Extremely-low distortion oscillator, half 1: how to not do it.

Editor’s Be aware: This DI is a two-part sequence.

Half 1 discusses audio oscillators, particularly the Wien bridge and biquad, state-variable, or two-integrator-loop configuration.

Half 2 will add distortion-free suggestions to the biquad to provide a pure sine wave.

Over time, the Design Concepts (DI) column has featured many attention-grabbing oscillators, however none that I can recall was particularly designed to provide a very clear sine wave. Placing that omission along with the necessity to rebuild my outdated sub-0.01% sine generator gave me the proper excuse to do some exploring, ending up with this DI, which is in two elements. First, we’ll take a look at methods to not do it, then half 2 will present the way to get Audio Precision® distortion ranges for RadioShack costs.

06.10.2024

06.08.2024

06.08.2024

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The options

We received’t even think about squashing a triangle wave to provide one thing fairly sinusoidal, as 0.3% THD is the perfect that this method may give with out complicated, multi-breakpoint “squashing” networks. Equally, phase-shift oscillators are out; their q-factor is low, and three-gang pots aren’t catalog gadgets. And if I had been designing one thing for contemporary manufacturing, the starting-point could be a 24-bit DAC fed by a small processor containing a big look-up desk, however that’s not one thing that may be knocked up from accessible elements in a day.

So, what’s flawed with a superb outdated Wien bridge circuit? The related Wikipedia web page incorporates a lot historic, sensible, and mathematical element, and it studies that distortion ranges right down to 0.0003% (3  ppm) may be achieved, so we now have one benchmark, although that’s more than likely for a spot frequency slightly than for a multi-range, fully-tunable gadget. A sensible goal is 96 dB or 0.0015%, which is absolutely the restrict for CD-type 16-bit linear PCM audio, whereas a extra arbitrary purpose is 120 dB, or 1 ppm. At these ranges, THD could also be dominated by circuit noise, which we’ll conveniently ignore for now.

Wien bridge oscillator

To verify issues out, I breadboarded a primary circuit utilizing an LM4562 op-amp, carefully-matched resistors and polystyrene capacitors, and amplitude-stabilised utilizing a photoconductive opto-isolator (basically an LED and an LDR) pushed by some heavy filtering. (A thermistor solely works for increased output ranges and could be very bouncy.) Determine 1 exhibits the schematic and Determine 2 the output spectrum at near 1 kHz for a degree of -20 dBV (about -22 dBu, or 0.283 Vpk-pk).

Determine 1 A easy Wien bridge oscillator, utilizing a photoconductive opto-isolator to assist stabilise the amplitude.

Determine 2 The spectrum of the oscillator operating at ~1 kHz, its output being at -20 dBV.

The spectrum implies a THD of about -76 dB or 0.02%: solely so-so. Nevertheless, I’ve learnt to be cautious of FFTs when the dynamic vary of the sign to be examined exceeds about 90 dB, and like to notch out a lot of the basic, permitting a clearer view of the harmonics. Determine 3 exhibits the results of this: a lot better, with a THD of maybe -88 dB, or 0.004%.

Determine 3 The spectrum of the identical sign, however with the basic largely notched out to indicate the harmonics extra precisely.

Higher, and never unhealthy for a lash-up, however nonetheless off-target. (Be aware that the dimensions now exhibits the relative degree of the harmonics, in dBc, because the oscillator’s output is at 20 dBV and the notch filter has a voltage achieve of 10 dB or 20 dB.) With a bit of extra thought and much more fiddling—or vice versa—we might most likely enhance its efficiency to the benchmark degree, however a special starting-point appears extra promising. The largest downside is the amplitude management loop as a result of eradicating all of the ripple results the damping badly, growing the loop settling time. The low Q-factor of a Wien bridge, 1/3, does us no favours in any respect.

Bi-quad loop filter

My favorite circuit for complete filters and oscillators has at all times been the bi-quad(ratic), state-variable, or two-integrator-loop configuration, one topology of which is proven in Determine 4.

Determine 4 A basic bi-quad or two-integrator-loop filter, with its high-pass, bandpass, and low-pass outputs.

It’s possible you’ll nicely recognise one thing like this from 100 and extra NatSemi/TI datasheets and app notes. Its fundamentals return to the Fifties, I believe, when “operational amplifiers” often meant racks of glowing bottles, and it’s versatile, designable, and controllable. This model is reduce for a Q-factor of ~16 and a achieve of ~10. We’ll now bundle it with a dashed line and deal with it as a module. Assume ±5 V to ±15 V provides, with loads of decoupling caps.

To make it oscillate, we take the bandpass (BP) output and feed it again to the enter at an acceptable degree. That is typically accomplished by limiting the BP sign with a pair of back-to-back diodes, a lot as proven in Determine 5.

Determine 5 The filter with added diode-limited suggestions turns into an oscillator, however with loads of harmonics, giving a THD of round 0.0%.

With the values proven, the diodes compress the sign to ~2/3 of the output degree. Lower than this, and we lose stability; extra, and the harmonics develop into extreme. The suggestions community proven retains the impedances across the diodes low to permit clear operation as much as 100 kHz and past, whereas the added thermistor improves the amplitude stability with temperature. Match the diodes for ahead voltage to minimise even-harmonic distortion. The third harmonic produced by the diodes is lowered by about 22 dB by the point it reaches the LP output, increased harmonics being attenuated much more.

The spectrum for the uncooked (LP) output exhibits a THD of ~0.08%, which is about the perfect that this method may give. (The “notched” spectrum—not proven—confirmed fewer and decrease peaks, however the third harmonic—the limiting issue—was nonetheless on the similar degree.) As a result of there is no such thing as a management loop as such, there may be no loop stability points, although the settling-time is considerable at low frequencies. It’s nonetheless a superb foundation for a multi-range general-purpose AF oscillator.

With correspondingly bigger capacitors and resistors, it additionally works nicely at very low frequencies, although FET-input op-amps are wanted to keep away from leakage. With tuning parts of 5µ7 (= 4µ7 + 1µ0; PET dielectrics) and 3M3 resistors, and with TL072s fitted instead of the LM4562s, the waveform at ~8 mHz, or a calculated 118.2 s/cycle, appears like Determine 6.

Determine 6 Utilizing µF and MΩ for tuning, a diode-stabilised bi-quad will simply work down within the mHz area—about 8 mHz, on this case.

Why anybody would wish to use a purely analog method to producing such low-frequency indicators escapes me, however making an attempt it was irresistible, even when it took an hour or so to calm down correctly. (I lacked the persistence to attempt even bigger values of timing parts. And don’t even consider asking for the spectrum.)

To be continued…

Partly 2, we’ll take the bi-quad filter and add distortion-free suggestions, much like that used with the Wien bridge however on steroids, to provide a severely pure sine wave.

—Nick Cornford constructed his first crystal set at 10, and since then has designed skilled audio tools, many datacomm merchandise, and technical safety package. He has finally retired. Largely. Type of.

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