Formula Sheets: Digital Voltmeter (DVM) | Electrical and Electronic Measurements - Electrical Engineering (EE) PDF Download

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Electrical and Electronic Measuremen ts: Digital
V oltmeter (D VM) F orm ula Sheet for Electrical
GA TE
D VM Measuremen t
• V oltage Measuremen t : Displa y ed v oltage based on digital con v ersion.
V = Coun t· Reference V oltage/2
n
where V is measured v oltage (V ), Coun t is the digital coun t, Reference V oltage is
the in ternal reference (V ), n is the n um b er of bits in the Analog-to-Digital Con v erter
(ADC).
• Resolution : Smallest detectable v oltage c hange.
Resolution=
F ull Scale V oltage
2
n
where F ull Scale V oltage is the maxim um measurable v oltage (V ).
• Num b er of Digits : Displa y resolution in terms of digits.
Digits=log
10
(2
n
)
F or example, a 3.5-digit D VM has a maxim um coun t of 1999.
Error Analysis
• Absolute Error : Difference b et w een measured and true v oltage.
E = V
m
-V
t
where E is absolute error (V ), V
m
is measured v oltage, V
t
is true v oltage.
• Relativ e Error : Ratio of absolute error to true v oltage.
Relativ e Error=
E
V
t
• P ercen tage Error : Relativ e error expressed as a p ercen tage.
P ercen tage Error=
E
V
t
×100
• D VM A ccuracy : T ypically sp ecified as a p ercen tage of reading plus a p ercen tage of
full scale.
Error=±(a%· Reading+b%· F ull Scale)
where a and b are accuracy sp ecifications pro vided b y the man ufacturer.
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Electrical and Electronic Measuremen ts: Digital
V oltmeter (D VM) F orm ula Sheet for Electrical
GA TE
D VM Measuremen t
• V oltage Measuremen t : Displa y ed v oltage based on digital con v ersion.
V = Coun t· Reference V oltage/2
n
where V is measured v oltage (V ), Coun t is the digital coun t, Reference V oltage is
the in ternal reference (V ), n is the n um b er of bits in the Analog-to-Digital Con v erter
(ADC).
• Resolution : Smallest detectable v oltage c hange.
Resolution=
F ull Scale V oltage
2
n
where F ull Scale V oltage is the maxim um measurable v oltage (V ).
• Num b er of Digits : Displa y resolution in terms of digits.
Digits=log
10
(2
n
)
F or example, a 3.5-digit D VM has a maxim um coun t of 1999.
Error Analysis
• Absolute Error : Difference b et w een measured and true v oltage.
E = V
m
-V
t
where E is absolute error (V ), V
m
is measured v oltage, V
t
is true v oltage.
• Relativ e Error : Ratio of absolute error to true v oltage.
Relativ e Error=
E
V
t
• P ercen tage Error : Relativ e error expressed as a p ercen tage.
P ercen tage Error=
E
V
t
×100
• D VM A ccuracy : T ypically sp ecified as a p ercen tage of reading plus a p ercen tage of
full scale.
Error=±(a%· Reading+b%· F ull Scale)
where a and b are accuracy sp ecifications pro vided b y the man ufacturer.
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D VM Sp ecifications
• Sensitivit y : Minim um input v oltage for a measurable output.
S =
F ull Scale V oltage
2
n
Same as resolution, expressed in V .
• Input Imp edance : T ypically v ery high for D VMs to minimize loading.
Z
in
˜10-100M?
• Con v ersion Rate : Sp eed of analog-to-digital con v ersion.
f
c
=
1
T
c
where f
c
is con v ersion frequency (Hz ), T
c
is con v ersion time (s ).
Common D VM T ec hniques
• Dual-Slop e In tegration : V oltage measuremen t b y in tegrating input signal.
V
in
= V
ref
·
T
2
T
1
where V
in
is input v oltage (V ), V
ref
is reference v oltage, T
1
is fixed in tegration time,
T
2
is de-in tegration time (s ).
• Successiv e Appro ximation : V oltage determined b y iterativ e comparison.
V
in
˜
n-1
?
i=0
b
i
·
V
ref
2
i+1
where b
i
are binary bits (0 or 1), n is n um b er of bits.
• Ramp-T yp e D VM : V oltage measured b y comparing with a linear ramp.
V
in
= k·t
where k is ramp slop e (Vs
-1
), t is time to matc h input v oltage (s ).
Key Notes
– Standard units: V oltage (V ), Time (s ), F requency (Hz ), Imp edance (? ).
– Dual-slop e in tegration is co mmon in D VMs for high accuracy and noise rejection.
– Resolution dep ends on ADC bit s ize (e.g., 10-bit ADC giv es 2
10
=1024 lev els).
– A ccuracy sp ecification includes b oth reading and full-scale errors.
– High input imp edance minimizes c ircuit loading effects.
– Use SI units for GA TE calculat ions.
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