AN_938| Application Note
AN-938 APPLICATION NOTE
One Technology Way P.O. Box 9106 Norwood, MA 02062-9106, U.S.A. Tel: 781.329.4700 Fax: 781.461.3113 www.analog.com
Digital and Analog Measurement Units for Digital CMOS Microphone Preamplifier ASICs
by Rebecca Reich
INTRODUCTION
The purpose of this application note is to explain the difference between analog and digital values when measuring the input and output of a digital microphone preamplifier with an audio analyzer. Specifically, the difference between peak and rms values, when measured digitally (FFS or dBFS) or in the analog domain (V or dBV), is examined. Some sample calculations in the following sections illustrate the necessary conversions between the various definitions. The definition of 0 dBFS as a full-scale sine wave is used by several audio analyzers, and the rms and peak values in the digital domain for a sine wave are equal for these analyzers. The same analyzers show the rms level that is measured at the output in the digital domain as being 3 dB too high compared to the definition of rms level in the analog domain. Thus, a square wave whose top and bottom are at the maximum digital codes has an rms value of 1.414 FFS or 3.01 dBFS, and the peak value is 1.0 FFS or 0.0 dBFS, whereas in the analog domain, the rms v
alue for the corresponding square wave is 0 dBV both for peak and rms value.
UNITS IN DIGITAL AND ANALOG DOMAINS
A system diagram is shown in Figure 1. The transfer function of the ASIC is labeled A.
TRANSFER FUNCTION A
ASIC
x(t) GAIN
T = 1/fCLK vo[n]
ADC
x(t)
ANALOG
vo[n] n T FFS 1.0
DIGITAL
1.0 V 1.0 MEASURING x(t): VAPEAK = 1.0V VARMS = VAPEAK 2 = 0.7V t
A X
1.0 n
MEASURING vo[n]: VDPEAK = 1.0FFS VDRMS(dB) = 20 log10 (VDRMS 1.0FFS) = 0dBFS
07038-001
VARMS(dB) = 20 log10 (1/ 2V) = 3dBV
/
VDRMS = 1.0FFS
/
Figure 1. Conversion Between Analog and Digital Domains, When A = 1.0
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