Σ
ph
ase
s
h
ift
Ph
ase
sh
ift
is
critical
in
areas
li
ke
servo,
RF
or
d
igital
system
d
esign
.
T
he
most
common
met
h
o
d
of
meas
u
ri
n
g
ph
ase
sh
ift
is
to
u
se
an
oscillosco
pe
in
t
h
e
Χ
-
Υ
or
d
elaye
d
swee
p
mo
de
.
Α
more
acc
u
rate
met
h
o
d
of
measuring
p
hase
is
wit
h
t
he
7D15
.
To
d
etermi
n
e
ph
ase,
t
he
time
betwee
n
t
he
same
voltage
level
on
t
he
lea
ding an d
lagging
sign
als
is
measure
d
an
d
d
ivi
d
ed by α
conversion
factor
(Time/Degree)
.
F
or
exam
p
le,
if
t
he p
erio
d
of
t
h
e
signal
(as
meas
u
re
d
wit
h
t
he
7D15)
is
2
its
(5
MHz),
t
he
Time/Degree
conversio
n
factor
is
:
2μ
s/360
degree
=
5
.55
ns/
d
e-
gree
.
If
t h
e time
interval
b
etwee
n
t
he
two
p
hases
is
meas
u
red
at
50
ns,
t
h
e
p
h
ase
d
ifference
is
t
hus
:
50
ns/5
.55
ns/
d
egree=9
.09
d
egree
of
p
h
ase
s
h
ift
.
F
ig
.
12
sh
ows
t
he eq
ui
pment
set up for
t
h
e
measurement
of
t
h
e
ph
ase
sh
ift
of
α
5
MH
z
signal
.
L
i
ke
t
he p
revious
p
ro
p
a-
gation
d
elay
meas
u
rement,
o
n
e
signal
is
app
lied
to
eac
htrigger
in
put to
t
he
7D15
.
Again
t
he
SO
UR
C
E
I
NPU
TΒ
p
us
h
butto
n
is
p
resse
d
to
enable
b
ot
h
in
pu
t
con
nectors
.
B
ot
h
t
he ch
a
nn
el
Α
and
ΒTR
IGG
ER
LEVEL
controls
are
set
to
PRE
SE
T,
w
h
ic
h
means
t
he
trig-
ger
circuits
will
trigger
on
t h
e zero
crossover
p
oint
.
Trigger
arming
is
not
re
q
uire
d
for
t
h
is
measurement
.
M
erely trigger
t
he
sco
p
e
on
t
he negative
goi
ng
slo
pe
of
channel
1
.
T
h
is
assures
t
h
at
t
h
e
p
seudo
gate
d
is
p
lay
is
on
t
he
C
RT
.
T
he p
seu
d
o gate
dis
p
lay
i
nd
icates
t
h
at
t h
e
measureme
n
t
is
being
made
b
etwee
n
t
he
two
zero
crossover
p
oints
.
In
t
h
is
case,
t
h
e
time
measure
d
is
75
.60
ns
for
ph
ase
sh
ift
of
75
.6
ns/5
.55
ns/ d
egree=13
.8
d
egrees
.
T
h
is
met
h
o
d
of
meas
u
ring
p
h
ase
sh
ift
can
be
use
d
for
si
n
gles
h
ot or re
p
etitive
sig
n
als,
wit
h
accuracies
of
0
.125°
an
d
0
.075°,
res
p
ectively
at
35
kH
z
.
Several
factors
affect
t
h
is
accuracy
:
1
.
Am
p
litu
d
e
of
t
h
e
two
signals-It
is
more
d
ifficult
for
t
h
e
7D15
trigger
cir-
cuits
to
d
etect
t
he zero
crossover
p
oint
on
low
am
p
litu
d
e
signals
.
2
.
R
elative
am
p
litu
d
e
of
t
he
two
signals
-I
d
eally
both
signals
sh
o
u
l
d
be
t
h
e
same
am
p
lit
ud
e
.
Cloc
k
In
p
ut
7TT
L
Gates
i
n
Series
L
ead
ing
Ph
ase
I
11
CH
1
L
aggi ng
Ph
ase
Delaye
d
Cloc
k
7
Α
18
Ι
7D15
Ι
7Β53
Α
C
H
Α
&
Β
D
L
Y'D
T
R
IG
CH
2
ςΗ
ΑARMC
F i
Β
IN
Ι
ο
7DIs
Out
p
ut
M
o
d
e
.
.
.
.
. . .
.
.
.
. . . . . . . . . . . . . . . .
Tim
Α
-
Β
Ave
r
g
. . . . . .
.
. . .
.
. . . . .
.
.
.
. . . . . . . .
.
. .
Χ
1000
Clock
. . . .
.
.
.
.
.
.
.
.
.
.. .
.
.. . . . . . . .
.
. . .
10
π5
Gate
. . . . .
.
. . . . . . .
.
. . . . . . . . . . . . . .
.
.
.
N
o
rm
Ti
m
e
B
ase
Displayed
W
avefor
m
.
.
.
.
.
.
.
. . .
Pse
ud
o
Gate
Main
Ti
m
e/Div
. .
.
. . . . . . . . . . . . . . . . . . . . . .
.
.
Trigger
Level
.
.
. . . . .
.
. . . . .
.
.
50%
A
mp
lit
ude
Delayed
Ti
m
e/Div
. . . . . .
.
.
.
. . .
.
.
.
.
.
. . . . . . . .
Slo
p
e
Α&
Β
.
.
. . . . . . . . . . . . . . . . . . . . . .
.
.
+
Triggering
.
.
Cou
p
l
Α
&Β
.
. . . . . . . . .
.
. . .
.
. . .
.
.
.
.
.
. . .
DC
Delaye
d
Trig
. . . . . . . . . .
Run
s
After
Dly
Time
So
ur
ce
. . . . . . . .
.
. . . . . . . . . . .
.
. . . . . .
Input
Β
V
e
r
tical
Am
p
lifie
r
M
ai
nfr
ame
Dis
p
lay
M
ode
.
. . . . .
.
. . . . . . . . . . . . .
Alternate
V
ertical
M
ode
.
.
.
.
.
.
. . . . . . . . . . . . .
Alte
r
nate
Trigger
So
urce
. . . . . . . .
.
.
.
. . .
.
.
.
.
.
. . .
C
h
1
T
r
igge
r
Sou
r
ce
. . . . . . . . . . . .
.
.
.
. . .
.
. . . .
L
eft
V
olts/Div
. . . .
.
.
.
. . . . .
.
. . . . . . . . . .
.
.
.
. . .
.
. .
F
ig
.
11
.
Eq
ui
p
ment
setu
p
for
p
ro
p
agation
d
elay
measurement
.
F
ig
.
12
.
Eq
uipment
setup
for
p
h
ase
s
h
ift
measurement
.
7603
7
Α
18
Ι
7D15
Ι
7Β53
Α
ο
Delaye
d
Swee
p
Gate
Out
M
ai
nfr
ame
7
ρης
V
e
r
tical
M
ode
. .
.
. . . . . . . . . . . . . . . .
Alte
r
nate
M
o
d
e
. .
.
. . . . . . . . . . . . . . . . . . . . . .
.
Ti
m
Α-
ιΒ
Trigger
So
u
rce
. . .
.
. . . . . . . . . . .
.
. . . . . .
.
Left
Averg
. .
.
. . . . . . . . . . . . . . . .
.
. . . . .
.
. . . .
1000
Χ
Ti
m
e
B
ase
Cloc
k
. . . . . . .
.
. . .
.
.
.
. . . . .
.
. . . . . . . . .
10
π
s
M
ai
n
Ti
m
e/Div
.
Gate
. . . . .
.
. . . . . . . . . .
.
. . .
.
.
.
.
.
.. .. . .
N
o
rm
I
r
igge
r
ing
-
. . .
.
. . . . .
.
. . . . . . . .
.
.
.
.. ..
. . . . . . . . .
.
. . . . .
.
. . . . . . . . . .
.
.
.
. .
Dis
p
laye
d
W
aveform
P
se
ud
o
Gate
. . .
.
. . .
.
.
.
T
r
igge
r
L
evel
. . . . .
.
. . . . . . . . . .
.
. . . . .
Pr
eset
V
e
r
tical
A
mp
lifier
Slope
Α
&Β
. . . . . . .
.
. . . . .
.
. . .
.
.
.
. . . . . . .
+
Dis
p
lay
M
o
d
e
. . . . . . .
.
. . .
.
. . . . . . . . . .
A
L
T
C
ουρΙ
Α&Β
. . .
.
. . . . . . . . . . . . . . . . . .
.
. . .
AC
Trigge
r
So
ur
ce
. . .
.
. . . . . . . . . . . . . . . . . .
C
h1
So
ur
ce
. . . . . . . . . . . .
.
.
.
.
.
. . .
.
.
.
. . .
.I
n
put
Β
V
olts/Div
.
.
. . . . .
.
. . .
.
. . . . . . . . . . . .
.
.. . . .
.
.