Synchro Handbook
o and R
Engineering Handbook
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industry for over 50 years. Our staff includes electrical,
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resolver requirements.
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© 2004 Moog Components Group Inc. MSG90020 12/04
Synchro and Resolver Engineering Handbook Contents
Section 1.0
Section 2.0
Synchros and Resolvers
Theory of Operation and Classic Applications
2.1.1 Transmitter
2.1.2 Receiver
2.1.3 Differential
2.1.4 Control Transformer
2.1.5 Transolver and Differential Resolver
2.1.6 Resolver
2.1.7 Linear Transformer
Brushless Synchros and Resolvers
2.2.1 Electromagnetic Type
2.2.2 Hairspring Type
2.2.3 Flex Lead Type
Section 3.0
Synchro and Resolver Parameters
Input Voltage and Frequency
Accuracy (Electrical Error)
Transformation Ratio and Phase Shift
Voltage Sensitivity
Input Current and Input Power
Null Voltage
DC Resistance
Dielectric Withstanding Voltage
3.10 Insulation Resistance
3.11 Frequency Response
3.12 Harmonic Distortion
3.13 Loading
3.14 Equivalent “T” Networks
3.15 Tolerances
Section 4.0
Electrical Parameters vs. Temperature
Accuracy (Electrical Error)
Phase Shift
Transformation Ratio
Impedances, Input Current and Input Power
Null Voltages
Section 5.0
Mechanical Parameters and Mounting Considerations
Mechanical Parameters
Mounting Considerations - Housed Units
Mounting Considerations - Unhoused Units
Effects of Improper Mounting
Section 6.0
Multispeed Synchros and Resolvers
Multispeed Characteristics
Speed vs. Size
Coupling Factor
Voltage Sensitivity
Impedance Levels
Phase Shift
Transformation Ratio vs. Air gap
EZ Coincidence
6.10 Cross Coupling
6.11 Frequency Response
6.12 Instrumentation and Test Procedures
6.13 Variable Reluctance Multispeed
6.14 Sectional Components
Section 7.0
Resolver to Digital Conversion
Angular Measurement Devices
7.1.1 Encoders
7.1.2 Resolvers
Angle Transmission Using Resolvers
7.2.1 Direct Angle Technique
7.2.2 Phase Analog Technique
7.2.3 Sampling Technique
7.2.4 Tracking Resolver to Digital Converter
7.2.5 Dual Converters
Practical R/D Converter Application
Resolver Commutation of Brushless Motors
7.4.1 Resolver to Digital Converter
7.4.2 Synchronous Demodulation
Section 8.0
Reliability, Environmental Requirements,
and Military Specifications
Environmental Requirements and Military Specifications
Section 9.0
Storage, Handling and Installation
Storage and Handling
Section 10.0
Appendix A
Appendix B
Appendix C
Definitions and Terminology
Multispeed Ratio Table
Binary to Angular Conversion Table
Moog Components Group Synchro and Resolver
Performance Parameters
Pancake Resolvers and Synchros
(Single and Multispeed Types)
Legend of Parameters and Abbreviations
Pancake Linear Transormers
Housed Brushless, Single Speed Size 8
Housed Brushless, Single Speed Size 11
C-2 through C-5
1.0 Introduction
Synchros and resolvers have performed as part of
electromechanical servo and shaft angle positioning
systems for over 50 years. With experience, the
market place has come to realize that, in conjunction
with appropriate interface electronics, a synchro or
resolver can form the heart of an outstanding digital
shaft angle measurement and positioning system. The
technology has been developed and the systems
based on it are unsurpassed in reliability and cost
resolvers include conventional and pancake designs.
These can be provided as brushless and/or
multispeed units. Moog Components Group is also a
leading manufacturer of brush and brushless DC
motors. Our machine shops contain modern
equipment to produce precision components for bar
and strip stock. Our in-house capability for making
lamination dies enables us to quickly change the
number of slots and inside and/or outside diameters,
to suit virtually any design requirement.
This handbook was written by the Moog Components
Group engineering staff, inspired by questions from
engineers working in the most sophisticated military
and space programs. Many of our products were
originally designed as state-of-the-art units. Some
have since become standards. The engineering
expertise of Moog Components Group is apparent in
our participation in all manned spaced missions,
many strategic missile programs, and our reputation
in the industry.
The components described in this handbook are just
a small selection from a broad spectrum of devices
that we manufacture. Dedicated people, with years
of experience in manufacturing products with high
standards, staff all of our facilities.
For five decades, Moog Components Group has also
been involved in the design, development, and
production of rotating components for commercial,
industrial and medical applications. Our synchros and
We look forward to working with you to meet your
component requirements.
We maintain a network of sales offices across the
United States and Internationally. Our staff engineers
are available to support your design efforts or to work
as part of your proposal team.
2.0 Synchros and Resolvers
2.1 Theory of Operation and Classic Applications
A synchro functions as an electromechanical transducer
which, as a circuit element, is essentially a variable
coupling transformer. The magnitude of the magnetic
coupling between the primary and secondary varies
according to the position of the rotating element. This in
turn varies the magnitude of the output voltage. In some
systems, a mechanical input, such as a shaft rotation, is
converted to a unique set of output voltages. In others, a
set of input voltages is used to turn a synchro rotor to a
desired position.
Synchros can be classified in two overlapping groups:
torque synchros and control synchros.
Torque synchros include transmitters (CG), differentials
(CD) and receivers (CR).
Control synchros include transmitters (CG), differentials
(CD) control transformers (CT), resolvers (CS), linear
transformers (LT) and the two hybrid units: transolvers
(CSD) and differential resolvers (CDS).
2.1.1 Transmitter
The synchro transmitter (CG) consists of a single-phase,
salient-pole (dumbbell-shaped) rotor and three-phase,
Y-connected stator. (In this discussion, the word “phase”
will always identify a space relationship unless a
timephase relationship is specifically indicated.)
The primary or input winding is usually the rotor, with the
stator as the secondary or output element. The rotor is
excited through a pair of slip rings with an AC voltage.
The field produced by this voltage induces a voltage into
each of the stator phases. The magnitude of the induced
voltage depends on the angle between the rotor fields
and the resultant axis of the coils forming that stator
phase. Since the axes of the three stator phases are
120° apart, the magnitudes of the stator output voltages
can be written as:
VS1-3 = KVR2-1 sin θ
VS3-2 = KVR2-1 sin (θ+ 120°)
VS2-1 = KVR2-1 sin (θ + 240°)
where K is the maximum coupling transformation
ratio (TR), which is defined as TR = Vout (max.) and
is a scalar quantity.
θ is the rotor position angle. VS1-3 is the voltage
from the S1 terminal to the S3 terminal. All other
voltages are similarly defined throughout this
These stator voltages are either approximately in
time phase or 180° out of time-phase with the
applied voltage. The amount by which the output
voltages differ from an exact 0° or 180° time-phase
relationship with the input voltage is known as the
synchro (time) phase shift.
For a synchro operating at 400 Hz working into
an open circuit, the output voltage will always lead
the input voltage by a few degrees (8 to 20° for
small sizes; 2 to 8° for larger sizes).
The transmitter equations show that no where over
the entire 360° rotation of the rotor will the same
set of stator voltages appear. The transmitter,
therefore, supplies information about the rotor
position angle as a set of three output voltages.
To convert this information, it is necessary to use
an instrument which will measure the magnitude
of these voltages, examine their time-phase
relationships, and return them to their original form:
a shaft position. Such a device is the synchro
receiver (CR). These two units form the most basic
synchro system.
2.1.2 Receiver
The construction of the receiver is electrically
identical to that of the transmitter. The output
voltages vary with rotor position in the same
manner as those of the transmitter. In use, the
receiver is connected back-to-back with a
transmitter. Like-numbered terminals are
connected together (see Figure 2.1.2) and the
rotors are excited in parallel. At the instant the
system is energized, voltage differences exist
across each pair of stator windings if the rotors of
the units are not at the exact same angle relative
to the stator phases. This causes current to flow
in both stators, producing a torque on each rotor.
Since the transmitter rotor is constrained, the resultant
torque acts on the receiver rotor in such a direction as to
align itself with the transmitter. When alignment occurs,
the voltages at each stator terminal are equal and
opposite, and no current flows. Perfect synchronization
is never achieved in practice because of the internal
friction (due to bearings and brushes) of the receivers.
To minimize this error, the receiver is designed to have a
very low starting friction, usually less than 2700 mg-mm.
Turning the transmitter rotor from the equilibrium position
will again exert a force on the receiver rotor. As soon as
this developed force exceeds the receiver’s internal
friction, the receiver will track the transmitter to its new
position. The torque developed on the receiver shaft is
proportional to the angle between the two rotors and is
usually expressed in mg-mm/deg. Methods of measuring
the torque produced by a transmitter-receiver pair can
be found in the Society of Automitive Engineers
Specification ARP-461B.
is also wound with three Y-connected phases. The
output voltages of the differential depend not only
on the input voltages but also on the rotor shaft
position. As shown in Figure 2.1.3(a) the
differential stator is normally excited from the
transmitter stator, and the differential rotor is
connected to the receiver stator. The output
voltages of the differential are now dependent
on both the transmitter rotor position θCG and
its own rotor position θCD. The receiver rotor will
seek a position θCR, where θCR = θCG ± θCD,
depending on how the CG and CD stators are
Figure 2.1.3(a)
Figure 2.1.2
Receivers are constructed to minimize oscillation, over
shoot, and spinning when the rotor is turning to a new
position. The time required for the rotor to reach and
stabilize at its new rest position is called the damping or
synchronizing time.This time varies with the size of the
receiver, the inertia of the load, and the system torque.
This type of basic system is used to transmit angular
information from one point to another without mechanical
linkages. The standard transmission accuracy for such
a system is 30 arc minutes. Information can be sent to
several locations by paralleling more than one receiver
across a transmitter. Multiple receivers decrease the
accuracy of the system and increase the power draw
from the source.
2.1.3 Differential
The differential (CD) is another type of synchro that may
be added to the basic torque system. The differential
stator has a three-phase, Y-connected winding and is
usually the primary element. The rotor is cylindrical and
Figure 2.1.3(b)
The differential may also be positioned between
two transmitters as shown in Figure 2.1.3(b). As
each transmitter is turned to its desired angle,
the differential rotor is forced to assume a position
which is either the sum or the difference of the
angles between the transmitter rotors (θCD = θ1
± θ 2). In this application, the differential is
sometimes called a differential receiver and is
constructed to have a low starting friction (5000
mg-mm) to minimize system errors. An accuracy
of one degree is standard.
Unit torque gradients are typically 3000 mg-mm
per degree of receiver displacement. This is
sufficient to turn a dial or a pointer but nothing
larger without increasing system errors. For large
torques, synchros are used to control other
devices which will provide the necessary torque
levels. An integral part of these control systems
is the synchro control transformer (CT).
2.1.4 Control Transformer
2.1.5 Transolver and Differential Resolver
The control transformer consists of a three-phase, Y connected stator and a single-phase cylindrical drum
rotor. In normal usage, with the stator as the primary
element, the unit is connected as shown in Figure
2.1.4(a). As the transmitter rotor turns (with the control
transformer rotor stationary) the magnitude of the
control transformer stator field remains constant. Its
direction matches that of the transmitter. The field
cutting across the control transformer rotor induces a
voltage in the rotor. The magnitude of this voltage
depends on the sine of the angle between the axis of
the rotor winding and the stator flux vector. Since the
angle of the flux field depends upon the transmitter rotor
angle, the control transformer output voltage provides
information about the transmitter rotor position.
The transolver (CSD) is essentially a control
transformer with a second rotor winding wound in
space quadrature to the main winding. When used
as a control transformer, the transolver’s second
rotor winding is dummy-loaded symmetrically with
the main winding to avoid unbalances. When using
the transolver as a transmitter, the unused rotor
winding is shorted to ground. This provides electrical
saliency and permits the transolver to operate as a
transmitter without introducing additional errors. The
differential resolver (CDS) is the inverse of the
transolver. The rotor is the three-phase element and
the stator the two phase element. In function, the
transolver and the differential resolver are identical.
Both find considerable use converting three-wire
data to four-wire data. These units form the bridge
between the three-phase devices (transmitters,
receivers, differentials, and control transformers)
and the two-phase devices (resolvers).
Figure 2.1.4(a)
If the control transformer rotor angle is not the same as
that of the transmitter, a voltage proportional to the sine
of the angular difference appears on the control
transformer rotor. This voltage is applied to a servo
amplifier connected to the control phase of a
servomotor. The motor, which is geared to the control
transformer rotor shaft, will rotate until the rotor is at
the same angle as the transmitter rotor. At this position,
the control transformer output voltage is theoretically
zero and motion will cease. With additional gearing,
the servomotor provides a mechanical output for other
useful work. This synchro system, which develops no
torque of its own, acts as the control device for the motor
which moves high torque loads. The accuracy of the
entire system depends on the synchro error, amplifier
gain, servo response, and gearing error. Using standard
components, system error is usually specified as 10
arc minutes maximum. If multi-speed pancake synchros
are used, accuracies in arc seconds are obtainable.
This basic control system is shown below.
Figure 2.1.4(b)
2.1.6 Resolver
The resolver (CS) consists of a cylindrical rotor with
each of the two phases of the rotor and stator in
space quadrature. The function of a resolver is to
resolve a vector into its components. Energizing one
phase of the input element, either rotor or stator,
with a voltage (V) induces a voltage into the
output windings. The magnitude of the output
voltage varies with the sine and the cosine of the
rotor position angle θ. The two outputs are V sin θ
and V cos θ (assuming a unity transformation ratio),
which are the components of the input vector V.
The vector resolution function is reversible. In
operation, two voltages, X and Y, are applied to the
inputs of the resolver and one output phase is nulled.
The rotor position then indicates the vector angle θ
equal to the arctan (X/Y). The other output phase,
which is at maximum coupling, indicates the
magnitude of the vector R equal to
X 2 + Y 2.
Exciting one input of a resolver with voltage A
produces outputs of A sin θ and A cos θ. Exciting the
other input with voltage B produces outputs of B sin
(θ + 90) or B cos θ and B cos ( θ + 90) or - B sin θ.
Energizing both windings at once therefore results
in two outputs, Y and X, whose magnitudes are of
the form:
Y = A sin θ + B cos θ
X = A cos θ - B sin θ
windings. The compensator winding is laid in the
same slots as the stator winding.
Analytic geometry demonstrates that these two
equations represent a transformation of axes by
rotation without translation. Y and X are the new
components obtained by rotating A and B through
the angle θ.
Figure 2.1.6(b)
Resolvers can be used wherever the transformation
of coordinates from one system to another is
desired. Space-craft and aircraft usually require
the craft’s pitch, roll, and yaw to be transformed back
to earth references. One resolver is needed for
two-axis transformation, while three are needed for
three axes.
Practically all the flux generated by the stator input
current links all the turns of the compensator.
Therefore the compensator output is essentially
equal to the input voltage, and is constant with rotor
position. The stator flux field induces both the output
voltage of the compensator and the rotor output
voltage. Therefore the time phase shifts of the two
voltages are identical. Because of the resolver’s
construction, any change in the stator flux due to
temperature or voltage, immediately produces a
change in the compensator voltage. The negative
feedback through the amplifier restores the stator
field to its original conditions. A resolver-amplifier
pair as shown in Figure 2.1.6(c) is therefore
basically error free, with respect to resolver chain
performance, over a wide range of environmental
Figure 2.1.6(a)
Figure 2.1.6(a) schematically represents the
interconnections of three resolvers necessary to
transform from inertial platform coordinates (N, E,
G) to an airborne vehicle’s coordinates (X, Y, Z). This
resolver chain essentially solves the matrix equation:
Resolver chains are commonly used to solve
trigonometric problems of varying degrees of
complexity. Computing resolver amplifier chains are
a combination of precision computing resolvers and
amplifiers. The resolvers in this application are
specifically designed to work with a buffer, booster,
or feedback amplifier. They are known as feedback
or compensated resolvers (CQ or CY).
The rotor of a compensated resolver, as shown in
Figure 2.1.6.(b), is identical to that of a standard
resolver. The stator, however, has two additional sets
of coils, called the compensator or feedback
Figure 2.1.6(c)
Resolvers are also used in time-phase-shifting
applications. A typical connection for a resolver
phase shifter is shown in Figure 2.1.6(d). The
resistance R is chosen to match the reactance of
the capacitor C at the operating frequency. Both R
and Xc are substantially higher than the resolver
output short circuit impedance. Under proper
operating conditions, the phase shifter output is:
Where K is the transformation ratio and θ is
the rotor angle.
Note that the output voltage is constant with
rotor position. However, the time-phase shift in
electrical degrees between the output and the
input is equal to the rotor position angle in
mechanical degrees. Using a balanced R-C network
and a stable frequency source, standard resolvers
can be used as phase shifters with an accuracy of
+0.25° or better.
Figure 2.1.6(d)
Resolvers are also used in control systems exactly
like those described for three-phase units. In these
applications, the units are sometimes referred to as
resolver transmitters, resolver differentials, or
resolver control transformers.
2.1.7 Linear Transformer
A linear transformer (LT) consists of a one-phase,
salient pole rotor and a single-phase stator. In all
other synchros, the output voltage is proportional to
the sine of the rotor position angle. But the linear
transformer is constructed so that the output voltage
is directly proportional to the angle itself. In equation
V OUT = Kθ (-50° < θ < +50°)
The angular band over which the output equation
remains valid is known as the excursion range.
Beyond the excursion range, the plot of output
voltage against rotor position tends toward a
sinusoid. The linear transformer acts as a circuit
replacement for a potentiometer with the chief
advantages of low starting friction and infinite
resolution over the excursion range. Because of
construction similarities, the LT also matches the
performance of resolvers over a wide range of
environmental service conditions.
2.2 Brushless Synchros and Resolvers
For applications where conventional commutation
with slip rings and brushes is either undesirable or
unwanted, several varieties of brushless synchros,
for either full or limited rotation, are available.
2.2.1 Electromagnetic Type
In the electromagnetic brushless synchro, energy
is transferred from/to the rotor by means of a
circular rotary transformer mounted in tandem
with the synchro or resolver. Since there are no
physical connections to the rotor, the life of the
unit is limited solely by the life of the bearings.
Tens of thousands of hours of operational life at
high rotational speeds are easily achievable with
this type of unit. The major disadvantage of this
brushless design is that the dual magnetic
structures, synchro and transformer, do not allow
the duplication of standard synchro parameters.
In general, when compared with a standard unit,
the brushless synchro or resolver will have higher
power consumption, lower impedance angle,
higher phase shift, and lower unit torque gradient.
This can be a problem if the intent is to replace a
synchro or resolver in an existing system. In new
applications, proper design can allow for
variations in unit performance. However, closer
conformance to existing synchro performance
can be achieved with additional unit length. Multiphase rotors require additional length, since each
rotor phase requires its own transformer.
Figure 2.2.1 Schematic and Phasing Equation of Typical Transformer Type Brushless Resolvers
Hairspring Type
conventional unit already in the system. There is no
effect on system performance except for the benefits
from the elimination of sliding contacts. Properly
designed hair springs will perform millions of
operations without failure.
A hairspring brushless synchro is designed with
spirally wound conductors used to transfer energy
from/to the rotor. These hairspring conductors allow
a limited rotation of as much as ±165° from the
electrical zero position. The units are normally
supplied with a mechanical stop to prevent damage
to the hairsprings from excessive shaft rotation. The
addition of the stop normally requires extra length.
The advantage of hairspring over transformercoupled brushless synchros is that any standard
electrical characteristics can be duplicated in a
hairspring design. If the application permits limited
rotation, a hairspring unit can simply replace the
Flex Lead Type
A flex lead brushless synchro is designed with thin
flexible lead wires to transfer energy from/to the rotor.
These units have all the advantages of the hairspring
type and are used in applications where short unit
length and low friction are required. Rotation is usually
limited to ±90°.
3.0 Synchro and Resolver Parameters
minus the mechanical or rotor position angle.
Electrical error is usually measured in arc minutes
or arc seconds. The tangent of the electrical angle
is calculated from the secondary voltages of all
secondary windings (two for resolvers, three for
synchros) when one primary winding is energized.
3.1 Input Voltage and Frequency
Synchros and resolvers can be designed to operate
with input voltages from 0.5 to 115 Vrms over a
wide range of frequencies from 60 Hz to 100 kHz.
Some of the standard input voltages are 11.8, 26,
90 and 115 Vrms. However, voltages between 5
and 26 Vrms and frequencies between 400 and
2600 Hz are preferred.
(b) Function error compares the output of each
winding separately. The error is defined as the
difference between the in-phase component of
the voltage of a secondary winding and the
theoretical value of that voltage. This is expressed
as a percentage of the maximum in-phase
component of the secondary voltage and is
equivalent to:
Depending on the size of the synchro or resolver,
the input voltage and/or frequency may have to
be limited so that an excessive input current will
not saturate the iron core.
Synchros and resolvers can be operated at voltages
and frequencies other than those specified, as long
as the input current is not exceeded. If the frequency
is doubled, the voltage can also be doubled. If the
frequency is halved, the voltage must also be
halved. However, some degradation in performance
may be experienced at frequencies other than those
Eα - sin α x 100 = %Error
where: Eα =The measured RMS value of the
fundamental component of secondary
voltage at any angle α.
E MAX = The measured RMS value of the
fundamental component of secondary
voltage at a rotor angle α = 90°.
For standard synchros and resolvers, the
functional error method is expensive. It is
subject to errors and unsuitable for production
(c) Interaxis error is the angular deviation of all null
positions for the rotor and stator combinations
at rotor angles of 90, 180, and 270 degrees.
This is expressed in arc minutes or arc seconds.
3.2 Accuracy (Electrical Error)
The accuracy of a synchro or resolver is based on
the ability of its output voltages to define the rotor
angle. Of all the parameters, this is probably the
most important. It is an exact measure of the
function which the synchro or resolver is designed
to perform. For any given rotor position, the output
voltages are designed to give precise electrical
information which corresponds uniquely to that rotor
angle. Several methods are used to measure and
define the error of a synchro or resolver. The most
common ones are delineated below:
(d) Linearity error describes the error of linear
transformers. Linearity error is the nonconformity
of the secondary voltage at any angular rotor
displacement within the effective electrical travel
limits. It is expressed as a percentage of the
secondary voltage at the maximum excursion.
(e) Velocity errors are caused by rotationally
generated voltages. They are a result of
conductors moving through a magnetic field (a
synchro rotating at high speeds). Velocity errors
are difficult to measure directly. Fortunately, many
synchro/resolver applications operate in a virtual
(a) Synchro or resolver error is defined as the
electrical angle, indicated by the output voltage,
static mode: rotational velocities are low. The
increased use of these devices, especially brushless
units, for high speed motor controls highlights the
potential problem of inaccuracy in these systems.
The following formula is used to calculate the critical
(synchronous) velocity:
Sc = 120(F)
where: Sc = synchronous rotational velocity in RPM
F = excitation frequency of the system in Hz
P = the number of poles of the synchro/
As a rule-of-thumb, speeds above one-quarter of
synchronous speed cause serious velocity errors
and should be avoided.
Example: A 32-speed (64 pole) resolver at 400
Hz has a synchronous velocity of:
Sc = 120 x 400 / 64 = 750 RPM
Therefore, rotational speed should be held below 180
1-speed synchros and resolvers have leading phase
shifts between 0° and 20°.
Phase shift can be approximated by the arctangent
of the ratio of the primary winding DC resistance to
its reactive component, as follows:
Phase shift θ = arctan
primary RDc
primary XL
3.4 Voltage Sensitivity
Voltage sensitivity is the output voltage expressed
as a function of the shaft angle in millivolts/degree.
This parameter (also referred to as voltage gradient)
is usually specified at a shaft angle of one degree. It
can be calculated by multiplying the output voltage
at maximum coupling by the sine of one degree.
3.5 Impedances
Impedances, expressed in ohms, are usually
specified in rectangular form as R + jX where R is
the sum of the DC and AC resistive components and
X is the reactive component. Impedances are
sometimes expressed in polar form as Z
θ where
Z is the total impedance and θ is the impedance
angle. The impedances which are universally defined
and apply to all synchro devices are:
ZPO: Primary impedance, secondary open circuit
ZPS: Primary impedance, secondary short circuit
ZSO: Secondary impedance, primary open circuit
ZSS: Secondary impedance, primary short circuit
3.3 Transformation Ratio and Phase Shift
Transformation ratio (TR) is the ratio of output
voltage to input voltage when the output is at
maximum coupling. Practical TR’S usually range
between 0.1 and 1.0. TR’S greater than 1.0 are
sometimes possible, depending on the design of the
unit. The most common TR’s are .454 and 1.0.
Phase shift (expressed in electrical degrees) is the
difference between the time-phase of the primary
voltage and the time-phase of the secondary voltage
when the output is at maximum coupling. Generally,
For three-phase devices, the impedance is measured
with two of the lead wires tied together. The
impedance is measured between those two and the
third wire.
The names “rotor” and “stator” are sometimes used
in place of “primary” and “secondary.” For example,
for rotor primary units the primary impedances would
be ZRO and ZRS. The secondary or stator impedances
would be Zso and Zss.
For compensated resolvers, two additional
impedances are required:
ZCO: Compensator impedance, secondary
open circuit
ZCS: Compensator impedance, secondary
short circuit
3.6 Input Current and Input Power
Input current is the current, in amps, flowing
through the primary winding at rated voltage and
frequency. Input power, in watts, is calculated
from input current and input impedance. In
synchros and resolvers, input current is typically
very low (less than 100 milliamps) and input
power is usually less than 1 watt.
fundamental null voltage is usually slightly less than
or equal to the total null voltage.
3.8 DC Resistance
DC resistance is the line-to-line resistance, measured
in ohms, for all winding combinations at room
3.9 Dielectric Withstanding Voltage
3.7 Null Voltage
Null voltage is the residual voltage remaining
when the inphase component of the output
voltage is zero. When the primary and secondary
windings are exactly perpendicular (at electrical
zero) there should be no induced voltage. The
secondary voltage should be exactly zero. However,
mechanical imperfections, winding errors, and
distortions in the magnetic circuit (such as grinding
smear), cause some voltage to be induced into the
secondary at the minimum coupling position.
A dielectric withstanding voltage test consists of
applying a voltage higher than the rated voltage, for
a specific time, between mutually insulated windings
and between insulated windings and ground. (This
is also called a high potential, Hi-Pot, or dielectric
strength test.) This test is used to prove that a
component can operate safely at its rated voltage
and withstand momentary over-potentials due to
switching surges. It determines whether the
insulating material and the separation of the
component parts is adequate.
When a part is defective, application of the test
voltage will result in either disruptive discharge or
The null voltage is composed of three components:
in-phase fundamental, quadrature fundamental,
and harmonics. The in-phase fundamental
component is an angular inaccuracy that can be
cancelled out by renulling the rotor, thereby
introducing an error (sometimes called null spacing
error). Quadrature voltage is 90° out of time-phase
with the in-phase component and cannot be nulled
by rotor rotation. The harmonic voltages consist
predominantly of the third harmonic which is three
times the excitation frequency.
Null voltages are usually specified as total null
voltage, which is the total of the quadrature
fundamental and the harmonics.
Depending on size, input voltage, and input
frequency, the total null voltage is approximately
1 to 3 millivolts per volt of input voltage. The
Care should be taken when testing, since even an
large voltage less than the breakdown voltage may
damage the insulation and reduce the reliability of
the unit. If subsequent application of the Hi-pot
voltage is required, it is recommended that
succeeding tests be made at reduced potential
(usually at 80% of specified voltage).
3.10 Insulation Resistance
Insulation resistance is a measure of the resistance
provided by insulating components to an applied
direct voltage. Inadequate resistance permits
leakage of current through, or on, the surface of
these materials. Usually, the insulation resistance
values in synchros and resolvers are very high
(greater than 50 megohms). Low insulation
resistances, by permitting flow of large leakage
currents, can disturb the operation of circuits intended
to be isolated. Excessive leakage currents can
eventually lead to the deterioration of the insulation
through heat or direct current electrolysis.
the synchro or resolver is at maximum coupling.
Zso for a three-phase winding is measured
between two leads tied together and the third lead.
Therefore the correction factor of 4/3 serves for
all calculations.
Insulation resistance measurements should not be
considered the equivalent of dielectric withstanding
voltage. Clean, dry insulation may have a high
insulation resistance, yet have a mechanical fault
that could cause failure in a dielectric withstanding
voltage test. Conversely, a dirty, deteriorated
insulation with a low insulation resistance may not
fail a dielectric voltage.
3.11 Frequency Response
The frequency response of synchros and resolvers
from input to output is similar to that of a transformer
with a high leakage reactance. Low corner and peak
frequencies will vary, depending on the impedance
level of the unit. The low corner frequency is usually
less than 100 Hz. The response is fairly flat from
about 200 Hz to 10 kHz. A peak normally occurs
between 10 kHz and 100 kHz.
Figure 3.14 “T” Network Formula
3.15 Tolerances
Typical tolerances for the electrical parameters for
standard synchros and resolvers at 25°C are as
Input voltage
Input frequency
Input current
Input power
Output voltage or TR
Phase shift
Null voltage
26 volt synchros
115 volt synchros
Figure 3.11 Typical One Speed Frequency Response
3.12 Harmonic Distortion
Harmonic distortion is an expression of the
percentage of distortion in the output voltage.
Typically, harmonic distortion in synchros and
resolvers is less than two percent.
3.13 Loading
± 1%
± 2%
± 10%
± 20%
± 3%
± 20% or 1 degree*
30 mV max
100 mV max
1 mV/Volt of input
Open circuit..........R: ± 15% or ± 2
XL: ± 15% or ± 2 ohms*
Short Circuit...........R: ± 15% or ± 2 ohms*
XL: ± 15% or ± 2 ohms*
DC Resistances
± 10%
The electrical loading of synchros and resolvers
should be ten or more times greater than the output
short circuit impedance of the unit. More severe loads
will decrease the output voltage, increase the input
current, power, and null voltage, and degrade the
3.14 Equivalent “T” Networks
*Whichever is larger
1) Null voltage is not measured on receivers.
2) Some brushless units, multispeeds, and nonstandard units may have different tolerances.
Please contact the Engineering Department.
To calculate the loading effect on synchro systems
(commonly called synchro chains) each synchro can
be treated as an equivalent “T” network. Chain
parameters can then be solved (Figure 3.14). The
formulas are based on line-to-line impedances when
4.0 Electrical Parameters vs. Temperature
All electrical parameters are specified at room
ambient (25°C). In actual use the operating
temperature may be different. The following are
typical changes to be expected.
4.1 Accuracy (Electrical Error)
Theoretically, the error of a given unit should not
change since errors are a result of design limitations
and manufacturing inaccuracies. However, mounting
stresses and differential expansion in the lamination
stack, windings, and hardware due to temperature
changes, may cause variations in a unit’s error
curve. The magnitude of the change will be different
from unit to unit. Single speed units are more
sensitive than multispeed units. A single speed
may change as much as a few minutes, while a
multispeed may only change a few seconds.
Even though there may be no change in the shape
of the error curve, there is another factor which can
add a bias. Referred to as EZ shift, this bias is due
to a shift in the electrical zero resulting from minute
mechanical changes with temperature. It cannot be
predicted or calculated. The changes expected are
similar to those mentioned above and are different
from unit to unit.
4.2 Phase Shift
4.3 Transformation Ratio
Transformation ratio changes are related to
changes in the phase shift. The change is
proportional to the ratio of the cosine of the
phase shift at the new temperature to the cosine
of the phase shift at room ambient. Higher
temperatures result in lower transformation ratios
and lower temperatures result in higher
transformation ratios. The new value may be
calculated as follows:
Where: TR1 = TR at room ambient usually 25°C
TR2 = TR at some other temperature
Φ = Phase shift at room temperature
Resistive changes in the copper magnet wire result
in changes in phase shift. The coefficient of
resistance of copper is approximately 0.4% per
degree C. Phase shift will change by the same
percentage. Increased temperatures result in higher
resistance and higher phase shift. Decreased
temperatures produce the opposite effects.
As an example, for a unit with the following room
temperature (25 ° C) input characteristics,
ZPO = 100 + j300
DCP = 60 ohms
the phase shift Φ can be approximated as follows:
= Calculated phase shift at
Using the parameters from the above example
and assuming a transformation ratio of .454, the
new value will be:
TR2 = .454 X cos 15.6 = .446
cos 11.3
4.4 Impedances, Input Current, and Input Power
Impedances, input current, and input power are also
affected by a change in the resistance of the copper
magnet wire.
The only change in impedance with temperature is
in the resistive portion, the R component. Using the
above example of an input impedance ZPO = 100 +
j300 (a total impedance ZT = 316.2 < 71.6°) with a
DC resistance of 60 ohms, assuming an input voltage
of 10 volts, and an increase in temperature of 100°
C, the expected changes are calculated as follows:
The DC resistance changes as before:
60 ohms x 100 deg. x 0.4% = 24 ohms
Therefore the impedance at 125° C is:
ZPO = 100 + 24 - j300 = 124 + j300 and
ZT = 324.6 67.5°
Input Current:
The input current at room ambient is:
IIN1 = EIN = 10 = 0.0316 amps
ZT 316.2
And at elevated temperature is:
IIN2 = EIN = 10 = 0.0308 amps
ZT 324.6
Input Power:
The input power at room temperature is:
PIN1 = (IIN1)2 R1 = (.0316)2 x 100 = .100 watts.
And at elevated temperature is:
PIN2 = (IIN2)2 R2 = (.0308)2 x 124 = .118 watts.
4.5 Null Voltage
Null voltage is also sensitive to mounting stresses
and differential expansion in the lamination stack,
winding, and hardware due to temperature
changes. Single speeds are more sensitive than
multispeeds. The magnitude of the change will
be different for various unit types and will be
different from unit to unit for the same type. As a
rule-of-thumb, the maximum change is less than
1% per degree C.
5.0 Mechanical Parameters and Mounting Considerations
5.1 Mechanical Parameters
5.2 Mounting Considerations - Housed Units
Unhoused units, called pancakes, are inspected for
all outline drawing dimensions. This includes outside
diameter, inside diameter, and overall height. Housed
units are checked for mounting dimensions and for
conformance to shaft end play, shaft radial play, and
starting friction requirements.
Since most housed units have standardized sizes
and are electrically coupled to the rotor by slip
rings, hairsprings or transformers, the mounting
considerations are minimal. The two major areas
of concern are the housing mounting and the shaft
Shaft end play is the total axial motion of the shaft
when an eight ounce reversing load is applied along
the axis. Shaft radial play is the total side-to-side
motion of the shaft measured as close to the bearing
as possible, when a four ounce reversing load is
applied radially to the shaft within 0.25 inch of the
bearing. Starting friction is the torque necessary to
overcome the internal friction of the bearings and
Normally the housing is mounted into a pilot
diameter and then secured in one of two ways.
The first is by means of synchro clamps mounted
and secured adjacent to the pilot diameter in the
circumferential groove in the housing. The second
method is to secure the housing with screws
entering the mounting face. If clamps are used,
especially for resolvers, two or four point contact
is suggested.
Because of the important relationship between
accuracy, shaft end play, and shaft radial play, these
parameters are controlled as rigidly as possible. If
end play and radial play are too loose, higher errors
and non-repeatablity of the error pattern result. If
they are too tight, performance over environmental
service conditions may suffer. Friction, except in
receivers, is relatively unimportant. A maximum
friction of four gram-centimeters is an optimum level
for both normal and extreme temperature ambients.
Coupling to the shaft is accomplished by means
of a solid coupling to another shaft, a bellows type
coupling, or by a gear arrangement. Care must
be taken to avoid applying excessive radial loads
to the shaft.
5.3 Mounting Considerations
- Unhoused Units
Unhoused units are usually supplied as separable
rotors and stators to be directly mounted in the
housings and on the shafts of the user’s system.
If an unhoused unit is to be used for other than
very limited angular rotations, some means must
be provided to couple electrically to the rotor
windings. This is usually accomplished with slip
rings mounted to the user’s shaft adjacent to the
rotor. A true brushless unit can be used, if space
and electrical parameters permit, eliminating the
need for slip rings.
The user, providing the mounting surfaces and
bearings when he designs the mechanics of the
mount, should consider these guidelines:
1. Eccentricities between the inner and outer
member mounting surfaces should not exceed
0.0005 inch.
2. Mounting shoulders should be perpendicular to
bores and shafts within 0.0005 inch.
3. The fit between the bore and the maximum stator
OD and between the shaft and the minimum rotor
ID should be from 0.0002 to 0.0007 inches loose.
This will assure that there is no line-to-line or
interference fit.
4. Axial misalignment or variation in mounting
dimensions between the rotor and the stator
mounting surfaces should not exceed 2% of stack
height. In other words, for a stack height of 0.250
the axial misalignment should not exceed 0.005
5. The designer should select housing and shaft
materials with thermal coefficients of expansion
similar to that of the unit’s ring material or, if it has
no rings, it’s lamination material, usually a high
nickel steel.
The above guidelines are for a typical unit.
Depending on unit size, air gap clearance, accuracy,
and other electrical requirements, these guidelines
may require looser or tighter tolerances.
5.4 Effects of Improper Mounting
If, due to system tolerance buildup or defective
system hardware, the preceding guidelines are
exceeded, some changes in electrical characteristics can be anticipated.
The magnitude of these changes will depend
upon unit size, air gap clearance, and whether it
is a single speed or multispeed. The performance
of the unit will be affected as follows:
1. For axial offset:
• Accuracy (electrical error) will increase only
• Null voltage will change
• Transformation ratio will decrease
• Phase shift will increase
• Input current and power will increase
2. For radial offset:
• Accuracy (electrical error) will increase
• Null voltage will change
• Transformation ratio will show little change
• Phase shift will show little change
• Input current and power will show little change
3. For rotor and stator tilt:
If rotor and stator tilt is slight, (about 0.001 or
0.002 inches with respect to each other), very
little change will occur in any parameter. Tilts
greater than this must be avoided in units with
small air gap clearances to prevent rotor and stator from making contact.
6.0 Multispeed Synchros and Resolvers
Multispeeds are electronically and mechanically
similar to standard synchros or resolvers. Their name
is derived from the following relationships: For every
mechanical revolution of the rotor, the unit electrically
produces “N” cosine waves on the cosine output
winding and “N” sine waves on the sine output
winding. “N” is the ratio or the “speed,” which is one
half the number of poles. A 36 speed, for example,
has 72 poles (36 pole pairs) and appears to be
mechanically geared through a 36:1 ratio. Multispeed
synchros have three output phases spaced 120°
apart electrically, and multispeed resolvers have two
output phases spaced electrically 90° apart.
6.1 Multispeed Characteristics
All the information on synchro and resolver
characteristics presented earlier in this manual
applies equally to multispeeds. There are, however,
additional factors to be considered when selecting
the proper multispeed for a specific application. This
chapter will highlight the options and variations the
user should consider.
The beginning of each sine cycle is designated as
an electrical zero (EZ) point. The deviation of all these
points from the theoretical true position is called the
cross-over error. The exploration of the deviation
from the true value for each sine and cosine output
over each individual cycle is called a tangent error.
This evaluation, using a tangent bridge and a null
meter, is identical to that performed on a normal
speed synchro or resolver.
6.2 Speed vs. Size
Typical multispeed synchros and resolvers range
in size from 1.1 inches (1-8x) to more than 3 feet
(1-150x) outside diameter.
Multispeed units have one cycle (360 electrical
degrees) in 360/N mechanical degrees. This may
present an ambiguity to the user, unless the total
excursion angle is less than one cycle. To be able to
distinguish between the individual electrical cycles,
a conventional single speed is inserted in the same
slots with the multispeed, creating a multiple speed
unit. (see Figure 6.0). For example, a 1-speed and a
36-speed will give a cycle (2 pole) output at one set
of output windings and a 36 cycle (72 pole) output at
the other. The 1-speed portion is generally called
the coarse output and the 36-speed portion is
called the fine output. The Master EZ is defined as
that multispeed EZ closest to the start of the
1-speed sine curve.
The table below presents a guideline of practical
dimensions for common speed ranges:
O. A. Width
64 or 72
4” - 6”
2” - 4”
32 or 36
3” - 5”
1” - 3”
8 or 16
2” - 4”
.5” - 2”
For a given speed, a large mechanical cross section
increases the rigidity of the unit. This provides stress
resistance to support the increased number of teeth
required for the greater number of poles.
6.3 Accuracy
The accuracy curve of a multispeed consists of three
individual components:
Mechanical, electrical, and slot ripple errors.
Mechanical error, caused by out-of-roundness, tilt,
Figure 6.0 Superimposed Output Waveforms for
Coarse (1-speed) and Fine (5-speed) Resolver
6.5 Voltage Sensitivity
The voltage sensitivity of multispeeds is the output
voltage expressed as a function of the shaft angle
times the speed of the unit.
This parameter (also refered to as voltage gradient)
is usually specified at a shaft angle of one degree
mechanical. For example, a 4-speed with a
maximum output voltage of 11.8 volts has
a voltage sensitivity of:
eccentricity, bearing run-out, and mounting stresses,
can be observed in the cross-over error curve.
Electrical errors, such as transformation ratio
unbalance or perpendicularity (sine and cosine zero
crossings not exactly 90 electrical degrees apart) will
surface in the tangent error curve. Electrical errors
can usually be designed or compensated out of a
unit. The main remaining errors will consist of
mechanical and slot ripple errors. Slot ripple is due
to the interaction between rotor and stator teeth. It
can be minimized by proper slot combination and/or
skewing of the slots. Typical errors for existing
multispeed units are 20 arc seconds for a 36- or a
64-speed, 30 arc seconds for a 16-speed, and 60
arc seconds for an 8-speed.
11.8 x sin (1 x 4) = 0.023 volts/degree.
6.6 Impedance Levels
Secondary open circuit impedances are usually
higher on multispeeds. The undesirable characteristics of the loading effect from additional units in a
chain is offset since multispeeds are relatively
insensitive to loading. If a lower short circuit
impedance is required, the input impedance can be
decreased, increasing the power level, or the
transformation ratio can be reduced. Impedance
imbalances, both resistive and capacitive, are lower
than on single speed units.
6.4 Coupling Factor
An increased winding turns ratio (secondary to
primary) is required because of the lower magnetic
coupling in multi-speed devices due to the larger
number of slots necessary.
In some cases, a low output impedance may be
necessary to prevent capacitive coupling between
the output windings. Capacitive coupling is an
apparent current flow between the sine and cosine
windings. It produces an error that can increase
electrical perpendicularity to such an extent that
manual compensation may be impractical.
Example: For a single speed unit with a 1:1 TR
(transformation ratio), the turns ratio would be
approximately 1.05:1. For a 16-speed unit it would
be approximately 2:1; for a 36-speed unit 2 1/2 or
3:1; for a 64-speed unit as high as 3 1/2 or 4:1 for
the same TR.
6.7 Phase Shift
The increased number of slots required by the larger
number of poles, results in smaller slot areas than
those used in conventional single speed units. This
necessitates a finer wire for the windings. In addition
to the smaller pole span ratio, this will normally result
in a much higher phase shift than that of a
comparable single speed device. For example, for a
given stack size, a unit wound as a regular one speed
might have a phase shift of approximately 4°. The
phase shift could be 20° for a 16-speed, 35° to 40°
for a 36-speed, and as high as 60° for a 64-speed.
To provide a reasonably high impedance, the
transformation ratio for multispeeds should be limited
to the following maximum values:
6.8 Transformation Ratio vs. Air Gap
6.11 Frequency Response
One of the critical characteristics of the multispeed
unit is its sensitivity to overall air gap size. For
example, a single speed unit with a radial air gap of
.006” and a transformation ratio with a tolerance of
2%, would probably stay within the tolerance even if
the air gap were ground .0005” over or under
nominal. On multispeed units, however, the 2%
tolerance would be exceeded for the same air gap
variation. The higher the speed, the more
pronounced the effect. If a 64-speed unit with a radial
air gap of .006” is 0.0005” oversize, it’s transformation
ratio can change by 10%. This puts an increased
burden on the manufacturer of the device to hold
tolerances much more closely than on single speeds.
Typical transformation ratio tolerances for multispeed
units should be specified as follows:
The frequency response of a multispeed is similar
to that of a one speed, except that it is not quite as
linear in the mid frequency range. At higher
frequencies, between 10 kHz and 100 kHz, two
peaks occur.
Figure 6.11
Typical Frequency Response of Multispeeds
Up to 10%
6.12 Instrumentation and Test Procedures
Instrumentation for testing multispeed devices is very
much the same as that used for high quality single
speed units. The synchro or resolver bridge used to
test the tangent error is normally accurate to within
two to four seconds. This is sufficient for even the
best multispeed, since the error of the bridge is
divided by the speed of the resolver. A 2 arc second
bridge error becomes .125 arc second for a 16-speed
unit and even less for a 64-speed unit.
6.9 EZ Coincidence
EZ coincidence is the mechanical angle between the
fine and course speed electrical zeros of a
multispeed synchro or resolver. This angle can be
included in the coarse speed accuracy specification,
and acts as a bias to the error curve of the one speed.
With phase angle voltmeters of sufficient accuracy,
the weak links in the instrumentation chain become
the mechanical mounting and the readout of angular
errors. Several instruments are available that will
suffice for testing very high accuracy units.
6.13 Variable Reluctance Multispeed
Variable reluctance multispeeds have both the input
and the output windings on the stator (the outer
element) and no windings at all on the rotor. They
are therefore true brushless devices. The rotor has
a number of teeth equivalent to “N”, the speed of
the unit. This type of design is therefore impractical
for single speeds, since the rotor would only have
one tooth. Units of this type are actually the original
version of the multispeed resolver or synchro. They
took the place of geared single speeds.
6.10 Cross Coupling
Cross coupling is the effect that a single speed input
winding has on a multispeed output winding and vice
versa. Null voltages and errors usually increase,
compared with values for the unit when energized
and tested individually. Careful design can usually
reduce these effects to less than a few millivolts and
insignificant changes in the error curves.
Variable reluctance multispeeds are now successfully used as commutation transducers for brushless
motors. In many cases, they are more reliable and
environmentally stable than other types of devices.
The position of each tooth during the rotation of the
rotor determines which of the output windings will
be coupled to the inut winding to produce an output
signal. All coupling conditions repeat themselves
every time a tooth moves to the position where an
adjacent tooth was previously. When this happens,
a complete cycle (360° electrical) of the sine and
cosine has taken place.
6.14 Sectional Components
Sectional resolvers, synchros, and linear transformers are hybrid variations of standard units. These
components distinguish themselves from all the
others previously discussed by their lack of
symmetry. While typical resolver functions rely on
symmetrical, round and concentric air gaps, the
rotors and stators of these devices are built as arc
This highlights the disadvantage of this design. Each
crossover (where the sine crosses from minus to
plus) is well defined by the mechanical precision of
the rotor teeth, but the point where the sine crosses
from plus to minus (180° electrical) is floating. It is
defined by the lack of a tooth. This results in much
larger tangent errors than those of rotor wound
Useful rotation of the rotor must be strictly limited,
unless a lack of signal for a large part of the travel is
allowable. Mounting of these devices is more critical
than that of standard synchros. Any air gap variations
due to eccentricities or rotor movement toward or
away from the stator element will result in errors.
The following list serves as an example of the
expected range of errors for similar sized units:
Reluctance Multispeeds
Overall Error
(arc minutes)
Cross-over Error
(arc minutes)
Applications range from a gun turret direction
indicator using a quasi-single speed device to a
partial 16-speed mirror elevation control unit.
Apparent diameters vary from a few inches to more
than 10 feet. Accuracies range from 5 arc minutes
to 20 arc seconds.
Tangent Error
(arc minutes)
7.0 Resolver to Digital Conversion
mounted where an angle needs to be measured and
the electronics can be located in a less hostile electronic equipment area. Signal transmission
requires only four signal lines for a single speed
and eight signal lines for a high precision
multispeed resolver. A resolver also provides signal
isolation and common-mode rejection of electrical
interference, and can withstand severe environments
of dust, oil, temperature, shock, and vibration.
7.1 Angular Measurement Devices
Two types of components are commonly used to
make angular measurements: encoders and
resolvers. A short description of these can help in
optimizing component selection for specific
7.1.1 Encoders
An encoder is an electro-optical device which uses
a glass disk inscribed with fine lines. The number of
lines determines resolution and accuracy. There are
two basic types of encoders: incremental and
Disadvantages of resolvers are that they require an
AC signal source and that their analog output must
be converted in interfacing with digital systems.
An incremental encoder produces output pulses as
its shaft is rotated. The direction of rotation is
determined by the phase relationship of two output
lines. A third line is used as a reference when the
encoder passes thru zero.
There are several methods of using a resolver to
obtain precise shaft angle position.
7.2 Angle Transmission Using Resolvers
7.2.1 Direct Angle Technique
In the direct angle method, the rotor winding is
excited by an alternating signal and the output is
taken from the two stator windings. Both outputs have
nearly the same time phase angle as the original
signal. However, their amplitudes are modulated by
sine and cosine as the shaft rotates.
The disadvantage of an incremental encoder is that
on power up or after a power interruption the true
angular position is lost and the system has to be
Absolute encoders give a parallel digital signal
indicating shaft position. However, this requires
extra lines to send a signal to the digital processor.
A unit with an accuracy of 20 arc seconds will
require 16 wires.
These outputs are fed to either a receiving type
resolver (resolver chain) or to an analog-to-digital
converter. Recent advances in conversion
techniques and manufacturing have simplified the
electronic interface.
The advantages of encoders are that they have
digital outputs, are easily computer interfaced, and
are generally well understood. The primary
drawbacks of encoders are: sensitivity to hostile
environments, reliability problems in certain
applications, and size of a given resolution and
Sources of error for this method are the resolver
accuracies and, if used, the converter accuracy and
7.2.2 Phase Analog Technique
In this method, the two stator windings are excited
by signals that are in phase quadrature to each other.
This induces a voltage in the rotor winding with an
amplitude and frequency that are fixed and a timephase that varies with shaft angle. This method is
referred to as the “phase analog technique.” It has
been the most widely used technique since it can
easily be converted to produce a digital signal by
measuring the change in phase shift with respect to
the reference signal.
7.1.2 Resolvers
A resolver is an electro-mechanical transformer
whose analog output voltages are a function of shaft
angle. It is, therefore, an absolute position
transducer, providing true angular information at any
time power is applied.
The advantages of a resolver are that it can be easily
converter operates ratiometrically. It uses only the
ratio of the sine and cosine stator outputs of a
rotor excited resolver. Since the resolver acts as a
transformer, any excitation waveform distortion or
amplitude variation appears in the correct ratio on
both sine and cosine and has little effect on
accuracy. A tracking converter contains a phase
demodulator. Therefore, frequency variation and
incoherent noise do not affect accuracy. Tracking
converters can operate with any reference
excitation, sine or square wave, with only minor
accuracy variations. Common mode rejection is
achieved by the isolation of the resolver.
The accuracy of this type of angle transmission is
determined by the accuracy to which the zero
crossing intervals can be measured.
Sources of error for this method are noise generated
by the environment of the resolver. This causes the
zero crossing point to be indeterminate and produces
variations in the excitation. Any variation of the
amplitudes or time-phases of the two excitation
signals directly influences the time phase of the
output signal.
7.2.5 Dual Converters
Dual converters are used to encode the resolver or
synchro of multispeed units. One channel, the coarse
portion of the converter, is connected to the single
or coarse speed section of the resolver. The other
channel, the fine portion, is connected to the fine
speed section.
The coarse channel supplies an approximate nonambiguous rotor position to the demodulator. When
the output error of the coarse channel drops below
a preset threshold, the crossover detector switches
the fine channel error signal into the demodulator.
The error angle is multiplied by the speed ratio of
the resolver. This increases the voltage sensitivity
and enables the servo system to seek a more
accurate null. The converter will continue to use the
fine error signal for continuous tracking.
7.2.3 Sampling Techniques
When using this method a sample is taken of the
sine and cosine output signals of a rotor excited
resolver at the peak of the reference input amplitude.
These are converted to digital signals by an analog
to digital converter. The resulting digital words are
used as a memory address to “look-up” the shaft
angles in a processor.
The basic accuracy and resolution of the converter
is therefore divided by the speed of the resolver.
Example: A 16 bit converter with an accuracy of 2
arc minutes has a single speed resolution of 20 arc
seconds. This can be coupled with a 32-speed (32 =
2 bits) resolver. The resulting converter accuracy is
2 x 60/32 = 3.75 arc seconds. The system resolution
is 16 bits +5 bits or 0.6 arc seconds.
The difficulty with this approach is it’s inability to deal
with noise. If a noise disturbance occurs on the signal
lines at the time of sampling, a wrong shaft angle
position results. If the noise causes only a single
wrong reading, the frequency pass band of the drive
systems acts as a filter with little resulting error.
7.3 Practical R/D Converter Application
Figure (7.3) shows a complete R/D converter
schematic. The 16 data lines and the seven control
lines are buffered by two 74LS245 and one 74LS244
IC’s respectively. These parts are used to isolate the
R/D converter from static electricity, and to increase
the drive capability for an LED display.
7.2.4 Tracking Resolver to Digital Converter
The tracking conversion technique overcomes all the
difficulties described above. Modern converters are
cost competitive with other methods and provide
superior accuracy and noise-immunity. A tracking
Figure 7.3 Typical Resolver to Digital Converter Schematic
7.4 Resolver Commutation of Brushless Motors
In this schematic, the carrier reference is a
symmetrical square wave drive. It consists of U14,
the oscillator; U15A, a divide by flip-flop used to
product a symmetrical waveform; and U17 and U18,
which are LM555 timer I.C.’s used as power drivers.
If noise is a problem an OSC1758 sine wave
oscillator can be substituted for the U14, U15, U17
and U18.
One of the most cost effective methods for
commutation in a brushless motor is the use of the
Hall effect switch and a magnetic code wheel to
sense the position of the motor as it rotates.
The Hall switch is an integrated circuit that is limited
to temperature extremes of -55 to 125°C. Hall
switches are available that operate at 150° C but
are limited to an operating life of 100 hours at this
temperature. Among other limitations, they cannot
provide accurate position and velocity information. A
resolver can operate at much higher temperatures
than integrated circuits, even above 180° C. The
actual operating temperature is a function of the unit’s
material and type of construction.
The heart of the converter is U11, which is a typical
16 bit parallel R/D converter I.C. This device (a 2S80
is shown) can be programmed for a resolution of
10,12, 14, or 16 bits. and an accuracy of 2 minutes
at 16 bits. At the 10 bit resolution, the maximum
tracking rate is over 62,000 RPM.
This chip also has a linear velocity output. Therefore,
no separate tachometer is needed to measure
angularity velocity with a single that is linear to 1%.
The tracking R/D converter generates a digital word
which tracks the input position with no time lag. The
digital output is always within one LSB (least
significant bit) of the input signal, up to the maximum
tracking rate of the converter.
7.4.1 Resolver to Digital Converter
A converter as shown in Figure 8.3 can also be used
for motor commutation. Digital angle information can
be converted to commutation signals by adding a
PROM Look-Up Table to the digital data.
The circuit shown provides a 16 line bar code display
and a four digit hexidecimal display for testing and
evaluating a resolver.
Figure 7.4.1 Typical Brushless Motor Drive Using a Resolver to Digital Converter
In a typical 12 bit converter (see Figure 7.4.1) there
are 4096 (4K) states that have to be decoded. A
three-phase brushless motor drive has six drive
signals for the six power driver transistors. It requires
six 4K x 1 PROMs or one 32K PROM (4K x 8). An
existing brushless motor driver can interface with Hall
switches, the R/D converter and the driver with three
4K x 1 PROMs or one 16K PROM (4K x 4).
7.4.2 Synchronous Demodulation
An R/D converter as described above is not
necessarily required when using a resolver to
commutate a brushless motor. If the only requirement
is to rotate the motor and accurate position data are
not required, a synchronous demodulator can be
used to process this information.
Figure 7.4.2(b) Modulated Synchro Output
Figure 8.4.2(b) shows one of the three outputs from
the synchro as the motor is rotating. All three outputs
are the same except that they are shifted in phase
by 120 degrees.
A three-phase motor will require a three-phase
synchro, usually with the same number of poles as
the number of magnet pole reversals in the motor.
An 8-pole motor has 4 pole reversals per revolution.
A 4-speed (8-pole) synchro would be idea as a
commutator. Most commutation can be done with
either 2- or 4-speed brushless synchros.
In this design the carrier frequency should be at least
ten times greater than the highest frequency of the
motor. For a motor that operates at a maximum of
5,000 RPM the carrier frequency should be higher
than 800 Hz. The shape of the carrier frequency has
little effect on the performance of the circuit. A square
wave is the least expensive to generate, while a sine
wave is optimum for system noise reduction.
A synchro that is used only for commutation is more
economical than a unit designed to provide high
accuracy angular information, since the analog
output is of little inportance. The significant parameter
is the zero crossing error. Careful mechanical design
can make this very accurate.
Figure 7.4.2 (a) shows a block diagram for a typical
commutation circuit. U1, U2, and U3 are phase
demodulators. One is required for each output of
the synchro. This integrated circuit separates the
carrier frequency from the modulation frequency
(motor rotation). It produces a sine wave which is
then level shifted and amplified by U4A, U4B, and
U4C to produce three digital outputs. At this point
the outputs A, B, and C are the same as those
produced by the Hall devices and can be handled
by standard brushless motor drivers.
Figure 7.4.2(a) Three Phase Synchro Decoder
8.1 Reliability
Since they are inductive devices, synchros and
resolvers have a very long life expectancy. The nature
of a transformer permits the isolation of the input
and the output circuits. The shortest life expectancy
would be expected for units with brushes and slip
rings, the longest for true brushless units using rotary
- Ambient temperature
- Temperature rise of the unit
- Size of unit (Size 8, 10, 11, 15, etc.)
- Number of brushes
- Type of application (e.g., ground, vehicle mounted
ground, shipboard, airborne, missle)
As an example, for a Size 8 synchro with two brushes
operating in a Ground Benign service environment,
with a frame temperature of 70° C, and an internal
heat rise of 5°C, the failure rate calculates to 0.062
failures/million hours. This translates to an MTBF
16.18 million hours or 1,847 years.
An average value for Mean Time Between Failures
(MTBF) cannot be stated because of the many
factors that influence the calculation.
The best guide available for MTBF calculations is in
the US Department of Defense Handbook MILHDBK-217. This handbook lists the many factors that
affect synchro and resolver failure rates and defines
a method of estimating them. It takes the following
factors into account:
8.2 Environmental Requirements and Military
establishing specifications for synchros which must
withstand environmental operating extremes.
The following military standards cover many
environmental service conditions to which our
standard synchros have successfully demonstrated
conformance. This list is by no means all-inclusive.
nor does it hint at the ultimate limits of our units’
capabilities. Rather it is meant as a guide for
MIL-STD-202G, Method 204D, Cond. B
SAE AS20708, Paragraph 3.7.1
MIL-STD-202G, Method 213B, Cond. A
SAE AS20708, Paragraph (Low Impact)
MIL-STD-202G, Method 105C, Cond. A, B, C, or F
MIL-STD-202G, Method 103B, Cond. A or B; Method 106E
SAE AS20708, Paragraph 3.7.6
MIL-STD-810E, Method 507.1, Procedure I
Ambient Temperature:
SAE AS20708, Paragraph 3.7.5
MIL-STD-810E, Methods 501.1 and 502.1
Thermal Shock:
MIL-STD-202G, Method 107D, Cond. A or B
MIL-STD-202G, Method 109B
Salt Spray:
SAE AS20708, Paragraph 3.7.8
Fungus Resistance:
MIL-STD-810E, Method 508.1
SAE AS20708, Paragraph 3.7.4 1000 hrs. min. at 100 rpm
9.0 Storage, Handling and Installation
9.1 Storage and Handling
Synchros and resolvers are supplied in either of two
ways: as completed housed units, or as unhoused
rotors and stators. Most pancake designs are
unhoused and may or may not have mounting rings,
Unhoused units are manufactured in matched sets
and should not be interchanged.
9.1.1 The units should remain in their original
packages until ready for use and should be stored
at room ambient in a clean dry area.
9.1.5 Do not drop parts or subject them to radial
forces (squeezing a diameter). This could cause
magnetic changes, affecting the performance of the
9.1.6 Never machine or drill housings, rings, shafts,
or lamination stacks. Internal damage, bearing contamination, or magnetic changes could occur.
9.2 Installation
9.1.2 Care in handling must be excercised at all
9.2.1 Housed units require no special procedures
except for the normal care required as stated above.
9.1.3 Use care when mounting and removing parts
to avoid damage to mounting surfaces, mounting
diameters, shafts, and air gap surfaces.
9.2.2 Unhoused units require more care than housed
units. Stators and rotors should be placed
in position with care so that parts do not become
cocked. In no case should these parts be pressed
into holes or onto shafts. Press fits should never be
used, since this would cause physical or magnetic
9.1.4 Avoid pinching or cutting lead wires. Be careful
not to damage terminals or connectors.
10.0 Definitions and Terminology
Excitation: The RMS voltage and frequency which
excites the primary winding.
Accuracy (Electrical Error): Electrical angle, as
indicated by the output voltage, minus the
mechanical or rotor position angle.
EZ Coincidence: The mechanical angle between
the fine and course speed electrical zeros of a
multispeed unit.
A/D Converter: Analog to digital converter, used to
convert common audio or video signals to digital for
computer interfacing.
Friction: The torque required to turn a shaft from a
stationary position.
Barcode Display: A set of simple ON/OFF lamps
that indicate the status of a digital output signal from
an A/D ot R/D converter.
Function Error: The difference between the inphase component of one secondary winding voltage
and the theoretical value of the secondary voltage.
This is expressed as a percentage of the maximum
in-phase component of the secondary voltage.
Brushless: Transferring energy from or to a rotor
by means of a circular rotary transformer, spirally
wound conductors (hairsprings), flex lead or variable
Hairspring: A spirally wound conductor, used for
limited rotation, to transfer energy to or from the rotor.
It can be used up to ±165 degrees.
Common Mode Rejection: Rejection by an input
device of large unwanted in-phase input noise without
affecting a small out-of-phase signal.
Hexidecimal: A convienient means to display the
16 possible states of a 4 bit binary word on a seven
segment display:
Compensated Resolver: A synchro with feedback
windings in parallel with primary windings.
Control Synchro: A synchro used to provide and
deal with control signals in servo systems where
precise angular transmission to a mechanical load
is required.
Input Current: The current, in amps, flowing through
a primary winding when excited at rated voltage and
Control Transformer: A synchro with a three-phase
primary winding, usually on the stator, and a onephase secondary winding. This is a high impedance
version of a torque receiver. It is excited by other
Input Power: The power, in watts, consumed by a
primary winding when excited at rated voltage and
Interaxis Error: The angular deviation of the null
positions for all rotor and stator combinations at rotor
positions of 90, 180, and 270 degrees.
Control Transmitter:
Crossover Errors: The deviations of all the
crossover points (sine output voltage passing from
negative to positive) from a master electrical zero of
a multispeed synchro or resolver.
ZPO: Primary impedance, secondary open circuit
ZPS: Primary impedance, secondary short circuit
ZSO: Secondary impedance, primary open circuit
ZSS: Secondary impedance, primary short circuit
ZCO: Compensator impedance, secondary open
ZCS: Compensator impedance, secondary short
Differential: A synchro with a three-phase primary
winding and a three-phase secondary winding. This
is an analog form of mechanical differential.
Differential Resolver: A hybrid synchro with a three
phase rotor winding and a two-phase stator winding.
This is the reverse of a transolver. It can be used in
either direction as a transmitter or control
Linear Transformer: A synchro with one-phase
primay and one-phase secondary. The generated
output voltage at any given rotor angle within the
rated excursion is directly proportional to that angle.
Electrical Error: See Accuracy.
Electrical Zero (EZ): The rotor angle at which the
sine output voltage is at an in-phase null.
Master EZ: The multispeed electrical zero closest
to the single speed electrical zero.
End Play: The total axial motion of the shaft when a
specified reversing load is applied along the shaft
Mechanical Zero: The angle at which the rotor and
stator are mechanically aligned by markings, pins,
slots, etc., usually close to the electrical zero.
Receiver: A synchro with a line excited rotor within
a three-phase stator connected to the corresponding
stator leads of a driving torque transmitter.
Multiple Speed: A synchro with a coarse and a fine
speed winding in the same lamination stack, usually
referred to as a multispeed.
Resolver: A synchro with a one-or two-phase primary
and a two-phase secondary that creates or recieves
sine-cosine signals.
Multispeed: A synchro that produces for one
mechanical revolution of the rotor “N” sine and “N”
cosine waves at the output windings. “N” is the speed.
There are two poles per speed. The name can apply
to resolvers or synchros and is commonly used for
multiple speed.
Secondary Winding: An output winding which is
inductively coupled to a primary winding.
Null Voltage: The residual voltage remaining when
the in-phase component is zero. The total null voltage
is the sum of the quadrature fundamental null voltage
plus the harmonics.
Output Voltage: The no load voltage at the
secondary windings at maximum coupling with rated
voltage and frequency applied to the primary winding.
Pancake: A name given to synchros and resolvers
which are flat in appearance. The term is derived
from the physical dimensions of these units which
typically have a diameter that exceeds the axial
Phase Demodulation: A technique for detecting
signals with a large degree of rejection of frequencies
outside the single band.
Phase Shift: The difference between the time
phases of the primary and secondary voltages when
the output is at maximum coupling.
Primary Winding: The winding which receives
power from another component or from a power
Radial Play: The total radial movement of the shaft
on it’s own bearings, measured on the shaft at a
specified distance from the housing when a specified
reversing load is applied radially to the shaft.
Sensitivity: Is the output voltage at one mechanical
degree. Is defined as the maximum output voltage
times the sine of 1 degree, and is expressed in mV/
Synchros: Rotating, transducing devices of various
types, used to convert shaft angle position to
electrical signals or the reverse. This term generally
refers to three-phase devices.
Tangent Errors: The electrical error (accuracy) of
each individual cycle of a multispeed synchro or
Torque Synchro: A synchro that transmits or
receives angular information while supplying a small
amount of motive power.
Transformation Ratio: The ratio of output voltage
to input voltage, usually referred to as TR.
Transmitter: A synchro with one input phase and
three output phases electrically 120 degrees apart.
This type of device transmits signals to a reciever
proportional to rotor position.
Transolver: A hybrid synchro with a three-phase
stator and a two-phase rotor. This type of device can
be used in either direction as a control transmitter or
a control transformer.
Variable Reluctance Unit: A brushless synchro or
resolver in which both the input and the output
windings are on the stator (the outer element), with
none on the rotor. Units of this type will always be
multispeeds. Single speeds are impractical.
R/D Converter: Resolver to digital converter. This
type of device is used to convert the analog output
of a resolver to a digital signal.
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