**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 **t****ransfer 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 transmitter?**

**an electromagnetic transducer commonly used to convert an angular position of a shaft into an electric signal**. It is usually called a synchro transmitter. Its construction is similar to that of a three phase alternator.

**Construction of Synchro Transmitter: **

#### The **constructional features**, electrical circuit and a schematic symbol of *synchro transmitter* are shown in the below figure. The two major parts of the **synchro transmitter** are stator and rotor. The stator is identical to the stator of the three-phase alternator.

It is made of laminated silicon steel and slotted on the inner periphery to accommodate a balanced three-phase winding. The stator winding is the concentric type with the axis of three coils 120° apart. The stator winding is star connected ( Y-connection). This basic construction will help you derive the **transfer function of Synchros**.

#### The rotor is of dumbbell construction with a single winding. The ends of rotor winding are terminated on two slip rings. A single-phase ac excitation voltage is applied to the rotor through slip rings.

**Working principle of Synchro Transmitter: **

#### When the rotor is excited by ac voltage, the rotor current flows, and a magnetic field is produced. The rotor magnetic field induces an emf in the stator coils by transformer action. The effective voltage induced in any stator coil depends upon the angular position of the coil’s axis with respect to the rotor axis.

#### Let,

#### er = Instantaneous value of ac voltage applied to rotor.

#### es1,es2,es3 = Instantaneous value of emf induced in stator coils S1 ,S2,S3 with respect to neutral respectively.

#### Er = Maximum value of rotor excitation voltage.

#### ω = Angular frequency of rotor excitation voltage.

#### Kt = Turns ratio of stator and rotor windings.

#### Kc = Coupling coefficient.

#### θ = Angular displacement of rotor with respect to reference.

#### Let, the instantaneous value of rotor excitation voltage, er = Er sin ωt

Let the rotor rotates in an anticlockwise direction. When the rotor rotates by an angle,θ EMFs are induced in stator coils. The frequency of induced emf is the same as that of rotor frequency. The magnitude of induced EMFs is proportional to the turns ratio and coupling coefficient. The turns ratio, Kt is a constant, but coupling coefficient, K is a function of rotor angular position.

#### Coupling coefficient,Kc for S2 = K1 cos θ

#### Coupling coefficient,Kc for S3 = K1 cos (θ-120°)

#### Coupling coefficient,Kc for S1 = K1 cos (θ-240°)

#### Hence the EMFs of stator coils with respect to neutral can be expressed as follows.

#### es2 = Kt K1 cos θ Er sin ωt = K Er cos θ sin ωt

#### es3 = Kt K1 cos (θ-120°) Er sin ωt = K Er cos (θ-120°) sin ωt

#### es1 = Kt K1 cos (θ-240°) Er sin ωt = K Er cos (θ-240°) sin ωt

#### With reference to the below figure by Kirchoffs voltage law the coil-to-coil emf can be expressed as ,

#### eS1S2 = eS1 – eS2 = √3 KEr sin (θ + 240° )sin ωt

#### eS2s3 = eS2 – es3 = √3 KEr sin (θ + 120° )sin ωt

#### eS3s1 = eS3 – es1 = √3 KEr sin θ sin ωt

#### When θ = 0, from equation the above equation we can say that maximum emf is induced in coil S2.But from equation above ,it is observed that the coil-to-coil voltage es3s1 is zero.This position of the rotor is defined as the electrical zero of the transmitter.

The electrical zero position is used as reference for specifying the angular position of the rotor. The input to the **synchro transmitter** is the angular position of its rotor shaft and the output is a set of three stator coil-to-coil voltages.By measuring and identifying the set of voltages at the stator terminals.