Formula sheet: Data Converters | Digital Circuits - Electronics and Communication Engineering (ECE) PDF Download

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Data Con v erters F orm ula Sheet for GA TE (Digital
Circuits)
Digital-to-Analog Con v erter (D A C)
• Output V oltage : Analog output for an n-bit D A C.
V
out
= V
ref
·
D
2
n
where V
ref
is the reference v oltage, D is the digital input (decimal), n is the n um b er
of bits.
• Resolution : Smallest c hange in output v oltage.
Resolution=
V
ref
2
n
• F ull-Scale V oltage : Maxim um output v oltage.
V
FS
= V
ref
·
2
n
-1
2
n
• W eigh ted Resistor D A C Output :
V
out
= V
ref
·
n-1
?
i=0
b
i
2
i+1
where b
i
is the i -th bit (0 or 1).
• R-2R Ladder D A C Output : Similar to w eigh ted resistor but uses only t w o resistor
v alues.
Analog-to-Digital Con v erter (ADC)
• Quan tization Step Size: V oltage p er digital lev el.
?=
V
ref
2
n
• Digital Output : F or an input v oltage V
in
.
D = flo or
(
V
in
?
)
• Quan tization Error : Error due to discrete lev els.
e
q
= V
in
-D·?, -
?
2
= e
q
=
?
2
• Sampling Rate : F requency of analog signal sampling.
f
s
=2f
max
( Nyquist Theorem)
where f
max
is the highest frequency comp onen t of the input signal.
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Data Con v erters F orm ula Sheet for GA TE (Digital
Circuits)
Digital-to-Analog Con v erter (D A C)
• Output V oltage : Analog output for an n-bit D A C.
V
out
= V
ref
·
D
2
n
where V
ref
is the reference v oltage, D is the digital input (decimal), n is the n um b er
of bits.
• Resolution : Smallest c hange in output v oltage.
Resolution=
V
ref
2
n
• F ull-Scale V oltage : Maxim um output v oltage.
V
FS
= V
ref
·
2
n
-1
2
n
• W eigh ted Resistor D A C Output :
V
out
= V
ref
·
n-1
?
i=0
b
i
2
i+1
where b
i
is the i -th bit (0 or 1).
• R-2R Ladder D A C Output : Similar to w eigh ted resistor but uses only t w o resistor
v alues.
Analog-to-Digital Con v erter (ADC)
• Quan tization Step Size: V oltage p er digital lev el.
?=
V
ref
2
n
• Digital Output : F or an input v oltage V
in
.
D = flo or
(
V
in
?
)
• Quan tization Error : Error due to discrete lev els.
e
q
= V
in
-D·?, -
?
2
= e
q
=
?
2
• Sampling Rate : F requency of analog signal sampling.
f
s
=2f
max
( Nyquist Theorem)
where f
max
is the highest frequency comp onen t of the input signal.
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P e rformance Metrics
• Differen tial Non-Linearit y (DNL) : Deviation of step size from ideal.
DNL=
V
step
-?
?
• In tegral Non-Linearit y (INL) : Cum ulativ e deviation from ideal transfer function.
INL=
?
DNL
• Signal-to-Noise Ratio (SNR) : F or an n-bit con v erter (ideal).
SNR=(6.02n+1.76)dB
• Effectiv e Num b er of Bits (ENOB) :
ENOB=
SNR-1.76
6.02
• Con v ersion Time : Time to complete one con v ersion (dep ends on ADC t yp e, e.g.,
Flash, SAR, Sigma-Delta).
T yp es of Data Con v erters
– D A C T yp es : W eigh ted Resistor, R-2R Ladder, Curren t Steering.
– ADC T yp es : Flash, Successiv e Appro ximation Register (SAR), Sigma-Delta, Dual
Slop e.
– Flash ADC Resolution : Num b er of comparators.
Num b er of comparators=2
n
-1
Key Notes
– Resolution impro v es with higher n but increases complexit y .
– Flash ADCs are fastest but r equire 2
n
-1 comparators.
– SAR ADCs balance sp eed and p o w e r e?iciency .
– Sigma-Delta ADCs are used for h igh-resolution, lo w-sp eed applications.
– T ypical V
ref
v alues: 5V , 3.3V , or 2.5V (c hec k problem sp ecifics).
– Ensure consisten t units (SI pre ferred for GA TE).
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