## Pulse Propagation in Shallow Water

Finally some physics! Ok, so it took 27.5 years to convert this to pdf, but worth the wait I hope: shallow_water_v16. The problem is the propagation of sound waves in shallow water and I will just quote from the note I added near the front of this first electronic version of the original hardcopy document:

“Green’s functions, emergence of geometrical acoustics from partial differential equations, Euler polynomials, asymptotic series, absorption handling in reflection coefficients together lead to analytical solutions and fast algorithms. This is a complete work: It includes all derivations and all programs and does not overly reference external material.”

Feedback welcome. Either here or at my email wagt@sbcglobal.net.

Paul

## Finite Resolution DAC Spectrum

Finally … managed to pull together esotheric mathematics related to data converters gathered over 18 years and different places around the globe into something that – to me at least – feels coherent.

The output spectrum of a finite resolution DAC including arbitrary DNL profile is expressed as a sum over all DAC output levels. The result is exact, allowing excel based fast numerical evaluation, short-ciruiting the normal route of time domain computation followed by Fourier transformation. It even contains a “Master formula,” an equation so compact and rich in consequences, encoding a connection between analog and digital, that it deserves that name. Enjoy!

The pdf file: DAC_finite_resolution_spectrum_v23

As an experiment, I add here the excel file that was used to compute the numbers and create the plots for the numerical examples in the paper: dac_spectrum_v13_8bit_64bins

## Two kT/C or not Two kT/C: That is the Question

Analysis of “kT/C” noise for a finite bandwidth switched-capacitor integrator: discreteIntegratorNoise_v2.

## DAC Spectrum with Output Clock Jitter

Exact results for a DAC signal spectrum in the presence of output clock white noise and close-in phase noise. Significantly updated and expanded the May 2010 version in August: DACspectrum_v14.

## Graphical Analysis of Non-Ideal OTA Integrator

Fast analysis of the archetypical non-ideal operational transconductance amplifier (OTA) integrator circuit: OTA_GBW_v3.