Continuous-Time Sigma-Delta A D Conversion: Fundamentals, by Friedel Gerfers, Maurits Ortmanns

By Friedel Gerfers, Maurits Ortmanns

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Extra info for Continuous-Time Sigma-Delta A D Conversion: Fundamentals, Performance Limits and Robust Implementations (Advanced Microelectronics, Volume 21)

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This topology has been widely used [34, 63, 71, 72] and optimal scaling coefficients were presented in [6]. In Fig. 18) . 19) 26 2 Basic Understanding of Σ∆ A/D Conversion u(n) a1 H(z) - aN H(z) a2 H(z) - y(n) DAC Fig. 14. N th order single-bit Σ∆ modulator consisting of a chain of integrators with distributed feedback ai When using DT integrators as filters H(z) = I(z), the NTF is approximated for low frequencies [6]: |NTF| ≈ 1 − z −1 N N i=1 ai kq . 20) Obviously, the complete scaling of the outermost feedback branch dominates the noise-shaping behavior.

Throughout this book, in some Matlab simulations dithering has been introduced to smooth the spectrum, especially when simulating second-order modulators; but this dither has been added in amounts, which are comparable to the thermal circuit noise of an actual implementation. 1 1 (b) Fig. 12. Simulated power spectrum of a DT first-order, single-bit Σ∆ modulator. ∆ = 2, OSR = 64, Psig = −20 dB at fsig = fB /3 and Pdc = −20 dB. Dashed : integrated noise power. 6 Performance Increase in Σ∆ Modulators 23 reduce the in-band quantization noise.

Only the signal itself is subtracted. – Signal-to-noise ratio. The SNR of a converter is the ratio of the signal power to the noise power at the output of the converter, specified for a certain input amplitude. Most often, the maximum SNR, the peak SNRp , is pointed out. , no signal distortion will appear in the band of interest (when no intermodulation occurs). – Signal-to-noise and distortion ratio. The SNDR is the ratio of the signal power to the noise and all distortion power components. Thus, the corresponding spectra are obtained by applying a signal at fsig ≤ fB /3 to include at least the second and third harmonic inside the band of interest.

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