Model a Sigma-Delta DAC Plus RC Filter

Neil Robertson

Sigma-delta digital-to-analog converters (SD DAC’s) are often used for discrete-time signals with sample rate much higher than their bandwidth. For the simplest case, the DAC output is a single bit, so the only interface hardware required is a standard digital output buffer. Because of the high sample rate relative to signal bandwidth, a very simple DAC reconstruction filter suffices, often just a one-pole RC lowpass. In this article, I present a simple Matlab function that models the combination of a basic SD DAC and one-pole RC filter. This model allows easy evaluation of the overall performance for a given input signal and choice of sample rate, R, and C.

DAC Zero-Order Hold Models

Neil Robertson

This article provides two simple time-domain models of a DAC’s zero-order hold. These models will allow us to find time and frequency domain approximations of DAC outputs, and simulate analog filtering of those outputs. Developing the models is also a good way to learn about the DAC ZOH function.

Decimators Using Cascaded Multiplierless Half-band Filters

Neil Robertson

In my last post, I provided coefficients for several multiplierless half-band FIR filters. In the comment section, Rick Lyons mentioned that such filters would be useful in a multi-stage decimator. For such an application, any subsequent multipliers save on resources, since they operate at a fraction of the maximum sample frequency. We’ll examine the frequency response and aliasing of a multiplierless decimate-by-8 cascade in this article, and we’ll also discuss an interpolator cascade using the same half-band filters.

Pentagon Construction Using Complex Numbers

Cedron Dawg

A method for constructing a pentagon using a straight edge and a ruler is deduced from the complex values of the Fifth Roots of Unity. Analytic values for the points are also derived.

Multiplierless Half-band Filters and Hilbert Transformers

Neil Robertson

This article provides coefficients of multiplierless Finite Impulse Response 7-tap, 11-tap, and 15-tap half-band filters and Hilbert Transformers. Since Hilbert transformer coefficients are simply related to half-band coefficients, multiplierless Hilbert transformers are easily derived from multiplierless half-bands.

Interpolator Design: Get the Stopbands Right

Neil Robertson

In this article, I present a simple approach for designing interpolators that takes the guesswork out of determining the stopbands.

Return of the Delta-Sigma Modulators, Part 1: Modulation

Jason Sachs

About a decade ago, I wrote two articles: Modulation Alternatives for the Software Engineer (November 2011) Isolated Sigma-Delta Modulators, Rah Rah Rah! (April 2013) Each of these are about delta-sigma modulation, but they’re...

Simple Discrete-Time Modeling of Lossy LC Filters

Neil Robertson

There are many software applications that allow modeling LC filters in the frequency domain.  But sometimes it is useful to have a time domain model, such as when you need to analyze a mixed analog and DSP system.  For example, the...