Editor’s word: The first half of this two-part design thought (DI) exhibits how modifications to an oscillator can produce a helpful and weird pulse generator; this second and remaining half extends that to step features.
In the primary a part of this DI, we noticed the way to gate an oscillator to generate well-behaved impulses. Now we learn how to increase that concept to producing well-behaved step features, or properly smoothed sq. waves.
The best right here is the Heaviside or unit step perform, which has values of 0 or 1 with an infinitely sharp transition between them. Simply because the Dirac delta impulse which we met in Half 1 is the acute case of a standard distribution or bell curve, the Heaviside is the restrict of the logistic perform (which I collect logisticians use about as typically as plumbers do bathtub curves).
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Sq. wave with easy edges
Anybody working with audio package could have employed square-wave testing with that infinity tamed by an RC time-constant, which is nice sufficient for on a regular basis use, however one other strategy is to exchange that still-sharp step with a portion of a cosine wave. Taking the circuit from Half 1 and including some extra gating implies that as a substitute of producing a full raised-cosine pulse for each set off enter, we get a half cycle at every transition, with alternating polarities. The outcome: a sq. wave at half the frequency of the set off and with easy edges. The revised circuit is in Determine 1.
Determine 1 Additional logic added to the unique circuit now provides half a cosine on every set off pulse, with alternating polarities, producing a sq. wave with smoothed edges.
In pulse or oscillator modes, U1b delivers a reset to U2 each time A1b’s output goes excessive, which supplies a full cycle of the raised cosine. Within the sq. wave mode, U2 is reset each time A1b adjustments, no matter polarity, on the half-cycle level. U1b and U3b/c act as a gated EXOR with delays by one leg to generate the reset pulse. Some waveforms are proven in Determine 2; examine these with these in Determine 2 of Half 1. As earlier than, A2 is jammed when the oscillator mode is chosen, forcing steady, sine-wave operation.
Determine 2 Some waveforms from the circuit in Determine 1.
A single, positive-going transition is proven in Determine 3, with our goal curve for comparability. These are each theoretical plots, however the precise output could be very near the cosine.
Determine 3 The goal step-function is a logistic curve; a phase of a cosine is proven for comparability.
In Half 1, we tried to get nearer to a standard distribution curve by some further squashing of our tri-wave. This labored up to a degree however was clunkily over-elaborate, partly owing to the waveform’s lack of symmetry. We now have a symmetrical perform to goal at, which must be simpler to emulate.
Constructing our goal curve
The spare part of mux U1 along with three new resistors presents a neat answer, and the circuit fragment in Determine 4 exhibits how.
Determine 4 Including the elements in crimson provides a significantly better match to our goal curve. The tri-wave amplitude is elevated and may now be squashed much more.
Placing 47k (R14) in collection with D3/4 will increase the journey factors’ ranges, in order that the tri-wave now spans ~4.3 V somewhat than ~1.1 V. The elevated drive to D5/6 by R7 leads to the diodes not a lot squashing the triangle right into a (co)sine as crushing it into one thing a lot squarer although with higher amplitude. R24 and R25, related throughout D7/8, pot the voltage throughout the diodes down in order that the peaks—which are actually mild curves—are cropped by A2b’s (rail-to-rail) output. (The resistive loading of D7/8 barely softens their response, which additionally helps.)
U1c does two jobs. When pulses or a steady sine wave are to be generated, it shorts out R14 and opens R24, giving our normal working situations, however in square-wave mode, R14 is left in circuit whereas R24 is grounded, as wanted for the additional tri-wave amplitude and crushing.
The waveforms now appear to be Determine 5 (word the change of scale for hint C) whereas a single, precise edge is proven in Determine 6 with a theoretical, supreme step for comparability—and the match is now superb.
Determine 5 Waveforms after including the mods proven in Determine 4.
Determine 6 Comparability of the goal curve with a part of the hint D in Determine 5.
There’s some fudging concerned right here, the 2 curves in Determine 6 having been adjusted for a similar slope on the half-height level. As a result of R24/R25 scale back the amplitude of the sign throughout the diodes by practically 20%, the slope can even be that a lot shallower than for the cosine model, which isn’t a sensible downside.
The ultimate circuit
To show all this right into a practical piece of package prepared for doing a little audio testing, we have to add some extras:
- A rail-splitter to outline the central, frequent rail
- Stage-control pot with an output buffer
- Easy oscillator to provide the set off pulses, with an enter in order that an exterior TTL sign can override the interior one
- A swap to pick the mode.
Placing all these collectively, we attain the complete and fairly remaining circuit of Determine 7. A number of ranges can simply be accommodated by including the extras detailed in Half 1, Determine 5. The modified pulse-shaping circuit proven in Half 1, Determine 6 is also added, however could also be extra fiddly than it’s price.
Determine 7 The complete circuit, which now produces sq. waves with well-shaped edges in addition to pulses and steady sine waves.
The absence of pin numbers is deliberate, as a result of their inclusion would suggest an optimized structure. Watch out to maintain the logic alerts away from analog ones, particularly at and across the earthy finish of R24, which might choose up switching spikes when open-circuited. U1’s E-not (pin 6) and VEE (pin 7) have to be at 0 V.
Whereas this strategy to producing nicely-formed pulses is maybe extra attention-grabbing than correct, it does present that crunching up triangles with diodes shouldn’t be restricted to producing sine(ish) waves, which was the starting-point for this concept. For something extra advanced, an AWG might be a greater answer, if much less enjoyable.
—Nick Cornford constructed his first crystal set at 10, and since then has designed skilled audio gear, many datacomm merchandise, and technical safety package. He has finally retired. Largely. Type of.
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