555 Delta-Sigma Modulator


Introduction

Inspired by the 555 Contest to come up with a novel use for the 555 timer, I crafted a Delta-Sigma Modulator circuit that can be used as the basis for an audio amplifier, servo amplifier, A/D circuit, or most anywhere you need an analog signal converted into a digital pulse stream. This circuit is original, at least to me. It seems like someone should have done this already, but I was unable to find anything similar online. There are lots of 555 based class-D amplifiers, but all the ones I found were using the control input and trying to PWM, rather than implement delta-sigma modulation. If you know of anything similar out there, please let me know via e-mail (charles at steinkuehler dot net).

Videos with operating waveforms of the basic circuit and improved circuit are available on youtube.

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Fully functional 555 based delta-sigma modulator

Background

A delta-simga modulator is formed by quantizing the integral of the input signal minus the output.

Ds.png

With a simple transform (inverting the quantizer and changing the signs on the adder inputs), the above circuit turns into something we can build with a 555.

Ds-inv.png

The 555 delta-sigma modulator begins with a basic 555 astable circuit using just two external components: a resistor and capacitor to set the timing.

555a.png

In the astable 555 circuit above, we already have two of the key delta-sigma components implemented. The resistor and capacitor from an integrator with positive feedback from the output, and the 555s internal comparators functions as an inverting quantizer. Essentially, you can think of the astable 555 timer circuit above as a delta-sigma modulator with a constant zero input, which yields a 50% duty cycle output.

Basic Working Circuit

To provide for a signal input, we need a way to add the input term to the RC integrator network of the 555. Assuming a voltage input, that means we need to connect a voltage to current converter between the input signal and the integrating capacitor, as shown in the following schematic. Q12 forms a constant 1 mA current source, while Q11 is biased to sink 0 to 2 mA. This yields a net +/- 1mA signal-based current being fed into the integrating capacitor C1, where it gets summed with the feedback from the output.

555b.png

At this point, the circuit is a completely functioning delta-sigma modulator. The output can be filtered and used to efficiently drive a load (class-D amplifier). You can also feed the pulse train into additional logic (ie: a micro-controller timer input) and create a sigma-delta A/D converter. Example waveforms of the operating circuit can be found on youtube.

Improved Circuit

As an improvement, while the input voltage to current converter and the timing capacitor form a true integrator, the RC integrator for the output feedback is less than ideal. The farther the output gets from 50% modulation, the more error is introduced by the RC feedback circuit not functioning as a true integrator. Adding an additional voltage to current converter, or implementing current-source feedback substantially improves the performance, particularly as the output level increases. Following is the basic delta-sigma modulator modified to include constant-current feedback from the output. Also shown is the output filter used for performance testing. Example waveforms of the improved circuit can be found on youtube.

555c.png

Circuit Notes

See below for real performance data at various operating points.

Performance

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Performance with 1 KHz sine wave
C1 value Test Circuit Center Frequency Output Level Performance
Volts P-P dBu THD % THD+N %
220 pF Improved 378 KHz 10 dBu 0.53%
Basic 460 KHz 2.89%
460 KHz 8 dBu 1.41%
330 pF Improved 270 KHz 10 dBu 0.54%
Basic 329 KHz 2.84%
329 KHz 8 dBu 1.34%
470 pF Improved 210 KHz 10 dBu 0.55%
Basic 257 KHz 2.85%
257 KHz 8 dBu 1.37%
680 pF Improved 145 KHz 10 dBu 0.56%
Resistor 178 KHz 2.93%
178 KHz 8 dBu 1.37%
Performance at various output levels
220 pF Improved 378 KHz 11 V 13.4 dBu 1.47% 1.51%
10 V 12.6 dBu 0.82% 0.83%
9 V 12.0 dBu 0.67% 0.69%
8 V 11.1 dBu 0.55% 0.56%
7 V 9.8 dBu 0.42% 0.44%
6 V 8.5 dBu 0.34% 0.36%
5 V 6.8 dBu 0.27% 0.32%
4 V 4.7 dBu 0.20% 0.30%
3 V 2.1 dBu 0.14% 0.33%
2 V -1.3 dBu 0.08% 0.46%
1 V -8.5 dBu 0.05% 1.03%

Updates

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Triangle wave generator with FET regulated current feedback

Feedback from the 'net: In this design, a FET based current regulator is used for the feedback loop to improve the performance of the triangle wave generator. This FET circuit could also be used to directly replace the 2-transistor / 2 resistor current regulator in my improved circuit, above.


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This information may have errors; It is not permissible to be read by anyone who has ever met a lawyer.
Use is confined to Engineers with more than 370 course hours of electronic engineering for theoretical studies.
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