11  Fundamentals of Data Acquisition

We will first finish reviewing electrical circuits, to finish up Chapter 5 and Chapter 2 of Dally, Riley, and McConnell (1993). Then we will start do discuss analog-to-digital conversion.

The first set of slides can be found here.

We are then ready to understand the following concepts, as illustrated in Chapters 6 and 7 of Figliola and Beasley (2019):

• Loading errors and impedance matching (Section 6.5, Example 7.8)
• Analog-to-Digital Converters (Equations 7.14, 7.15, Example 7.4)
• Filters: (maybe Example 7.9)

Technical Questions

1. When conneting different stages of our instrument (e.g., an analog device to an A/D converter), why is it that for current source inputs, we want to have \(Z_2\) (the impedance of the next stage) be smaller than that of the source? Can you derive the expression for the loading error in this case (i.e., \(e_I = I_2 - I_1\) where \(I_1\) is the current that would circulate if we short-circuit the terminals of our first device – the source – and \(I_2\) is the current that is pushed through the second device when connected)? Why is it \(e_I = V_1 \frac{-Z_2}{Z_1^2 + Z_1 Z_2}\)?

2. Can you show that equation 7.6 from Figliola implies a folding point for aliased frequencies, that is exactly at \(f_s / 2\)?

Dally, James W., William F. Riley, and Kenneth G. McConnell. 1993. Instrumentation for Engineering Measurements. 2nd ed. New York: Wiley.

Figliola, Richard S., and Donald E. Beasley. 2019. Theory and Design for Mechanical Measurements. Seventh edition. Hoboken, NJ: Wiley.