MP8799
Accuracy of Conversion: DNL and INL
DNL
LSB
V
(N+1)
(N)
The transfer function for an ideal A/D converter is shown in
Figure 4.
Analog
Input
V
DIGITAL
CODES
N + 1
N
Output
Codes
0.5 LSB
0.5 LSB
OFW = 1
N – 1
(N+1) Code Width = V
LSB = [ V
– V
(N)
] / 1024
OFW = 0
3FF
(N+1)
REF(–)
– V
REF(+)
1 LSB
3FE
DNL = [ V
– V ] – LSB
(N)
(N)
(N+1)
3FD
V
002
001
000
LSB
V
Figure 5. DNL Measurement
On Production Tester
V
REF(–)
V001
V002
V
V V
0FW REF(+)
3FE
3FF
Figure 4. Ideal A/D Transfer Function
The formulas for Differential Non-linearity (DNL), Integral
Non-Linearity (INL) and zero and full scale errors (EZS, EFS) are:
The overflow transition (VOFW) takes place at:
IN = VOFW = VREF(+) – 0.5 LSB
DNL (001) = V002 – V001 – LSB
: : :
V
The first and the last transitions for the data bits take place at:
VIN = V001 = VREF(–) + 0.5 LSB
DNL (3FE) = V3FF – V3FE – LSB
E
FS (full scale error) = V3FF – [VREF(+) –1.5 LSB]
VIN = V3FF = VREF(–) – 1.5 LSB
EZS (zero scale error) = V001 – [VREF(–) + 0.5 LSB]
LSB = VREF / 1024 = (V3FF – V001) / 1022
Notethattheoverflowtransitionisaflagandhasnoimpacton
the data bits.
DIGITAL
CODES
0.5 LSB
1.5 LSB
In a “real” converter the code-to-code transitions don’t fall
exactly every VREF/1024 volts.
E
ZS
E
FS
3FF
3FE
A positive DNL (Differential Non-Linearity) error means that
the real width of a particular code is larger than 1 LSB. This error
is measured in fractions of LSBs.
002
001
000
V
A Max DNL specification guarantees that ALL code widths
(DNL errors) are within the stated value. A specification of Max
DNL = + 0.5 LSB means that all code widths are within 0.5 and
1.5 LSB. If VREF = 4.608 V then 1 LSB = 4.5 mV and every code
width is within 2.25 and 6.75 mV.
V
REF(–)
V001
V002
V
V
V
3FE
3FF REF(+)
Figure 6. Real A/D Transfer Curve
Figure 6. shows the zero scale and full scale error terms.
Rev. 3.00
7
EXAR [ EXAR CORPORATION ]
