Transfer Function of Synchro Control Transfromer Construction and Working principle

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Transfer Function Of Synchros:

The term synchro is a generic name for a family of inductive devices which works on the principle of a rotating transformer(Induction motor). The trade names for synchros are Selsyn, Autosyn and Telesyn. Basically, they are electro-mechanical devices or electromagnetic transducers which produces an output voltage depending upon the angular position of the rotor. Here we will learn the transfer function of Synchros.

A synchro system is formed by the interconnection of the devices called the synchro transmitter and the synchro control transformer. They are also called Synchro pair. The synchro pair measures and compares two angular displacements and its output voltage are approximately linear with an angular difference of the axis of both the shafts. They can be used in the following two ways,

1. To control the angular position of the load from a remote place/long distance. 

2.For automatic correction of changes due to the disturbance in the angular position of the load.

What is Synchro control transformer?

A synchro control transformer is used in conjunction with a synchro transmitter to act as error sensor of mechanical components. Basically, the construction of a synchro control transformer is very similar to that of the synchro transmitter, except that the rotor is cylindrically shaped so that the air gap flux is uniformly distributed around the rotor.

Construction of Synchro Control Transfromer:

The construction of synchro control transformer is similar to that of synchro transmitter except the shape of rotor.The rotor of the control transformer is made cylindrical so that the air gap is practically uniform.This feature of the control transformer minimizes the changes in the rotor impedance with the rotation of the shaft.The constructional features, electrical circuit and a schematic symbol of control transformer are shown in the below figure.

transfer-function-construction-working-synchro-error-detector
transfer-function-construction-working-synchro-error-detector

Working of Synchro Control Transfromer:

The generated emf of the synchro transmitter is applied as input to the stator coils of control transformer. The rotor shaft is connected to the load whose position has to be maintained at the desired value.Depending on the current position of the rotor and the applied emf on the stator, an emf is induced on the rotor winding.This emf can be measured and used to drive a motor so that the position of the load is corrected.

Synchro as error detector: 

The synchro error detector is formed by the interconnection of a synchro transmitter and synchro control transformer. In this arrangement, the stator leads of the transmitter are directly connected to the stator leads of the control transformer.The angular position of the transmitter-rotor is the reference input (or the input corresponding to the desired output) and the rotor is excited by ac supply with frequency, ω.

The control transformer rotor is connected to a servo motor and to the shaft of the load, whose position is the desired output. The induced emf (error voltage) available across the rotor slip rings of control transformer is measured by a signal conditioning ciruit.The output of signal conditioning circuit is used to drive motor so.that desired load position is achieved. A simple schematic diagram of synchros as error detector is shown in the below figure.

Initially, the shafts of transmitter and control transformer are assumed to be in aligned position.In this position, the transmitter rotor will be in electrical zero position and the control transformer rotor will be in null position and the angular separation of both rotor axis in aligned position is 90°.The null position of a control transformer in a servo system is defined as position of its rotor for which the output voltage on the rotor winding is zero with the transmitter in its electrical zero position.

transfer-function-construction-working-synchro-error-detector

When the transmitter rotor is excited, the rotor flux is set-up and emfs are induced in stator coils, These induced EMFs are impressed on the stator coils of control transformer.The currents in the stator coils set up flux in control transformer. Due to the similarity in the magnetic construction, the flux patterns produced in the two synchros will be the same if all losses are neglected. The flux patterns are shown in the below figure.

transfer-function-construction-working-synchro-error-detector

Let the rotor of the transmitter rotate through an angle θ from its electrical zero position. Now the rotor of the control transformer will rotate in the same direction through an angle α from its null position.The net angular separation of the two rotors is equal to (90-θ+α) and the voltage induced in the control transformer rotor is proportional to the cosine of this angle.


The error voltage is amplified and used to drive a servo motor.The motor drives the shaft of the synchro control transformer until it comes to a new aligned position at which the error voltage is zero.

Transfer Function Of Synchros:

Voltage across slip rings of control transformer (modulated error voltage)

                em = K’ Er cos(90 – θ + α) sin ωt

                    = K’ Er cos(90 – (θ – α)) sin ωt

                    = K’ Er sin(θ – α) sin ωt

       where K’ is a proportional constant

Let φ(t) = θ – α

For small values of φ(t), sin(θ – α) = sin φ(t) ≈ φ(t)

                     em = K’ Er φ(t) sin ωt

From the above equation we can say that the output voltage of the synchro error detector is a modulated signal with carrier frequency, ω (which is same as supply frequency of the transmitter rotor).


The magnitude of the modulated carrier wave is proportional to φ(t) and the phase reversals of the modulated wave depend on the sign of φ(t).The signal conditioning circuit demodulates the voltage available across slip rings and develops a demodulated and amplified error voltage to drive the motor.

The demodulated error voltage, e = Ks φ(t)

where  K = Sensitivity of synchro error detector in Volts/deg.

On taking Laplace transform of equation above we get,

                          E(s) = Ks φ(s)

                    ∴  E(s)/φ(s) = Ks

The equation above is the transfer function of the Synchro error detector.

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