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TECHNICAL
ROTASYN
Understanding Resolvers and Resolverto-Digital Conversion
TECHNICAL
TECHNICAL
An introduction to resolvers and resolver-toAn introduction to resolvers and resolver-to-digidigital
converters.
resolvers
work, resolAnconverters.
introduction
toHow
resolvers
resolver-to-digital
How
resolvers and
work,
resolver sigver
signal
format,
and
how
to
use
tal format,
converters.
work,resolvers
resolver
signal
and How
how resolvers
to use resolvers
with comwith
available
resolver-to-digital
nalcommercially
format,
and how
to use resolvers
with commercially
available
resolver-to-digital
converters.
converters.
mercially available resolver-to-digital converters.
Talk
Fundamentally, then, all resolvers produce signals
proportional to the sine and cosine of their rotor
T A
S Y
N has a unique combinatiangle. O
Since
every
angle
O Tand
A cosine
S Y values,
N
on of sine
a resolver provides
absolute position information within one revolution (360°) of its rotor. This absolute (as opposed
WHAT IS A RESOLVER?
to incremental) position capability is one of the
resolver’s main advantages
over incremental enUnderstanding Resolvers and Resolver-to-Digital
Conversion
A resolver
is a position sensor
or transducer
coders.
Understanding
Resolvers
and Resolver-to-Digital
Conversion
which measures the instantaneous angular position of the rotating shaft to which it is attached.
ELECTRICAL CHARACTERISTICS
What isand
a resolver?
Electrical
Resolvers
their close cousins, synchros, have
Electrically,Characteristics
the Rotasyn, like a traditional resolver,
What
is asince
resolver?
Electrical
Characteristics
been
in use
before World War II in military
is
a transformer
in which the coupling between
A resolver is a position sensor or transducer which meaElectrically, the Rotasyn, like a traditional resolver, is a
applications such as measuring and controlling
the primary and the secondaries varies as the
A resolver
is a positionangular
sensor or
transducer
meaElectrically,inthe
Rotasyn,
like a traditional
resolver,
is a
sures
the instantaneous
position
of thewhich
rotating
transformer
which
the coupling
between the
primary
the angle of gun turrets on tanks and warships.
sine and cosine of the rotor angle. Whereas a trasures
the
instantaneous
angular
position
of
the
rotating
transformer
in
which
the
coupling
between
the
primary
shaft to which it is attached. Resolvers and their close
and the secondaries varies as the sine and cosine of the
Resolvers
are typically built like small motors with
ditional resolver has its primary on the rotor and
shaft to synchros,
which it ishave
attached.
Resolvers
andbefore
their close
and angle.
the secondaries
varies
as the sine
and has
cosine
of the
cousins,
been
in
use
since
World
rotor
Whereas
a traditional
resolver
its pria rotor (attached to the shaft whose position is to
its secondaries
in the
stator (necessitating
brucousins,
synchros,
have
been
in
use
since
before
World
rotor
angle.
Whereas
a
traditional
resolver
has
its
priII in militaryand
applications
as measuring
and
mary
theslip
rotorrings
and its
the stator (necesbeWar
measured),
a stator such
(stationary
part)
sheson
and
orsecondaries
a rotatingintransformer
to
War II in military
applications
suchonastanks
measuring
and
mary on the rotor
and
secondaries
in thetransformer
stator (necescontrolling
the angle
gun turrets
and warsitating
and
slipits
rings
or a rotating
to
which
produces
theofoutput
signals.
couplebrushes
signals
into
the
primary),
the Rotasyn concontrolling
the
angle
of
gun
turrets
on
tanks
and
warsitating
brushes
and
slip
rings
or
a
rotating
transformer
ships.
Resolvers
are typically
built like
small
couple
signalsprimary
into the primary),
the Rotasyn
contains in to
The
word
resolver
is a generic
term
formotors
such with
de- a
tains both
and secondary
windings
the
ships.
Resolvers
are
typically
built
like
small
motors
with
a
couple
signals
into
the
primary),
the
Rotasyn
contains
rotorderived
(attachedfrom
to thethe
shaftfact
whose
position
is tomost
be meaboth
primary
and secondary
in thetostator
and
vices
that
at their
bastator
and uses
a uniquewindings
solid rotor
directly
rotor
to the
shaft
ismechanical
to be meabothaprimary
and
windings
inthe
thecoupling
stator
and
a operate
stator
(stationary
part)position
which
the
uses
unique
solidsecondary
rotor
to directly
vary
besicsured),
level(attached
they
by whose
resolving
theproduces
vary
the
coupling
between
the
primary
andand
the
sured),
and
a
stator
(stationary
part)
which
produces
the
uses
a
unique
solid
rotor
to
directly
vary
the
coupling
beoutput
signals.
tween
the
primary
and
the
secondaries.
angle of their rotor into its orthogonal or Cartesisecondaries.
output
signals.
tween
the
primary
and
the
secondaries.
an (X and Y) components. From a geometric perLike all transformers, the Rotasyn (as well as a
The word resolver is a generic term for such devices deLike all transformers, the Rotasyn (as well as a traditional
spective, the relationship between the rotor angle
traditional resolver) requires an AC carrier or reThe word
resolver
is a at
generic
termbasic
for such
devices
deLike all transformers,
the carrier
Rotasynor(as
well as signal
a traditional
rived
from the
fact that
their most
level
they operresolver)
requires an AC
reference
(some(θ) and its X and Y components is that of a right
ference signal (sometimes also called the excitatirived
from
the
fact
that
at
their
most
basic
level
they
operresolver)
requires
an
AC
carrier
or
reference
signal
(someate
by
resolving
the
mechanical
angle
of
their
rotor
into
times
also
called
the
excitation
)
to
be
applied
to
its
pritriangle:angle sensors are used, often built into
on) to be applied to its primary. The amplitude of
ate
by resolving
the mechanical
angle
of their rotorFrom
into
times The
alsoamplitude
called the of
excitation
) to besignal
applied
to its modupriits
orthogonal
or Cartesian
(X and
Y) of
components.
mary.
reference
is then
the
driving
motors.
On the
basis
their physicala
this reference
signalthis
is then
modulated
by the
its
orthogonal
or
Cartesian
(X
and
Y)
components.
From
a
mary.
The
amplitude
of
this
reference
signal
is
then
modugeometric
perspective,
relationship between
the rotor
lated
thecosine
sine and
of theangle
rotor angle
to produce
design,
these
angularthe
transducers
can be classisine by
and
ofcosine
the rotor
to produce
the
geometric
perspective,
the
relationship
between
the
rotor
lated
by
the
sine
and
cosine
of
the
rotor
angle
to
produce
angle
(θ)two
andmain
its X and
Y components is that of a right
the
outputsignals
signals on
secondaries.
fied
into
groups:
output
onthe
thetwo
two
secondaries.
angle (θ) and its X and Y components is that of a right
the output signals on the two secondaries.
triangle:
R1 (Red/White)
S1 (Red)
triangle:
θ
R1 (Red/White)
S1 (Red)
θ
1
Secondary
Primary
sinθ
1
(Cosine)
Secondary
Primary
sinθ
(Cosine)
θ
θ
cosθ
cosθ
Resolving an Angle into its Components
Resolving
Angleinto
intoits
itsComponents
Components
Resolving
ananAngle
Fundamentally, then, all resolvers produce signals proFundamentally,
then,and
all resolvers
signals
portional
to the sine
cosine of produce
their rotor
angle.proportional
the sine
cosinecombination
of their rotorofangle.
Since
everytoangle
hasand
a unique
sine and
Since every
has a provides
unique combination
of sineinforand
cosine
values,angle
a resolver
absolute position
cosine
values,
a
resolver
provides
absolute
position
information within one revolution (360°) of its rotor. This abmation(aswithin
one revolution
(360°)position
of its rotor.
This absolute
opposed
to incremental)
capability
is
solute
incremental)
position
capability is
one
of (as
the opposed
resolver’s tomain
advantages
over incremental
one of the resolver’s main advantages over incremental
encoders.
R
R
R2 (Yellow/White)
S3 (Black)
R2 (Yellow/White)
S3 (Black)
S2 (Yellow)
S2 (Yellow)
Rotasyn Schematic
Rotasyn Schematic
Rotasyn
Schematic
Secondary
(Sine)
Secondary
(Sine)
S4 (Blue)
S4 (Blue)
By convention, the primary and secondary leads of all
By convention,
the primary
and
secondary leads
of all
resolvers
are identified
with the
nomenclature
and wire
resolvers
are
identified
with
the
nomenclature
and
wire
colors shown above. For best performance, the reference
colorsshould
shownbe
above.
best performance, the reference
signal
a sineFor
wave.
signal should be a sine wave.
In any transformer, there is a value which relates the out-
Talk
TECHNICAL
ROTASYN
By convention, the primary and secondary leads
of all resolvers are identified with the nomenclature and wire colors shown above. For best performance, the reference signal should be a sine
the
primary. For resolvers, this quantity is called the transwave.
the primary. For resolvers, this quantity is called the transformation
ratio
TR and
isthis
specified
atisthe
pointrelates
of transmaxiIn any
transformer,
there
isquantity
a value
which
the
primary.
Fororresolvers,
called
the
formation
ratio
or TR and
is specified
at
thesecondary
point of maxithe
output
voltage
produced
by
the
mum
coupling
between
primary
and
secondary.
For
in- to
formation ratio or TR and is specified at the point of maximum
coupling
between
primary
and
secondary.
For
inthe
primary.
For
resolvers,
this
quantity
is
called
the
transthat
fed
into
the
primary.
For
resolvers,
this
quandustrial
resolvers,
the de-facto
standard
transformation
mum
coupling
between
primary
and secondary.
For industrial
resolvers,
de-facto
standard
formation
ratio
or the
TR
and
is
specified
at transformation
theor
point
maxitity isis called
the
transformation
ratio
TR of
and
is
ratio
0.5,
which
means
that
the maximum
voltage
produstrial
resolvers,
the
de-facto
standard
transformation
ratio
is
0.5,atwhich
means
that
theand
maximum
voltage
promum
coupling
between
primary
secondary.
For
inspecified
the
point
of
maximum
coupling
betduced
either
secondary
is half
amplitude
of theproratio is by
0.5,
which
means that
the the
maximum
voltage
duced
either secondary
is half
the
amplitude
of the
ween by
primary
and
secondary.
For
industrial
resoldustrial
resolvers,
the
de-facto
standard
transformation
reference
signal.
duced
by
either
secondary
is
half
the
amplitude
of
the
vers,isthe
de-facto
standard
transformation
ratio
reference
signal.
ratio
0.5,
which means
that the
maximum voltage
pro-is
reference
signal.
0.5,
which
means
that
the
maximum
voltage
proIfthe
we
define
the
reference
voltage
V
as
V
,
then
the
duced
by
either
secondary
is
half
the
amplitude
of
the
primary. For resolvers, this quantity
is calledRthe trans(R1–R2)
Ifduced
we define
the reference
voltage
V(R1–R2)
as
VR, then the
by
either
secondary
is
half
the
amplitude
voltages
on
the
secondaries
are
given
by
the
following
signal.
TR and isvoltage
specified
at theas
point
maxiformation
ratio
VR, of
then
the
Ifreference
we define
theorreference
V(R1–R2)
voltages
on the secondaries
are given
by the following
of the
reference
signal.
equations
mum
coupling
between
primary
and
secondary.
For
involtages on the secondaries are given by the following
equations
If we
we define
define
the
reference
voltage
V
VR, the
Ifdustrial
the
reference
voltage
V(R1–R2)
as Vas
(R1–R2)
R, then
resolvers,
the
de-facto
standard
transformation
equations
then
the
voltages
on
the
secondaries
are
given
by
Sine
Secondary:
V
≡
V
=
V
TR
sin
θ
voltages
on the
secondaries
are
given
following
(S2–S4)
S by the
R voltage
ratio
is 0.5,
which
means that
the
maximum
proSine Secondary:
V(S2–S4) ≡ VS = VR TR sinθ
the
following
equations
Cosine
Secondary:
V(S1–S3)
V
=V
VR TR
TR sin
cos
equations
duced
by
either
secondaryV
is half ≡
ofθθthe
≡the
VCSamplitude
=
Sine
Secondary:
R
Cosine Secondary: V(S2–S4)
(S1–S3) ≡ VC = VR TR cosθ
reference
signal.
Cosine
Secondary:
Vangle
≡V
=rotor
V TR
cos
θ
where
θSine
is the
mechanical
of
the
assin
shown
Secondary:
V(S1–S3)
≡V
VRRTR
TR
θ
Sine Secondary:
V(S2–S4)
º VS
=CS =
VR
sinq
(S2–S4)
where θ is the mechanical angle
of the
rotor
as shown
as TR
, cosq
then
If
weCosine
define
the
reference
voltageº≡VC
V(R1–R2)
previously
the
Rotasyn
schematic.
Cosine
V(S1–S3)
VR
Secondary:
Vangle
V
θ the
Rshown
where
θ Secondary:
is in
the
mechanical
the
rotor
asVcos
(S1–S3) of V
C =
R TR
previously
thesecondaries
Rotasyn schematic.
voltages oninthe
are given by the following
previously inSignal
the Rotasyn
schematic.
Resolver
Format
where
mechanical
angle of the rotor as shown
equations
whereθθisisthe
the
mechanical
Resolver
Signal
Formatangle of the rotor as
previously
inSignal
the Rotasyn
schematic.
Resolver
previously
inFormat
the
Rotasyn
schematic.
Ifshown
we excite
Rotasyn
primary
) with
the recom≡RV
Sine the
Secondary:
V(S2–S4)(V
S = VR TR sinθ
If we excite the Rotasyn primary
(VR) with
the recommended
sinusoidal
reference
signal
as
shown
below,
Secondary:
V(S1–S3)(V
≡ Vwith
cosθ the
Resolver
Signal
Format
Ifmended
weCosine
excite
the
Rotasyn
primary
recomC = Vthe
R TR
sinusoidal
reference
signalR)as
shown
below, the
mended
reference
signal
as shown
FORMAT
where
θ sinusoidal
is the
mechanical
angle
of )the
rotor asbelow,
shownthe
IfRESOLVER
we excite
theSIGNAL
Rotasyn primary
(V
R with the recompreviously
in the Rotasyn
schematic.
mended sinusoidal
reference
signal as shown below, the
If we excite the Rotasyn primary (VR) with the reResolver Signal Format
commended sinusoidal reference signal as shown
below,
the the
secondary
voltages
sinusoidal
If
we excite
Rotasyn primary
(VR)are
withalso
the recomat the same
frequency
and
nominally
in below,
phase the
mended
sinusoidal
reference
signal
as shown
For instance, with the rotor at 0° (called Electrical
Zero or EZ and marked on the Rotasyn PC
board), the amplitude of the sine secondary is 0
(since sin0° = 0) and the amplitude of the cosine
tude
of the cosine
secondary
will be at its
of
secondary
will be
at its maximum
ofmaximum
half the refetude of the cosine secondary will be at its maximum of
half
the
reference
(since
1):
rence
(since cos0°
=cos0°
1): its=maximum
tude
of amplitude
the
cosine amplitude
secondary
will be
at
of
half the reference amplitude (since cos0° = 1):
half the reference amplitude (since cos0° = 1):
tude of the cosine secondary will be at its maximum of
half the reference amplitude (since cos0° = 1):
tude of the cosine secondary will be at its maximum of
half the reference amplitude (since cos0° = 1):
Ref
Ref
Sin
Ref
Sin
Cos
Sin
Cos
Ref
Cos
Resolver Signals with Rotor at 0° (EZ)
Sin
Resolver
Signals with
with Rotor
Rotorat
at0°
0°(EZ)
(EZ)
Resolver Signals
Cos
Resolver
Signals
with
at 0° voltages
(EZ)
With
the rotor
at 45°,
theRotor
secondary
are the
With
the
rotor
at
45°,
the
secondary
voltages
are the are
With but
theonly
rotor
at 45°,
the maximum
secondary
voltages
same
70.7%
of
their
since
sin45°
Resolver
Signals
with
at 0° voltages
(EZ)
With
the rotor
at 45°,
theRotor
secondary
are the=
same
but only
70.7%
of theirof
maximum
since
sin45°
=
the
same
but
only
70.7%
their
maximum
since
Ref
cos45°but
= only
0.707:
same
70.7% of their maximum since sin45° =
cos45°
0.707:
sin45°
=rotor
cos45°
= 0.707:
With
the=
at 45°,
the secondary voltages
are
the
Sin
cos45° = 0.707:
same but only 70.7% of their maximumCos
since sin45° =
cos45° = 0.707:
Resolver Signals with Rotor at 0° (EZ)
With the rotor at 45°, the secondary voltages are the
same but only 70.7% of their maximum since sin45° =
cos45° = 0.707:
Ref
Ref
Sin
Ref
Sin
Cos
Sin
Cos
Ref
Resolver Signals with Rotor at 45° Cos
Sin
Resolver Signals with Rotor at 45°
Sinusoidal Reference Applied to Rotasyn Primary
Sinusoidal Reference Applied to Rotasyn Primary
Sinusoidal
Reference
to Rotasyn
secondary voltages
are Applied
also sinusoidal
at thePrimary
same fre-
secondary voltages are also sinusoidal at the same frequency
and Reference
nominally inApplied
phase with
the reference.
Their
Sinusoidal
to Rotasyn
secondary
areinalso
sinusoidal
thePrimary
sameTheir
frequency andvoltages
nominally
phase
with the at
reference.
amplitude is proportional to the amplitude of the referquency
and
nominally
in
phase
with
the
reference.
Their
amplitude
isvoltages
proportional
to the
amplitude
refer-fresecondary
are also
at of
thethesame
ence,
the transformation
ratiosinusoidal
of the Rotasyn,
and the
amplitude
is
proportional
to
the
amplitude
of
the
reference,
the
transformation
ratio ofwith
theRotasyn
Rotasyn,
and
the
quency
and
nominally
inApplied
phase
the
Their
Sinusoidal
Reference
to
Primary
sine
or cosine
of the mechanical
angle
ofreference.
the rotor.
Using
Sinusoidal
Reference
Applied
to Rotasyn
Primary
ence,
the
transformation
ratio
of
the
Rotasyn,
and
the
sine
or cosine
of the mechanical
angle of the
rotor.
Using
amplitude
is
proportional
to
the
amplitude
of
the
referthe
industry-standard
0.5also
TR, we
can lookatatthe
thesame
secondsecondary
voltages are
sinusoidal
fresine
orthe
cosine
of the mechanical
angle
of the
rotor.
Using
the
industry-standard
0.5 TR,
can
look
at the
secondence,
transformation
ratiowe
ofwith
thethe
Rotasyn,
and
the
quency
and
nominally
in rotor
phase
reference.
Their
ary
voltages
for different
angles
as
they
would
apwith
the
reference.
Their
amplitude
is
proportional
the
industry-standard
0.5 rotor
TR, we
can look
at the
secondary
voltages
forofdifferent
asofthey
would
apsine
or
theof
mechanical
angle
the
rotor.
Using
amplitude
proportional
theangles
amplitude
oftransformathe
referto the
amplitude
thetoreference,
the
pear
oncosine
anisoscilloscope.
ary
voltages
for
different
rotor
angles
as
they
would
appear
on
an
oscilloscope.
the
0.5 TR,
we
ator
thecosine
secondence,
the transformation
ratio
ofcan
thelook
Rotasyn,
and
theof
tionindustry-standard
ratio
of the Rotasyn,
and
the
sine
pear
on an oscilloscope.
For
with
the
rotor
0°
(called
Electrical
ary
voltages
rotor
angles
they
ap-or
sine
or cosinefor
ofdifferent
the
mechanical
angleasof
the would
rotor.
Using
theinstance,
mechanical
angle
ofatthe
rotor.
Using
theZero
indusFor instance, with the rotor at 0° (called Electrical Zero or
EZ
and
on the
Rotasyn
board),
the
amplitude
the
industry-standard
0.5
TR,can
wePC
can
look
at
the
secondpear
onmarked
an oscilloscope.
try-standard
0.5
TR,
we
look
atElectrical
the
secondary
Zero or
For
instance,
with
at 0°PC
(called
EZ and
marked
onthe
therotor
Rotasyn
board),
the amplitude
ary
voltages
for
different
rotor
angles
as
they
would
apof
the
sine
secondary
is
0
(since
sin0°
=
0)
and
the
amplivoltages
for
different
rotor
angles
as
they
would
EZ
and
marked
onthe
therotor
PC
board),
of
the
sine
secondary
isRotasyn
0 (since
sin0°
= Electrical
0) the
andamplitude
theZero
ampliFor
instance,
with
at
0°
(called
or
pear
on
an
oscilloscope.
appear on an oscilloscope.
of
secondary
0 (sincePC
sin0°
= 0) the
andamplitude
the ampliEZthe
andsine
marked
on theisRotasyn
board),
For instance, with the rotor at 0° (called Electrical Zero or
of the sine secondary is 0 (since sin0° = 0) and the ampliEZ and marked on the Rotasyn PC board), the amplitude
of the sine secondary is 0 (since sin0° = 0) and the ampli-
Resolver Signals with Rotor at 45°Cos
Resolver
Signals
with
at 45°is at maximum and
With
the rotor
at 90°,
theRotor
sin voltage
With the rotor at 90°, the sin voltage isRef
at maximum and
the
cosine Signals
voltage is
zero:
Resolver
with
Rotor
at voltage
45°isSin
With
the
rotor
at
90°,
the
sin
voltage
at maximum
and
With
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rotor
at
90°,
the
sin
is at maxithe cosine voltage is zero:
the
cosine
voltage
is zero:
mum
and
theatcosine
is zero:
With
the
rotor
90°, thevoltage
sin voltage
isCos
at maximum and
the cosine Signals
voltage is
zero:
Resolver
with
Rotor at 45°
With the rotor at 90°, the sin voltage is at maximum and
the cosine voltage is zero:
Ref
Ref
Sin
Ref
Sin
Cos
Sin
Cos
Ref
Resolver Signals with Rotor at 90° Cos
Sin
Resolver Signals with Rotor at 90° Ref
Cos
Resolver Signals
Resolver
Signals with
with Rotor
Rotorat
at90°
90°Sin
Resolver Signals with Rotor at 90° Cos
Resolver Signals with Rotor at 90°
Talk
Talk
Talk
TT EE CC HH NN I I CC AA LL
TECHNICAL
T ECHNICAL
With the rotor at 135°, the amplitudes of the secondary
R ROTASYN
O T A S Y N
With the rotor at 135°, the amplitudes of the secondary
R O T A S Y N
voltages are
the
same
as
at
45°,
but
the
phase
of
the
coWith the rotor at 135°, the amplitudes of the secondary
R O T ATS EY C
N H N I C A L
voltages are the same as at 45°, but the phase of the covoltages
are since
the same
as at 45°,
but the phase of the cosine voltage
reverses
cos135°
is –0.707:
process
of removing
the carrier
signal—leaving
sine voltage
since
cos135°
is –0.707: of the se- TheThe
Withreverses
the rotor
at 135°,
the amplitudes
process
of removing
carrier
signal – lea-just
The process
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the the
carrier
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just
sine voltage reverses since cos135° is –0.707:
With
the rotor
at 135°,
amplitudes
secondary
The
process
of removing
carrier
just
Rthe
O is
T called
A S signal—leaving
Y N
condary
voltages
arethe
the
same asof
atthe
45°,
but the the ving
just the
envelope
–
demodulation
envelope—is
called demodulation
and
is Iperformed
T
E
C
H
N
C
A
L
demodulation
and
is performed
thetheenvelope—is
called
voltages
thecosine
same as
at 45°, reverses
but the phase
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and
isThe
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phase ofare
the
voltage
since
is performed
by demodulation
the
Resolver-to-Digital
(R/D)
by and
the envelope—is
Resolver-to-Digital
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converter.
demoduby
the
Resolver-to-Digital
(R/D)
converter.
The
demodusine
voltage
reverses
since
cos135°
is
–0.707:
by the Resolver-to-Digital
(R/D) converter.
Thecosine
demoducos135° is –0.707:
converter.
The demodulated
sine and
reThesine
process
removing
the carrier
signal—leaving
just
lated
andofcosine
resolver
signals
are shown below:
With the rotor at 135°, the amplitudes of the secondary
R O Tbelow:
Asignals
S Y are
N are
lated
and
resolver
shown
below:
solver
signals
are shown
latedsine
sine
and cosine
cosine
resolver
signals
shown
below:
voltages are the same as at 45°, but the phase of the cosine voltage reverses since cos135° is –0.707:
Ref Ref
Ref
Sin Sin
Sin Cos
Cos Ref
Cos
Resolver Signals with Rotor at 135°
Sin
Resolver Signals with Rotor at 135°
Resolver Signals with Rotor at 135°
Cos
Other rotor angles may be shown similarly.
Ref
Other rotor angles may be shown similarly.
Resolver
Signals
with
Rotor
at 135°
Other rotor
angles
may be
shown
similarly.
Sin signals apResolver
with
Rotor
While it isSignals
helpful to
know
how at
the135°
resolver
Talk
Talk
the envelope—is called demodulation and is performed
by the Resolver-to-Digital (R/D) converter. The demoduSine
The
of cosine
removing
the carrier
signal—leaving
just
Sine
latedprocess
sine and
resolver
signals
are shown below:
Sine
Cosine
Cosine
and
is
performed
the envelope—is called demodulation
Cosine
by the Resolver-to-Digital (R/D) converter. The demoduSine
lated sine and cosine resolver signals
are shown below:
Cosine
Sine
Cosine
0°
90°
180°
270°
360
0° Demodulated
90° Resolver Secondary
180°
270°
360
Signals
Signals
0°Demodulated
90°Resolver Secondary
180°
270°
360
rotor
may
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shown
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While it isOther
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time
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While it is helpful to know how the resolver signals apDemodulated Resolver Secondary Signals
when oneoflooks
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ResolverConversion
Secondary Signals
0°
90°
180°
270°
360
pear as functions
timeatwith
since
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Resolver-to-Digital
Rotor
at
While
itrotor
isSignals
helpful
know
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resolver
pear asResolver
functions
of angles
timetosince
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isthe135°
what
onesignals
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Demodulated Resolver Secondary Signals
when onemore
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often
Resolver-to-Digital
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pear
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RESOLVER-TO-DIGITAL
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when one
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atangles
themfrequency)
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Other
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may
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the
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with
Resolver-to-Digital
Conversion
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more convenient
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when
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While
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the
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sigmore convenient
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tions: demodulation
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resolver format270°
signals to re-360
Resolver-to-Digital
90°
180°
to rotor position.
the rotor
the resolver
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resolver-to-digital
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two basic
at the reference
frequency)
of the
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with
While
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know
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resolver
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nals appear
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sincerespect
that
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The
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resolver-to-digital
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move
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provide
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Demodulated Resolver Secondary Signals
a rate such that it makes one complete revolution in the
tions:
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the resolver
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one
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The
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to rotor position.
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at
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the
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the resolver
rotor angle.
The most
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tions:
demodulation
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the rotor
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it
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theConversion
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anthe
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itturned
isthe
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Resolver-to-Digital
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thisthat
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move
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The
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.
Since
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tracking
conversion
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understanding),
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therotor
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the resolver-to-digital
rotor
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The
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10difficult
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thecause
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method
ofrepresentation
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is The
called
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represent
the sine andthese
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of the rotor
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ratio
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are
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and
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of
the
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signals
can
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clearly
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betion.
If
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forming
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isfunctions
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these
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called
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isratiometric
called
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turned
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aredifficult
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signal
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the
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. Since
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with
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cking
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Since
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asi.. Since
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tracking
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practice,apractice,
but
useful
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rate are
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ituseful
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but
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Thus
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,
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represent
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of the
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the ratio
in
the time
of 10position:
cycles
of the seen.
excitation
frequengnals represent
thecosine
sine and
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the rotor
of the secondary
signals
can
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Shown
bedigital
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ofcosine
the rotor
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the
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therotor
rotor
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represent
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ofsecondary
10signals
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nal signal
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cy
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the
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the
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low is thethis
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the
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method
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is
called
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thesignal
signal amplitudes
amplitudes isisthe
of thethe
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high
are
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other
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ofof
the
thetangent
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theand
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low is the
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with
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inof
practice,
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tangent
of angle,
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,,isis
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.
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Vs
sin
θ
Thus
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the
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rotor the
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is the
the =arc
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θ ≡ arctan
arctan
derstanding),
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therotor
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sine
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divided
by sigrespect respect
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cos
θ
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the
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represent
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and
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nal
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thecosine
cosine
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canShown
be clearly
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nals
be clearly
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below
the enthe
cosineby
signal:
nal
divided
the
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signal:
of
theratiometric
signal amplitudes
is the tangent
of theanrotor
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low
is theofenvelope
the sine secondary
signal
with
The
tracking converter
performs
implicit
arc
velope
the sineofsecondary
signal with
respect
VsVs
sin
sinθθ arc
Thus
the
rotor
angle,
θ
,
is
the
tangent
of
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sigθ
≡
arctan
=
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arctan
respect
to
rotor
position:
to rotor position:
q
q q º calculation
arctan sinon
= arctan
Vs
tangent
the
ratio
of
the
resolver
signals
by
sin
θ
Vc
cosθ = arctan
Vc
θ ≡ arctancos
nal
divided
by thetocosine
signal:
Vcresolver. This
cosposition
θ
cos
Vs aVc
forcing
counter
track the
of the
ratiometric
tracking
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ananimplicit
arcarc
implicit
arc tangent
calculation
is based
on the
trigonoTheThe
ratiometric
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converter
performs
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Vs
sin θ = arctan
The
ratiometric
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converter
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implicit
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θ
≡
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The
ratiometric
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converter
performs
an
tangent
calculation
on
the
ratio
of
the
resolver
signals
by
metriccalculation
identity
Vc
θ of the resolver
tangent
on the cos
ratio
signals by
tangent
calculation
the
ratio
of the
implicit
tangent
calculation
on
the
ratiosignals
of This
the by
forcing
a arc
counter
to on
track
the
position
of resolver
the resolver.
forcing a counter to track the position of the resolver. This
resolver
signals
by
forcing
a
counter
to
track
the
sin(
θ
−
δ
)
≡
sin
θ
cos
δ
−
cos
θ
sin
δ
The
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tracking
converter
performs
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aarc
counter
tocalculation
track
the position
of
resolver.
implicit
tangent
is based
on the
theimplicit
trigono-arcThis
implicit
arccalculation
tangent
calculation
is
based
on
the
trigonoposition
of
the resolver.
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arc
tangent
tangent
on
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ofisimplicit
the
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signals
by
metric
identity
0°
90°
180°
270°
360 implicit
arc
tangent
calculation
based
on
the
trigonoThis
equation
says
that
the
sine
of
the
difference
between
metric
identity
calculation
is based
onthe
the
trigonometric
identity
forcing
a
counter
to
track
position
of
the
resolver.
This
metric
identity
Modulation Envelope of Sine Secondary Signal
two angles
can
byδcross
multiplying
the
sin(θbe
− δcalculated
) ≡ sinθ cos
− cos
θ sin
δ trigonoimplicit arc tangent
calculation
is based
on
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angles
and
subtracting
the
re− δ cosd
) ≡ sin-θcosq
cos δsind
− cos θ sinδ
sin(q - dsin(
) º θsinq
0°
90°
180°
270°
360
metric
identity
sin(says
θ − that
δ ) ≡the
sinsine
θ cos
cos θ sinδbetween
This equation
of δthe− difference
0°
90°
180°of Sine Secondary
270°
360
Modulation
Signal360
angles
can
bethat
calculated
bysine
crossofdifference
multiplying
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Thistwo
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the
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between
0°
90° Envelope
180°
270°
This
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sin(
θ says
− δthat
) ≡that
sin
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δof−the
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θthe
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This
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theθthe
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the
between
sine
and cosine
ofcalculated
the two
angles
and subtracting
thethe
reModulation Envelope of Sine Secondary Signal
between
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can
be
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by cross
two
angles
can
by
cross
multiplying
0°
90° of Sine180°
360 two angles can be calculated by cross multiplying the
Modulation
Envelope
Secondary270°
Signal
This
equation says
that the
sine
of theof
difference
between
multiplying
the
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and
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the
two
angles
sine and cosine of the two angles and subtracting the resine
and
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of calculated
the
angles
and
subtracting
Modulation
two
angles
can be
byFurther,
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Envelopeof
ofSine
SineSecondary
SecondarySignal
Signal
and
subtracting
the two
results.
as longthe
as the rethe and
difference
the two
is relasine
cosine ofbetween
the two angles
andangles
subtracting
the retively small (δ = θ ±30°), the approximation
Talk
T
E C H N I C A L
stored in the counter, is then incremented or decremented
using a voltage controlled oscillator until this error is zero,
R O T A S Y N
at which point δ = θ (the digital angle output of the conTECHNICAL
sin(θ − δ ) ≅ θ − δ
verter is equal to the resolver angle). This incrementing
sults. Further, as long as the difference between the two
stored
in the counter,
thendigital
incremented
decremented
and decrementing
ofis the
angle, δor
, causes
it to
ROTASYN
may also be used, further simplifying the equation. Thus,
angles is relatively small (δ = θ ±30°), the approximation
using
a
voltage
controlled
oscillator
until
this
error
is type
zero,of
track
the
resolver
angle,
θ
,
hence
the
name
of
this
if the two angles are within 30° of each other, the differatconverter.
which point δ = θ (the digital angle output of the conence
using the The results
(q
- dbetween
) @ q - dthe angles
are subtracted, demodulated by mulsin(θ − can
δ ) ≅ be
θ −calculated
δ
verter is equal to the resolver angle). This incrementing
tiplying
by
the
reference signal, and filtered to
cross multiplication shown above.
A more detailed description
of tracking
converter
operaof the digital
δ, causes
may
bebeused,
further
simplifying
the the
equation.
mayalso
also
used,
further
simplifying
equati-Thus, give and
a DCdecrementing
signal proportional
to theangle,
difference
or it to
tionthe
is available
from the
converter
Seeofthe
resolver
angle,
θ, hence
the manufacturers.
name
of this type
Thus,
if converter,
the are
twowithin
angles
areofwithin
30°
ofthe
each
between
the resolver
angle,
θ, and
the
digiIn the
this equation
is implemented
usingerrortrack
if on.
the
twoR/D
angles
30°
each
other,
differ2S80
and digital
2S90 series
data
sheets and applicaother,
the difference
between
the
angles
can be
tal angle,
δ. The
angle,product
δ, stored
in the
converter.
multiplying
D/A
converters
the resolver
ence
between
the angles
can to
bemultiply
calculated
using
thesignals
calculated using the cross multiplication shown
counter,
is notes
then incremented
or decremented
tion
from
Analog
Devices,
the
19200
series data
(proportional
to sin
θ andabove.
cosθ) by the cosine and sine of
cross
multiplication
shown
above.
usingAamore
voltage
controlled
oscillator
until this
erdetailed
description
of
tracking
converter
operasheets from ILC Data Devices Corp. (DDC), or the
168
the digital angle, δ, which is the output of the converter, ror is zero,
In the R/D converter, this equation is implemenat
which
point
δ
=
θ
(the
digital
angle
tion
is
available
from
the
converter
manufacturers.
See
In as
the R/D converter,
equation is implemented using
and 268 series data sheets from Control Sciences Inc.the
below. thisD/A
tedshown
using multiplying
converters to multiply
output of the converter is equal to the resolver
2S80 and information
2S90 series product
data sheetsisand
applicamultiplying
D/A
converters
to multiplytothe
resolver
companies
the resolver
signals
(proportional
sinθ
and signals angle).Contact
This incrementing for
andthese
decrementing
of given below.
tion
notes
from
Analog
Devices,
the
19200
series
data
The results
are
subtracted,
demodulated
by and
multiplying
(proportional
tocosine
sin
θ and
θ) by
the cosine
sine of by
cosθ)
by the
andcos
sine
of the
digital
angle,
the digital angle, δ, causes it to track the resolver
Devices
sheets
from the
ILC name
Data Devices
Corp.of(DDC),
or the 168
the
reference
and
filtered
to give
a DC
signal proδ,
which
is thesignal,
output
ofisthe
as
shown
angle,
θ, hence
of thisAnalog
type
converter.
the
digital
angle,
δ, which
theconverter,
output
of the
converter,
Phone:
+1
617.329.4700
and 268 series data sheets from Control Sciences Inc.
portional
to the difference or error between the resolver
asbelow.
shown below.
Fax: +1is617.326.8703
Contact information for these companies
given below.
angle, θ, and the digital angle, δ. The digital angle, δ,
The results are subtracted, demodulated by multiplying by
Internet: www.analog.com
Analog Devices
R
the Vreference
signal, and filtered to give a DC signal proPhone: +1 617.329.4700
portional to the difference or error between the resolver
Fax: +1 617.326.8703
angle, θ, and the digital angle, δ. The digital angle, δ,
ILC Data Devices Corp.
Internet: www.analog.com
Phone: +1 516.567.5600
+
sin θ cos δ
VRV
Synchronous
Cos Multiplying
Σ
S
Fax: +1 516.567.7358
Demodulator
D/A Converter
–
Internet: www.ilcddc.com
ILC Data Devices Corp.
Phone: +1 516.567.5600
+
sin θ cos δ
Synchronous
Cos Multiplying
VS
Σ
cos
θ
sin
δ
Fax: +1 516.567.7358
Demodulator
D/A
Converter
Sin Multiplying
VC
Control Sciences Inc.
–
D/A Converter
Filter
Internet: www.ilcddc.com
Phone: +1 818.709.5510
Fax: +1 818.709.8546
Internet:
δ
cos θ sin δ
Sin Multiplying
VC
Control
Sciences Inc.
www.controlsciences.com
D/A Converter
Filter
Phone: +1 818.709.5510
Voltage
Fax: +1 818.709.8546
Tracking
Controlled
Counter
Internet:
Oscillator
δ
www.controlsciences.com
sults. Further, as long as the difference between the two
angles is relatively small (δ = θ ±30°), the approximation
(θ − δ )
(θ − δ )
Talk
δ
Tracking
Counter
Digital Angle Output
of Converter
Voltage
Controlled
Oscillator
Digital Angle Output
of Converter
©1997–1998 by Admotec Inc.
TT02-0598
©1997–1998 by Admotec Inc.
TT02-0598
Advanced Motion Technology
Admotec Inc.
85 Mechanic Street
Lebanon NH 03766-1500 USA
Tel: +1 603.448.7000
Advanced
Motion Technology
Fax: +1 802.448.7007
Admotec Inc.
E-mail: [email protected]
85 Mechanic Street
Lebanon NH 03766-1500 USA
Tel: +1 603.448.7000
Fax: +1 802.448.7007
E-mail: [email protected]
admotec
δ
Typical
Converter
TypicalTracking
TrackingResolver-to-Digital
Resolver-to-Digital
Converter
Typical Tracking Resolver-to-Digital Converter
admotec
Admotec Precision AG
Kieselgasse 12
CH-8008 Zürich
Telefon +41 44 422 22 75
Fax +41 44 422 22 76
www.admotec.com
© 2016 by Admotec Inc. All rights reserved.