MP8798
Accuracy of Conversion: DNL and INL
DNL
LSB
V
(N+1)
Analog
Input
V
(N)
DIGITAL
CODES
0.5
∗
LSB
N+1
0.5
∗
LSB
Output
Codes
N
N–1
OFW = 0
1 LSB
3FE
001
000
LSB
V
V
REF(–)
V001
V002
V
3FE
V
3FF
V
0FW
V
REF(+)
002
3FD
3FF
OFW = 1
(N+1) Code Width = V
(N+1)
– V
(N)
LSB = [ V
REF(+)
– V
REF(–)
] / 1024
DNL
(N)
= [ V
(N+1)
– V
(N)
] – LSB
The transfer function for an ideal A/D converter is shown in
Figure 4.
Figure 5. DNL Measurement
On Production Tester
The formulas for Differential Non-linearity (DNL), Integral
Non-Linearity (INL) and zero and full scale errors (E
ZS
, E
FS
) are:
Figure 4. Ideal A/D Transfer Function
The overflow transition (V
OFW
) takes place at:
V
IN
= V
OFW
= V
REF(+)
– 0.5
∗
LSB
The first and the last transitions for the data bits take place at:
V
IN
= V001 = V
REF(–)
+ 0.5
∗
LSB
V
IN
= V
3FF
= V
REF(+)
– 1.5
∗
LSB
LSB = V
REF
/ 1024 = (V
3FF
– V001) / 1022
Note that the overflow transition is a flag and has no impact on
the data bits.
In a “real” converter the code-to-code transitions don’t fall
exactly every V
REF
/1024 volts.
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.
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 V
REF
= 4.608 V then 1 LSB = 4.5 mV and every code
width is within 2.25 and 6.75 mV.
DNL (001) = V002 – V001 – LSB
: : :
DNL (3FE) = V
3FF
– V
3FE
– LSB
E
FS
(full scale error) = V
3FF
– [V
REF(+)
–1.5
∗
LSB]
E
ZS
(zero scale error) = V
001
– [V
REF(–)
+ 0.5
∗
LSB]
DIGITAL
CODES
0.5
∗
LSB
E
ZS
002
001
000
V
V
REF(–)
V001
V002
V
3FE
V
3FF
V
REF(+)
3FE
1.5
∗
LSB
E
FS
3FF
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 ]
