going to examine some component test circuits which make use of a sine wave and an oscilloscope to determine the properties of unknown components. Some methods of generation are more complex than others. Some are just more accurate, while some are cheap and easy while being far from perfect. What one is the 'best' one depends on what you need to achieve, and how much you have to spend on achieving it.

One thing to note is that some circuits suit certain frequency ranges better than others. Even the dedicated test equipment may not respond high enough for a given need, so always check the specifications. Because we have covered so many methods in one article, there isn't necessarily space to go into serious depth in some cases.

We've tried to cover what is needed, with enough information for you to know what to look for to research further if needed. The reality is that if you need a sine wave generator circuit that can produce, say, 3GHz, you're probably not learning anything new from this article anyway!

# METHOD 1: BUY A FUNCTION GENERATOR

The easiest, but most expensive method of generating a sine wave is to buy a function generator. Function generators are highly versatile, and can generate much more than sine waves. They can, at the lower end, generate sine, square, triangle, and sawtooth (ramp) waves. As you climb the product ladder, you can find things like arbitrary waveforms (where you define the points and can make an array of non-linear waves that may not even conform to an algebraic pattern), combine waves, and a host of other features.

Some time ago, we finally got around to buying one of our own. We didn't go too far up the ladder, but didn't buy the cheapest, either. Ours has two outputs, plus a pulse output. Frequency, amplitude, phase, and DC offset can all be specified for each of two individual waveforms. It can be made to sweep across a range of signals repeatedly, or continuously emit one frequency.

It also has a burst mode. Many of the sine wave oscilloscope screenshots seen in this article were generated with this function generator. The one we bought is digital, using a stepped voltage to generate its waves. Some use this method, some are full digital synthesis (and priced accordingly) and some are based on analog circuitry or a hybrid of both.

Function generators range in size and price. Some are handheld, while others take up most of your workbench. Many are in between. Altronics has the Q1542 handheld for \$135, while Element14 has products ranging from around \$270 to \$24,000. Ours came from Element14, and is the GW Instek MFG 2230M.

This retails for close to \$900 at the time of print, but because Element14 is constantly importing and the value of the AUD (and the world economy in general) is so unstable at the moment, that could change either way before you read this.

This product has a frequency counter function; different modulation types such as AM, FM, ASK, PWM, and more; a 30MHz upper frequency limit although this varies depending on the waveform; and a 25MHz pulse generator separate to the two function outputs. For some readers, this is nowhere near enough. For others, it's too much. So don't be tempted to just get what we got! Think about your needs and budget, and do a bit of research. Also, our decision was influenced by what was in stock at the time.

# METHOD 2: BUILD A FUNCTION GENERATOR KIT

If you don't need that much functionality, or you are not going to use a function generator often enough, you might consider a DIY or kit option. Way back in Issue 18, we published a square wave generator and a frequency counter project. While not capable of sine waves, this project illustrates the concept. These generally use one or other of the methods outlined below, so be careful: The sine wave may be of varying quality!

The Sparkfun FG085 Function Generator kit is available from some Australian online retailers, but that was the main one we could find currently in stock. There are some others from online sellers that we could find out nothing about, and quite a few out-of-stocks, too.

Be careful when shopping for function generator kits: Many cheaper ones, aimed at kids, are from some learning series or other and only generate square and triangle waves, not sine waves.

# METHOD 3: SHAPING SQUARE WAVES

The first fully DIY method involves first generating a square wave, then shaping it. This is done by a series of RC networks forming a series of filters. While you would never know it by looking at a square wave on an oscilloscope, there is something called Fourier theory which shows that a square wave is made up of a fundamental wave and a bunch of harmonic frequencies of different magnitudes. That fundamental frequency happens to be a sine wave, and we can select it with filters.

Any square wave generator will do, but the NE555 square wave generator is the easiest for most people to recognise, and also the most common we found in our research. Some sources suggest the CMOS 555, but the standard NE555 is ok too, particularly at lower frequencies. The RC stages are a low pass filter, and strips off most of the harmonics. We have shown the output on the oscilloscope, but we only have a two-channel scope, so the first shot is the first two test points, while the second shot is the last two test points.

There are other similar options, including LC (inductor/capacitor) filters instead, or op amp based bandpass filters with a very narrow pass range. However, the one presented is the easiest for most makers. It is tuned for 1kHz.

In the reading and Resources section, we have linked to a great calculator for Low Pass filters so you can choose a different frequency. Also, you could use trimpots to precisely set a resistance value, against a measured capacitor value rather than the nominal stamped value.

The disadvantage of this method, and many of the others, is that it generates a fixed frequency.

# METHOD 4: WIEN BRIDGE OSCILLATOR

The Wien bridge oscillator is nearly as old as the field electronics itself, but is still a valid and reliable way of generating sine waves. Today, it is generally done with an op amp, but transistorised variants are to be found as well. The Wien bridge part is formed from two resistors and two capacitors. One RC network in series, connected to one in parallel. The components have the same value in each case, and the system relies on some sort of feedback. This is why drawings of it often show 'Voltage In' in some form on one side, and 'Voltage Out' on the other. The voltage in is, in reality, the voltage out from some other part of the circuit built around the Wien bridge.

If we add this to an op amp, with a purely resistive feedback path to the inverting input and the Wien bridge on the non-inverting input, with the output connected to the input of the bridge, we get a sine wave generator. The circuit oscillates because of the positive feedback it receives from the output to the Wien bridge with no phase shift (or, more technically, a 0° phase shift). The op amp produces a gain of three, because the RC networks in the Wien bridge have losses totalling a factor of three. The gain of the amplifier needs to offset this and end up with a total at unity. If more gain is required, a second amplifier stage should be used rather than trying to increase the gain of the bridge amplifier.

The frequency of oscillation is determined by:

where ƒ is the frequency, R is the value of both R1 and R2, and C is the value of both C1 and C2. Remember to calculate in base units.

There are some issues with this circuit. It can become unstable in both gain and phase, and either stop oscillating altogether, or saturate to produce at best a clipped sine wave but often a square wave. Because the gain is set by the formula: 1 + (R3 ÷ R4), it would be desirable for R3 to change itself. This can be achieved by using a small incandescent globe instead. The resistance of the globe increases as the filament heats, reducing the gain, which reduces the current that was heating the filament, and so a good stability is introduced. Because the gain is set at the inverting input by the relationship of these resistors rather than their absolute value, you can change the value of R4 to suit different incandescent globes. The values shown should work with most small grain of wheat globes.

The op amp Wien bridge oscillator is generally said to be good for up to 1MHz, however, this is due more to the limitations of the op amps involved rather than the Wien bridge. There are high-frequency op amps around, while some op amps would have issues well before 1MHz. If in doubt, check the op amp's datasheet.

# METHOD 5: PHASE SHIFT OSCILLATOR

The phase shift oscillator uses a series of RC networks to alter the phase of a feedback path to the inverting input of an operational amplifier by 180°. There are also versions which use a transistor and a couple of extra resistors and capacitors, but these tend to produce a much rougher sine wave than a dedicated op amp. There are different arrangements, too, of the RC networks, including shifts of 45° and 60°, so a different number of filters is needed to make 180° depending on the contribution of each. While it would theoretically be possible to create filters with differing angles that add up to 180°, we have not seen any designs during our research which do not use a set of identical filters.

The design shown was one of the most common we encountered. As with most of the other designs here, it produces a fixed frequency. This may or may not be a disadvantage. In many situations, a single frequency is good enough, such as a test signal for an amplifier in a go/no-go context. Note that we have not shown an output from the op amp output.

The output from here is a distinctly distorted sine wave, and the pure output is from the point indicated. In reality, this would need some sort of amplification or buffering for use, but is good enough as-is when the destination for the signal is something like an op amp or preamplifier, or some other high-impedance, low power use.

The frequency of the wave is determined by the formula above. All the R and C values are the same, in this case. We stated before that the RC networks can be different values if a combination of different phase angles is used to add up to 180°, but the situations which would demand that are well beyond the scope of this article.

The formula assumes three RC stages, and the 2.6 multiple will be different for a different number of stages. R4 and R5 are selected to be as high as practical in value, as the high-impedance input of the op amp requires little current, and thus the signal power is preserved for the output.

Other designs using transistors often feature additional components for this reason. Note also that the formula is reasonably accurate but still approximate. The full maths involves a huge square root, because each stage loads the next. For the values given, this circuit produces close to 1kHz.

The gain for the op amp should be set to around 30 because of the loading effects of the RC networks on each other. It is possible to use a buffer, such as an op amp connected as unity gain, between each stage on the RC network. Once again, however, that is a topic for independent research now that you have a foundation.

This circuit, with its variations, is so popular that you can even buy books on the subject! There are versions with a transistor instead of the op amp, too.

# METHOD 6: DIGITAL REPLICATION

It is possible to produce a sine wave digitally. How desirable it is to do this depends on both the cleanliness needed in the resulting waveform, and the sample rate available with the digital hardware you have available. In commercial form, it is called Direct Digital Synthesis, abbreviated as 'DDS'. The basic premise is to create a series of steps in voltage, which approximate an analog waveform.

How well they do this depends on the sample rate. For example, a device which has a digital to analog converter (DAC) which can perform ten samples per second, will produce a much rougher waveform than one which can perform ten thousand or more samples per second. The diagram is exaggerated to show the point.

Many commercially produced function generators are DDS machines. While it may be tempting to regard a digital replication of an analog wave as inferior, they are quite often not. In the case of a DAC in a very basic microcontroller which can only achieve ten samples per second, maybe this is true. However, most of the analog circuits presented produce an imperfect waveform anyway. It is common for a DDS system to produce a cleaner waveform than most 'home-made' oscillator circuits.

While this might be obvious when regarding a \$10,000 + test instrument, the consideration becomes more real when performing DDS DIY. An Arduino, for example, does not come with a DAC capability, with a couple of exceptions. DAC can be performed using an external circuit. This can be a dedicated DAC IC, or a circuit based around an op amp, and an RC filter. In the latter case, the RC filter acts to smooth a PWM signal issued from the digital pin of the Arduino into a voltage which the op amp buffers.

The code written has to perform the maths of varying this PWM duty cycle in order to produce a sine wave at the output of the op amp.

The circuit is a regular active low-pass filter, and turns the PWM output into a voltage waveform. Depending on the load, you could even, by many accounts, get away without the op-amp. The values of the components will vary depending on the frequency needed, or frequency range, but the maths for low-pass filters is pretty easy to find. So much so that we haven't included it.

Also, we don't feel this is a very strong method. In basic terms, the value is changed using the 'analogWrite' function, and how often you change the value (in combination with your component values) determines the frequency, and the smoothness of the wave.

Dedicated DAC ICs can work numerous ways. Some use a PWM input from any digital pin, while others require ISP or I2C communication. Of those, there are different ways in which the code generates the analog output. Some use a PWM value but sent over ISP or I2C, while others use completely different information. The DAC0800LCN, for example, is an 8-bit device needing eight digital inputs to control its output.

# METHOD 7: CRYSTAL OSCILLATOR

RC and LC circuits have a limit to their accuracy. The resonant frequency can be affected by supply voltage, temperature, load changes, and more. One of the ways around this, if the application is critical, is a crystal. This is a tiny sliver of quartz crystal with plates on either side and electrodes attached. More correctly, the metal plate is chemically coated onto the crystal. The equivalent circuit for a crystal gives a good idea of why this device is so useful.

Applying a current to the crustal causes an oscillation at a very specific frequency. It is very, very accurate and is the reason crystals used to be the norm for setting the frequency of 27MHz band radio control equipment, among other things. Because of their accuracy, crystals can be used with a variety of oscillators which would otherwise use RC networks. Colpitts and Hartley oscillators can both be modified for crystal operation. We are describing a modified version of the Colpitts oscillator without a crystal subsequently. The Pierce oscillator is also to be found, and is worth a mention for its simplicity.

The Perce Oscillator uses a Radio Frequency Choke, and a FET, making it different from anything else in this article. It is still a 180° phase shift oscillator, however. It also relies on a variable capacitor, which are far less common at the retail level now than they once were. As such, we've only shown the Pierce in concept, and not with values as a buildable circuit. They do make for interesting reading though, if it catches your attention.

Be very careful if reading further, however. Many crystal oscillator designs are square wave oscillators. Because crystals are often used for very accurate clock pulsing, it is often assumed by the text describing them that the reader knows this is the output. You can, of course, use the square wave filtering option above to modify this to a sine wave if desired.

# METHOD 8: FUNCTION GENERATOR ICs

There are self-contained function generator ICs, some of which are dedicated to one waveform, while others can handle multiple waveforms. One which is very popular online, and that we have looked at several times for projects, is the XR2206.

Originally made by Exar Technologies, the XR2206 is a monolithic Function Generator IC, which is just a fancy way of saying it is all on one wafer of silicon and the only external components needed are to select timings. It does its job extremely well. Except that it does not.

The original Exar Technologies chips were accurate, reliable, and versatile, as well as being easy to use. Unfortunately, Exar has long since disappeared, and the chips on the market now are generally Chinese copies. Not very good ones, either, by every account we have read. There is also evidence that they are easy to spot by a certain date code that every single one carries, but we could not verify this.

If you can manage to find some new old stock, or if you're willing to risk it with one where the origin is uncertain, the XR2206 is a great choice. There are some other function generator ICs around, but they are hard to get besides from commercial suppliers and often in commercial quantities. We found a great one at RS Components, but the smallest quantity was a tube of twenty-five of them.

# METHOD 9: SALLEN-KEYS FILTER

This circuit is another square-wave to sine-wave generator/convertor, in which the first half generates a square wave, while the second stage filters the sine wave from it. This particular arrangement of filter is called a Sallen-Keys filter, and the example here is designed at unity gain: What goes in, comes out.

The op amp in question can be any device, but the better the specifications, the better the result. Don’t hope for great performance from a UA741, for example.

The best published design we found came from Texas Instruments via an Application Note paper, and this is that design with some value changes. The original was tuned for 1MHz, while we wanted a value of 1KHz. The original IC is a LMH6622, but we substituted for the retail-available LM833N.

In the square wave oscillator section, the frequency is controlled by C1 and R1. In the filter, it is controlled by R5, R6, C2, and C3. However, the calculations all flow from the frequency, and the nominal value of C1. R2, R3, and R4 need to be a tight tolerance, 1% or better.

If practical, measure them and choose values as close together as possible. For the other values, choose a value for C1 and use your chosen frequency to calculate the rest of the components. You may need to fiddle somewhat to get a good match between capacitor values and resistor values in the standard ranges.

# METHOD 10: CLAPP OSCILLATOR

Earlier, we mentioned the Colpitts oscillator. This oscillator is common in radio frequency situations, as it can cope with higher frequencies than many other designs.

Ideally, these use a tapped capacitor but there is no such thing at a retail level, so most makers will use two separate capacitors as closely matched in value as possible.

An LCR meter will be your friend here. With the addition of just one variable capacitor, the Colpitts oscillator becomes a Clapp oscillator.

There is also a way to build a variable Clapp oscillator, and these are popular with radio engineers and hobbyists in particular, because of the high frequencies they can achieve. Because that is not the target of this article, we've added a link in the Reading and Resources section, to a good concise bit of information on these, including a build.

# CONCLUSIONS AND NOTES

Most of these circuits have variations you can find all over the internet. In particular, there are quite a few variations of the phase shift oscillator out there, and all are valid. In some cases, a different way of making a circuit suits a particular frequency range.

Other changes are for different impedances, and still others are for differing signal strengths and levels. There is no 'right' way to make most of these circuits. However, sometimes there is a wrong way, although even then the concept of 'wrong' can be situation-dependent.

The Wien Bridge oscillator also has a huge variety of variations available. It was this circuit, featuring the now-common light globe element, that was the basis of an audio oscillator produced by Bill Hewlett and David Packard in a garage in Palo Alto, California, in 1938. Those two engineers landed a contract with Disney using tis device and other inventions, and began the Hewlett-Packard company that we know today as HP Inc.

When deciding in a sine wave oscillator for a particular need, it is always worth reading and researching far and wide. As noted, some designs are more suitable for certain frequency ranges and tasks than others. However, some may simply suit your build skills and comforts more than others. Higher RF frequencies, for example, involve making sure there are no leakage paths in the circuit and that interference between components is kept to a minimum.

You may find this easier with one design compared to another. However, it is unlikely that a design would be good for, say a 500Hz audio frequency, but unsuitable for 15kHz. The statement usually refers to whole different bands: The 20Hz to 20kHz audio band, for example, compared to the 433 MHz UHF radio band.

Don't hesitate to play around. We found some circuits took to breadboards well, while other suffered from noise and interference. Component availability may also affect your decision. Above all else, remember: There is almost always more than one option. Don't get too disheartened if one design does not work: Troubleshoot it first, but then, try another!

# Square Wave Oscillator

Parts Required:IDJaycarAltronicsPakronics
1 x 13kΩ ResistorR1RR0599R7585DF-FIT0119 ^
3 x 15kΩ ResistorsR2, R3, R4RR0600R7586DF-FIT0119
3 x 10nF MKT CapacitorsC3, C4, C5RM7065R3013BDF-FIT0118 #
1 x 47nF MKT CapacitorsC2RM7105R3021BDF-FIT0118 #
1 x 100nF MKT CapacitorC1RM7125R3025BDF-FIT0118 #
1 x 1N4004 Rectifier DiodeD1ZR1004Z0109DF-FIT0323
1 x NE555 Timer ICIC1ZL3555Z2755-
1 x 8-Pin IC Socket-PI6500P0550-
7 x PCB PinsTP1, TP2, TP3, TP4, TP GND, +V, GNDHP1250H0804A-

## Parts Required:

* Quantity shown, may be sold in packs. You’ll also need a breadboard and prototyping hardware.

^Use nearest value. # Ceramic values will work acceptably in this case.

We have chosen to build the Square Wave Shaper circuit as our hands-on build this month. This is the first one we came across when we needed a sine wave generator for another project and decided to fact-check what was in our heads. It also seemed to be one of the most common designs (alongside the Wien bridge), is among the most forgiving, and has a great array of variations. We're aiming to build ours at around 1kHz as an audio signal test instrument. We're building it with PCB pins at the test points indicated, for easy connection to an oscilloscope.

The schematic is the same as earlier in the article, as we calculated our values there for around 1kHz anyway. The only real changes here are the fact the circuit has been laid out on a board, and that we now have a Fritzing to help. We chose our standby, solder breadboard, because solderless breadboards are not the best when it comes to audio circuits. In addition, we will poke and prod this circuit quite a lot to take measurements, which is something else solderless breadboards do not cope well with.

If you like the end result, the use of a solder breadboard means you can keep it as a signal injector for future use. When building, go through your stock of components with a tester, and try to match values as closely as possible. Capacitors in particular can be a challenge, as the tolerance on common ranges is 10%, and may even be 20%. Many multimeters will measure capacitance, although some have little accuracy. All multimeters will measure resistance, but we used an LCR meter for both jobs.

Assembly is reasonably straightforward if you follow the Fritzing in combination with the circuit diagram and photos, so we will not describe the steps in text per se. All that needs to be said is that regular construction practices apply: Work from low-profile to high-profile components; make mechanical connections to the board (bend the legs); work a few components at a time so you can access each solder joint and don't miss any; and double-check at each stage. The other note is that we used a 1mm drill bit to enlarge the 0.8mm holes in the PCB to accept the PCB pins without blistering the fibreglass and tracks underneath.

The finished product produces 857Hz, disappointingly far from the target. However, we realised that with this arrangement of equal mark/space astable 555, the calculations are a bit different. We dropped the 15kΩ resistor R1 shown in the photos to a 13kΩ resistor, and then we were at 991Hz. Much better!

Also in the photos, you can see we added the diode later on, after some of the higher profile components were fitted. This was just an oversight from rushing too much. This circuit is the one we used to gain the oscilloscope screenshots shown in the square wave shaper section earlier. You can see the attenuation in the signal at each stage, as the signal level drops.

We did not adjust the voltage scale so you can see this
more clearly. Here is a screenshot with the voltage scale adjusted so that the wave can be more clearly seen to be a sine wave.