SBOA550 October   2022 OPA1671 , OPA2990 , SN74HCS04 , SN74HCS164 , SN74HCS30 , SN74LVC1G00 , SN74LVC1G123 , TLC04 , TLC14 , TS5A9411

 

  1.   Abstract
  2.   Trademarks
  3. 1 Introduction
  4. 2 The Davies Generator
  5. 3 Optimizing Standard Resistance Values for THD Performance
  6. 4 Simulation Examples
  7. 5 Compensating for Shift Register Output Resistance
  8. 6 Voltage-Mode Thevenin Equivalent
  9. 7 Harmonic Filtering
  10. 8 Tracking Harmonic Filter
  11. 9 Multiphase Output
  12. 10Conclusion
  13. 11Acknowledgment
  14. 12References
  15.   A Analytical Solution for Resistance Network Values
  16.   B Forbidden States of the Johnson Counter

4 Simulation Examples

Using the values from Section 3 and assuming no random resistor variation, the following TINA-TI SPICE simulation of Figure 4-1 based on the SN74HCS164 shift register demonstrates the upper limit of THD performance while using a realistic model of the shift register but neglecting the output resistance. Using 0-V, +5-V logic levels as shown results in a common-mode DC offset of 2.5 V in the output. Depending on the application, subsequent circuit stages can require AC coupling or some other method to remove the offset if it is undesirable. The additional 1-kHz square-wave source shown is used as a reference to sanity-check the simulated THD estimates since the Fourier series is well known. The scaled mid-supply common-mode voltage, VCM, provides the virtual ground that the op amp of Figure 2-1 otherwise provides.

Figure 4-1 Simulation Schematic of MSI Logic Based “Davies” Generator With Square Wave Reference Source for THD Comparison

Clocking the circuit at 16 kHz results in an 8 × oversampled 1-kHz stepped-sinusoidal current into the virtual ground node, along with the reference square wave current.

Transient Simulation Results of Figure 4-1.
Figure 4-2 Transient Simulation Results Previous Image Showing Stepped Sinusoid and Square Wave Reference Waveforms

From within the TINA-TI diagram window, each curve is selected and a Fourier analysis estimates THD. As a sampled data system, only harmonics in the first Nyquist zone are considered and higher Nyquist zones ignored. This indicates that even without harmonic filtering < 0.17% THD is achieved, see Figure 4-3 and Figure 4-4.

GUID-20220531-SS0I-VJ9R-VJGH-M0KTJMGPQM1C-low.pngFigure 4-3 Simulated THD Results of Stepped Sinusoid Compared to Reference Square Wave
GUID-20220531-SS0I-RPHR-4ZXX-0QXX0JPQQ0FR-low.pngFigure 4-4 Simulated THD Results of Stepped Sinusoid Which Shows > 47-dB Improvement in 3rd Harmonic Suppression

The Fourier expansion of an ideal square wave is y ( t )   =   4 π s i n ω t + 1 3 s i n ( 3 ω t ) + 1 5 s i n ( 5 ω t ) + ∙ ∙ ∙ where ω = 2 π f O . From this expansion it is clear the ratio of the 3rd harmonic to the fundamental is 1/3 (–9.54 dB) and verified in simulation in Figure 4-4. This indicates the TINA-TI THD computation appears correct. The 3rd harmonic of the stepped sinusoid is –57.2 dB relative to the fundamental, a > 47-dB improvement over the square wave.