I've tried this a few different ways so far. One way was to do Down-Conversion Frequency Synthesis to audio, heterodyning pure sinusoids from a 32768 Hz Local Oscillator (LO), based on a sinusoidal reference crystal oscillator. This technique has the advantange that square wave mixers and BFOs can heterodyne with the crystal oscillator sine wave output to produce sine waves at audio. And the BFO range is compressed to < 2:1 for the wide audio range, virtually DC to beyond the range of hearing, > 1000:1. For example, a BFO with 24576-32768 Hz range will produce very low frequencies to 8192 Hz sine waves. It's certainly easier to make a 2:1 or less range oscillator more linear than a wide-ranging on, but there is also a compression effect with this smaller range. The sense of range is also inverted. Low-frequency output is produced when the BFO is near 32768 Hz, and high-frequency output is created when the BFO is at 24576 Hz. The compression comes into play in that the control voltages needed to create larger and larger musical intervals for higher frequency become smaller and smaller. For a wide range of musical scale, the high-frequency end becomes increasingly cramped, allowing noise and offset voltages to affect results. Interestingly, the harmonic relationships above a fundamental remain simple multiples of a base output frequency, but nevertheless a cramped, sense-inverted antilog control voltage is required. For multi-harmonic generation, a set of BFOs is needed, and they all must be precisely calibrated against each other, and the 32768 Hz reference frequency. Not impossible, but difficult. And while phased relative to the reference frequency, any indivdual harmonics are not really phase-locked against a fundamental frequency. This is what I would call an Oscillator Array approach to a Harmonic VCO.
Over the years, I've also researched and developed various frequency multiplication and division techniques that use waveform signal processing. A common example is a frequency doubler for a specific wave shape. For example, passing a bipolar triangle wave through a precious full-wave rectifier produces a 2x frequency triangle wave at notionally 1/2 the amplitude. Another technique I developed in early 2017 used several phased trapezoidal triangle wave generators from which more than one simultaneous frequency can by generated from processing the trapezoids; which harmonics constructed depends on the radix of the phasing used. For example, three trapazoidal generators have 6-phases enables generation of a fundamental frequency f1 and a triple frequency f3 and 1/3 of the fundamental amplitude. This approach is what I would call an Oscillator Chain. Other radix chains can be created, and more harmonics produced by combining chains with frequency doublers. But it becomes increasingly difficult with higher-numbers of phases, and again each chain must be calibrated for equal-time generation of trapezoids.
Another forms of frequency multiplication can use waveshaping techniques other than doubling. One that I developed also in early 2017 developed a quantized stairstep waveform that tracks a sawtooth primary wave. By setting various radixes for the quanta in multiple circuits, various higher-frequency sawtooth waves can be emitted by subtracting the stair step from the primary sawtooth. I prototyped this circuit in radix-9 with LM339A comparators, a precsion resistor ladder divider driven from a voltage reference, and LMC6484A for precision rectifiers. It did actually work to a degree. But!
One common thread in all these type of circuits is non-linear switching response times, and also variable, frequency-dependent times for non-linear switching events. When these types of delays enter into the circuits, signal leakage develops. The resulting multiplied frequency has a sound with some clang or shimmer: harmonics other than intended. This was especially the case with my LM339A/LMC6484A circuit design. The comparators actually switch slower and slower with declining sawtooth frequency.
Another technique is an A/D. The digital outputs of fast A/D are de facto frequency multipliers of the input waveform (which can be a variety of waveshapes). But like the case of all of the above circuit designs, the A/D has to be really fast. Something like the nearly unobtainable 6-bit CMOS CA3300D flash A/D is needed, even for audio frequencies. The more obtainable half-flash convertor like the ADC0820 is not nearly fast enough with conversion times of a bit less 2µS. An alternative is constructing one's own flash A/D, but that still requires very fast comparators, and it's probitively expensive above perhaps 3-4 bits.
I'm presently contemplating a universally programmable triangle wave frequency multiplier. Based on prior experience, I'm zooming in on an essential component to any such technique: a fast comparator. So, this evaluation report is about the LM319N dual comparator, which I wanted to characterize for high-speed, as well as any implementation difficulties.
Comments
Post a Comment