Extremely-low distortion oscillator, half 2: the true deal

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

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

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

In Half 1 of this text, we briefly seemed on the Wien bridge oscillator earlier than homing in on the bi-quad filter as our greatest candidate for an oscillator able to giving <0.0001%/-120dB distortion, and confirmed its full circuit. Treating it as a module, it’s prepared for including distortion-free suggestions within the type of a linear limiter.

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Making an attempt a J-FET for that limiting proved disappointing. Even when the circuit was optimised to minimise its inherent non-linearity, it added about -92dB/0.0025% of third harmonic to the suggestions sign. As famous in Half 1, the attenuation of a 3rd harmonic from the enter to the low-pass output is ~22 dB, so we ended up with 0.0002% or -114 dB distortion on the output. Shut, however no cigar.

Let’s return to the photoconductive opto-isolator which we used to stabilise the Wien bridge circuit in Half 1. The LDR or photo-resistor a part of it’s after all linear, however the LED wants cautious driving to stop any vital feed-through of ripple which might modulate the suggestions and thus add distortion. Determine 1, displaying the management loop added to the essential bi-quad module, incorporates a neat method of minimising ripple whereas retaining cheap loop dynamics.

Determine 1 Utilizing a good management loop for the suggestions stabilises the oscillation degree with out including vital distortion.

As a result of the bi-quad has two outputs (HP and LP) that are in anti-phase, we are able to simply get full-wave rectification, however we are able to do significantly better. The BP output is at 90°/270° to these, so we are able to additionally use each that and its inverse to get 4-phase rectification, reducing the ripple to 1 / 4 of the single-phase worth. The ripple may even be at 4 occasions the bottom frequency, so we’re (roughly) sixteen occasions higher off than we had been with the Wien bridge. 

With accurately-matched time constants within the bi-quad, all three outputs have similar sign ranges at resonance, however any offsets or mismatches will introduce ripple as sub-harmonics of the 4× part (if that is smart). The diodes have to be well-matched, and the op-amps have to have low voltage offsets, or not less than decrease than any diode mismatches. Good monitoring between the tuning pot sections is required; typically an additional resistor paralleled with the higher-value half provides satisfactory outcomes.

R16, C3, and C4 kind the loop filter wanted for steady operation, whereas R17 and C5 give further filtering of the 4× part. These values are compromises; the loop is considerably underdamped however provides respectable efficiency over the complete tuning vary and takes lower than 500 ms to stabilise. A5 interprets the filtered voltage right into a present to drive the LED, thus controlling the LDR’s resistance. The opto-isolator used was a Silonex NSL-32SR3; a home-brew system constituted of a (recycled) NSL-19M51, a transparent white T-1 LED, and thick black heatshrink labored properly; although with about half the sensitivity. (I used that when experimenting with squashed tri-waves, despite the fact that it wasn’t wanted within the last reduce.) R18—the one adjustment wanted—units the LED drive, and thus the AF output degree.

The suggestions loop is closed via the community of R10, R11, and the LDR. At startup, the LDR has a excessive resistance, however there’s sufficient suggestions to begin oscillation, after which it progressively shorts R11 to offer the specified sign degree.

LDRs are pretty sluggish of their response occasions. This one has a resistance of about 1.7k at our drive degree we, responding to gentle in ~6 ms and to darkish in ~30 ms (measured 63% figures). This provides us some helpful further ripple filtering.

All crucial op-amps are proven as LM4562s, that are my present favourites for common audio work, given their stability of low noise, distortion, and offset figures, coupled with straightforward availability as DIP-8s. (However what do they sound like, you say? Dunno; can’t even hear eight of them, chained between phono enter and mixer output.) Their quoted THD+N of 0.00003%/-130dB will set the restrict for our efficiency: time to have a look at some outcomes (Determine 2).

Determine 2 The spectrum from the low-pass output, after unity-gain buffering.

Not very spectacular! However bear in mind from Half 1: I don’t belief my FFT if the enter dynamic vary is >~90+ dB, so attempt to take away a lot of the elementary first. (Is it a coincidence that 96 dB ≈ 2¹⁶:1?) Passing the sign via the—now deeper—notch filter, exhibits Determine 3.

Determine 3 The spectrum after notching out a lot of the elementary, displaying the harmonics far more cleanly.

That’s higher! Be aware that these spectra concerned very lengthy runs, averaging the sign over tens of 1000’s of samples. This was wanted to keep away from lacking legitimate peaks or eradicate spurious ones in addition to simply letting us see what would in any other case have stayed buried in noise. All checks had been run with energy from a 12-V accumulator—no mains hum or different nasties—with an op-amp as a rail-splitter, and in an earthed Faraday cake-tin.

I selected to make use of a working degree of 20 dBV as being a superb compromise between distortion and value. My last unit has further output acquire, given by a virtual-earth/pseudo-log-pot stage (LM4562, after all). Determine 4 exhibits the notched spectrum from that, measured at +6dBu (~+4 dBV, or ~1.54V RMS, or ~4.4V pk-pk), displaying a THD of near -120dB, or 1ppm, most of that being second harmonic (supply as but unidentified).

I feel we’re there, so far as distortion goes.

Determine 4 Spectrum (notched) after amplification to +6dBu. Be aware the altered scale.

As a result of I used sockets for A1‒A4, this being a re-build of a defunct unit, making an attempt another op-amps was straightforward. Determine 5 exhibits the outcomes for the KA5532, previously well-regarded for audio work, TL072/TL082 (or TL0n4 quad-packs), LM358 (with further 10k resistors to Vs- tacked onto the outputs), and even the venerable MC1458—primarily twin 741s. Frequency and output degree had been trimmed for every run to permit correct comparisons. The LM358 shocked me; needed to double-check it. By no means did just like the sound of them, and now I do know why.

Determine 5 Distortion spectra for numerous different gadgets.

All this work was at a nominal 1 kHz (truly 1003.4 Hz). I can’t converse for different frequencies, missing appropriate notch filters, although their un-notched spectra look a lot the identical as that for 1 kHz. As drawn, the oscillator will tune from <500 Hz to >5 kHz in a single vary, which makes it a helpful little bit of package in its personal proper. For different ranges, the loop filters would have to be modified to keep up satisfactory loop stability whereas retaining good filtering.

These outcomes might present THD ranges beneath 140 dBc, or 0.00001%, or 100 ppb, however they may nonetheless be buried in noise, and the THD+N determine—which has conveniently been ignored to date—appears to be like a lot worse than the easy THD one. Calculations utilizing the datasheet figures for the LM4562 below our situations indicate noise from the output buffer (inverting, unity-gain) of ~-114 dBV or -112 dBu in a 20 kHz bandwidth, with (resistive) Johnson noise dominant, so we could also be left with a THD+N of “solely” about 92 dB, or 0.0025%, or 25 ppm. An AC microvoltmeter (BW = 10 kHz) related to the output, with R5/6 within the bi-quad disconnected and C2 shorted, measured 113 dBu, which is according to the calculations. Utilizing totally different op-amps might assist barely with present noise however can by no means scale back the resistors’ noise. Analog Units publish a superb, primary tutorial on op-amp noise, in addition to a number of far more detailed analyses.

Clearly, when utilizing this as a supply to measure the THD in an audio chain, averaging will likely be wanted to extract the harmonics from the noise, precisely as we used all through this DI—however ensure you can belief your FFT or, use notch filtering to scale back the elemental.

We now have an oscillator able to delivering a sinewave with distortion (alone) measurable in elements per billion—OK, tons and many them, however hey! Who’s counting? That sounds good—and which, given the suitable elements, will be inbuilt a day.

—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 ultimately retired. Principally. Type of.

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