Formula Sheets: Oscilloscopes | Electrical and Electronic Measurements - Electrical Engineering (EE) PDF Download

 Page 1


Electrical and Electronic Measuremen ts:
Oscilloscop es F orm ula Sheet for Electrical GA TE
V o ltage Measuremen t
• P eak V oltage : Measured from w a v eform p eak to zero.
V
p
= Divisions·
V olts
Division
where V
p
is p eak v oltage (V ), Divisions is the n um b er of v ertical divisions on the
oscilloscop e screen.
• P eak-to-P eak V oltage : Measured from p ositiv e to negativ e p eak.
V
pp
= 2·V
p
where V
pp
is p eak-to-p eak v oltage (V ).
• RMS V oltage (Sin usoidal W a v e) :
V
rms
=
V
p
v
2
˜ 0.707·V
p
where V
rms
is ro ot mean square v oltage (V ).
Time and F requency Measuremen t
• Time P erio d : Measured as time for one complete cycle.
T = Divisions·
Time
Division
where T is time p eri o d (s ), Divisions is the n um b er of horizon tal divisions.
• F requency : In v erse of time p erio d.
f =
1
T
where f is frequency (Hz ).
• Angular F requency :
? = 2pf
where ? is angular frequency (rads
-1
).
Phase Measuremen t
• Phase Difference : Measured using t w o w a v eforms.
? =
Time Shift
T
·360
?
1
Page 2


Electrical and Electronic Measuremen ts:
Oscilloscop es F orm ula Sheet for Electrical GA TE
V o ltage Measuremen t
• P eak V oltage : Measured from w a v eform p eak to zero.
V
p
= Divisions·
V olts
Division
where V
p
is p eak v oltage (V ), Divisions is the n um b er of v ertical divisions on the
oscilloscop e screen.
• P eak-to-P eak V oltage : Measured from p ositiv e to negativ e p eak.
V
pp
= 2·V
p
where V
pp
is p eak-to-p eak v oltage (V ).
• RMS V oltage (Sin usoidal W a v e) :
V
rms
=
V
p
v
2
˜ 0.707·V
p
where V
rms
is ro ot mean square v oltage (V ).
Time and F requency Measuremen t
• Time P erio d : Measured as time for one complete cycle.
T = Divisions·
Time
Division
where T is time p eri o d (s ), Divisions is the n um b er of horizon tal divisions.
• F requency : In v erse of time p erio d.
f =
1
T
where f is frequency (Hz ).
• Angular F requency :
? = 2pf
where ? is angular frequency (rads
-1
).
Phase Measuremen t
• Phase Difference : Measured using t w o w a v eforms.
? =
Time Shift
T
·360
?
1
or
? =
Time Shift
T
·2p radians
where ? is phase difference, Time Shift is the horizon tal shift b et w een w a v eforms ( s ),
T is time p erio d.
• Lissa jous Figures : Phase difference from elliptical pattern.
sin? =
V ertical In tercept
Maxim um V ertical Amplitude
F or 90° phase shift, pattern is circular; for 0° or 180°, pattern is a straigh t line.
Oscilloscop e Sp ecifications
• Bandwidth : Maxim um frequency for accurate measuremen t.
f
max
˜ Bandwidth
T ypically , bandwidth is where signal amplitude drops to 0.707 of actual v alue.
• Rise Time : Time for signal to rise from 10
t
r
˜
0.35
Bandwidth
where t
r
is rise time (s ), Bandwidth is in Hz .
• Sampling Rate : Minim um samples p er second for accurate w a v eform reconstruction.
f
s
= 2·f
max
where f
s
is sampling rate (Hz ), f
max
is maxim um signal frequency (Nyquist criterion).
Prob e Comp ensation
• Prob e A tten uation : V oltage reduction b y prob e.
V
actual
= V
displa y ed
· A tten uation Ratio
Common ratios: 1:1, 10:1, 100:1.
• Comp ensated Prob e Capacitance : A djust for flat frequency resp onse.
C
prob e
= C
oscilloscop e
where C
prob e
,C
oscilloscop e
are capacitances (F ).
2
Page 3


Electrical and Electronic Measuremen ts:
Oscilloscop es F orm ula Sheet for Electrical GA TE
V o ltage Measuremen t
• P eak V oltage : Measured from w a v eform p eak to zero.
V
p
= Divisions·
V olts
Division
where V
p
is p eak v oltage (V ), Divisions is the n um b er of v ertical divisions on the
oscilloscop e screen.
• P eak-to-P eak V oltage : Measured from p ositiv e to negativ e p eak.
V
pp
= 2·V
p
where V
pp
is p eak-to-p eak v oltage (V ).
• RMS V oltage (Sin usoidal W a v e) :
V
rms
=
V
p
v
2
˜ 0.707·V
p
where V
rms
is ro ot mean square v oltage (V ).
Time and F requency Measuremen t
• Time P erio d : Measured as time for one complete cycle.
T = Divisions·
Time
Division
where T is time p eri o d (s ), Divisions is the n um b er of horizon tal divisions.
• F requency : In v erse of time p erio d.
f =
1
T
where f is frequency (Hz ).
• Angular F requency :
? = 2pf
where ? is angular frequency (rads
-1
).
Phase Measuremen t
• Phase Difference : Measured using t w o w a v eforms.
? =
Time Shift
T
·360
?
1
or
? =
Time Shift
T
·2p radians
where ? is phase difference, Time Shift is the horizon tal shift b et w een w a v eforms ( s ),
T is time p erio d.
• Lissa jous Figures : Phase difference from elliptical pattern.
sin? =
V ertical In tercept
Maxim um V ertical Amplitude
F or 90° phase shift, pattern is circular; for 0° or 180°, pattern is a straigh t line.
Oscilloscop e Sp ecifications
• Bandwidth : Maxim um frequency for accurate measuremen t.
f
max
˜ Bandwidth
T ypically , bandwidth is where signal amplitude drops to 0.707 of actual v alue.
• Rise Time : Time for signal to rise from 10
t
r
˜
0.35
Bandwidth
where t
r
is rise time (s ), Bandwidth is in Hz .
• Sampling Rate : Minim um samples p er second for accurate w a v eform reconstruction.
f
s
= 2·f
max
where f
s
is sampling rate (Hz ), f
max
is maxim um signal frequency (Nyquist criterion).
Prob e Comp ensation
• Prob e A tten uation : V oltage reduction b y prob e.
V
actual
= V
displa y ed
· A tten uation Ratio
Common ratios: 1:1, 10:1, 100:1.
• Comp ensated Prob e Capacitance : A djust for flat frequency resp onse.
C
prob e
= C
oscilloscop e
where C
prob e
,C
oscilloscop e
are capacitances (F ).
2
Key Notes
– Standard units: V oltage (V ), Time (s ), F requency (Hz ), Phase (
?
or rad ).
– Use correct V olts/Div and Tim e/Div settings for accurate measuremen ts.
– F or Lissa jous figures, ensure e qual amplitudes for accurate phase measuremen t.
– Bandwidth limits high-frequency measuremen ts; ensure signal frequency is within
oscilloscop e bandwidth.
– Use 10:1 prob es for high-fr equency signals to reduce loading effects.
– Use SI units for GA TE calculat ions.
3