on the input pin and “A” is the gain of the pre-amplifier in deci-
bels.
Written into voltages, the equation is:
(2)
Or in decibels:
Digital Output (dBFS) = Input (dBV) - Reference (dB) + A
Where,
Input = 20 Log V
INPUT (VRMS)
Ref = 20 Log V
REF (VRMS)
A is the Gain (dB)
For the LMV1022/ LMV1023 the reference voltage V
REF is
1.5V
P (1.06 VRMS) and the Gain A is 21dB. These parameters
are fixed inside the device. Knowing this,
Equation 2 can be
simplified:
Digital Output (dBFS) = V
INPUT (dBV) - 0.5 + 21
Digital Output (dBFS) = V
INPUT (dBV) + 20.5
The sensitivity of the digital microphone is the sensitivity of a
conventional microphone plus the input to output transfer of
the LMV1022/ LMV1023. The sensitivity of a typical digital
microphone is therefore: 44 + 20.5 = 23.5dB(FS/Pa).
Digital Output = SP + C + S
Where,
SP is the Sound Pressure in dB SPL
C is the dB SPL to dBPa conversion (94dB)
S is the Sensitivity in dB(V/Pa)
Taking the example of busy traffic (70 dB SPL) again results
in the following digital output (dBFS):
Digital Output (dBFS) = SP - C + S
Digital Output (dBFS) = 70 - 94 - 23.5= 47.5dBFS
ANALOG-TO-DIGITAL CONVERTER
The ADC used in the LMV1022/ LMV1023 is an one bit sigma-
delta converter with a Pulse Density Modulated output signal
(PDM). The output of this ADC can be either High (one) or
Low (zero). Assume that the LMV1022/ LMV1023 input is at
the minimum level. In that case the DATA output will produce
almost only “zeros”. When the input increases, the amount of
“ones” increases too. At mid-point, where the input is 0V, the
number of “zeros” will equal the number of “ones”. At the time
that the input approaches the maximum level, the DATA out-
put produces a majority of “ones”.
Figure 6 shows the result-
ing DATA output as function of the input.
20212472
FIGURE 6. DATA Output versus Input Amplitude
An important characteristic of the sigma-delta converter is
that the noise is shifted out of the band of interest to frequen-
cies above the band of interest. The band that can be used
(Audio Bandwidth) relates directly the applied clock frequen-
cy.
Table 1 shows the relation between the Clock Frequency
and a couple of common Audio Bandwidths.
TABLE 1. Audio Bandwidth vs. Clock Frequency
Clock
Frequency
(MHz)
Sample Rate after
Decimation
(kbit)/s
Audio Bandwidth
(kHz)
0.8
16
7
1.2
24
10
1.6
32
14
2.4
48
20
The high corner of the band of interest (knee) is determined
by the clock frequency divided by 2 times the Over Sampling
Ratio (OSR). The factor of two comes from the Nyquist theo-
rem. The OSR of this particular ADC is chosen at 60. This
sets the high corner of the band at the clock frequency divided
by 120. For instance when a bandwidth of 10kHz is desired,
the clock frequency needs to be 1.2MHz or higher.
Figure 7depicts the noise shaping effect in a frequency spectrum plot,
where a 1 kHz signal is applied.
13
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202124 Version 2 Revision 1
Print Date/Time: 2011/07/08 14:36:52
LMV1022/LMV1023