Datasheet

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last update
November 30, 2010
reference
smtutin
page
8/27
5.3 Resolution
The output signal of the UTI is digitized by the microcontroller. This sampling introduces quantization noise,
which also limits the resolution. The quantization noise of any phase measurement, as given by the relative
standard deviation σ
q
, amounts to:
σ
q
s
phase
t
T
=
1
6
(2)
where t
s
is the sampling time and T
phase
the phase duration. When, for example, the sampling time is 1 µs and
the offset frequency is 50 Hz (phase duration = 20 ms), the standard deviation of the offset phase is
1/45,000, which results in a resolution of maximum 15.5 bits in the slow mode. In fast mode the resolution
would be 12.5 bits.
Further improvement of the resolution can be obtained by averaging over several values of M . When P values
M
1
… M
P
is used to calculate
M
, the value of σ
q
decreases with a factor of P
1/2
.
Besides quantization noise, another limitation of the resolution is the thermal noise of the oscillator itself and
the possible effect of a parasitic (cable) capacitance C
p
( see paragraph 5.5). For the CMUX mode, the
resolution as a function of the parasitic capacitance C
p
(see Fig. 7) is shown in figure 4.
0.0E+00 2.0E+02 4.0E+02 6.0E+02 8.0E+02 1.0E+03 1.2E+03
Parasitic capacitance (pF)
Resolution (pF)
4.5E-4
4.0E-4
3.5E-4
3.0E-4
2.5E-4
2.0E-4
1.5E-4
1.0E-4
5.0E-5
0.0E-0
Figure 4. The resolution versus the parasitic capacitance C
p
5.4 Linearity
Typically, the linearity of the UTI has values between 11 bits and 14 bits, depending on the mode.
For the CMUX mode, the nonlinearity as a function of the parasitic capacitance C
p
(see Figure 7 ) is shown in
Figure 5.