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AN-938
APPLICATION NOTE
One Technology Way • P. O. Box 9106 • Norwood, MA 02062-9106, U.S.A. • Te l: 781.329.4700 • Fax: 781.461.3113 • www.analog.com
Digital and Analog Measurement Units for
Digital CMOS Microphone Preamplifier ASICs
by Rebecca Reich
Rev. 0 | Page 1 of 2
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.
UNITS IN DIGITAL AND ANALOG DOMAINS
A system diagram is shown in Figure 1. The transfer function of
the ASIC is labeled A.
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 value for the corresponding square wave is 0 dBV both for
peak and rms value.
ADC
GAIN
ASIC
v
o
[n]x(t)
TRANSFER FUNCTION
A
A × X
n
T
1.0
–1.0
ANALOG
1.0
–1.0
DIGITAL
tV nFFS
x(t) v
o
[n]
T = 1/f
CLK
MEASURING x(t):
V
A
PEAK
= 1.0V
V
A
RMS
= V
A
PEAK
/
2 = 0.7V
V
A
RMS(dB)
= 20 × log
10
(1
/
2V) = 3dBV
MEASURING v
o
[n]:
V
D
PEAK
= 1.0FFS
V
D
RMS
= 1.0FFS
V
D
RMS(dB)
= 20 × log
10
(V
D
RMS
/
1.0FFS) = 0dBFS
07038-001
Figure 1. Conversion Between Analog and Digital Domains, When A = 1.0
