• Higher-order sigma-delta converters

Lecture 10: Higher-order sigma-delta converters

Exercise

• Exercise 10

• Exercise 10 Reference Solution

• Material for Matlab Exercise 10 (contains solution to Exercise 9)

Matlab Exercise

The 50-MHz bitstream from the previous exercise would be too fast to drive a loudspeaker through power transistors. 2 MHz is the maximum that can be achieved with most chips from Texas Instruments.

So: build a digital sigma-delta converter of higher order that brings (low) audio quality at a sampling rate of at most 2MHz; use asf_ex10.zip

Three comments:

1. Don't forget to run setup_project.m to get the paths set up properly.
2. Use synthesizeNTF and realizeNTF as it was done in dsdemo1.m and dsdemo2.m, and play also with the parameter Hinf.
3. When you turn to sd3 and sd4, and are frustrated because none of your first attempts work, remember that a sigma-delta converter can be unstable for higher signal magnitudes, so that turning ASig down may be a good idea.

Use Matlab or your tool of choice to simulate a Sigma-Delta converter. Assume an input, an integrator transfer function H(z)= z^-1/(1-z^-1), a comparator and a lowpass filter.

• Verify that your setup works in principle.
• Choose a sin-input and increase the frequency. Where should the cutoff of the lowpass be?
• Check for idle tones.
• Ramp up the input and check when the Sigma-Delta converter becomes unstable.