An LVDT Displacement Transducer comprises 3 coils; a primary and two secondaries.
The transfer of current between the primary and the secondaries of the LVDT displacement transducer is controlled by the position of a magnetic core called an armature.
In position measurement LVDTs, the two transducer secondaries are connected in opposition.
At the centre of the position measurement stroke, the two secondary voltages of the displacement transducer are equal but because they are connected in opposition the resulting output from the sensor is zero.
As the LVDTs armature moves away from centre, the result is an increase in one of the position sensor secondaries and a decrease in the other. This results in an output from the measurement sensor.
With LVDTs, the phase of the output (compared with the excitation phase) enables the electronics to know which half of the coil the armature is in.
The strength of the LVDT sensor's principle is that there is no electrical contact across the transducer position sensing element which for the user of the sensor means clean data, infinite resolution and a very long life.
The reason why you apply frequency is because you are using the 'Transformer Action' to make the LVDTs output a signal, proportional to the armature movement..... and Transformer action would not be possible if you didn't apply a time varying signal..... Hence the frequency.....
But I still have another basic question.... The I/P voltage applied to the primary is AC Voltage... In my case it is 7 Volts RMS.... This will also have frequency i.e. 50 Hz. So why a separate frequency I/P needs to be applied? In our case it was 2920 Hz.... And from where is this frequency input generated or obtained?
The coils are physically small and using such a low frequency as 50 Hz would not work well with the low inductances. The excitation signal would usually come from the device reading the LVDT as it needs to be compared to the output.
Check the above link to see how Transformer size varies with frequency....... Transformer coils can be made less bulky with increase in frequency....... Higher frequencies are also used in SMPS design where coil size is vastly reduced.....
7 Vrms and 2920 Hz sounds like the LVDT used for a Turbine Governer feedback......
Basic electronics, (XL) Inductive reactance = 2piFL. For the instrument to operate at reasonable currents and voltages, the inductive reactance needs to be at least in the 10s or 100s of Ohms. Since XL is proportional to both (L)Inductance and (F) Frequency, if you have low inductance because you need physically small coils you need a higher frequency to get a good working XL. The Inductance needed for 50 Hz would require larger coils.
Can you describe the trouble(s) you are having with an LVDT?
Most manufacturers employing LVDTs apply them in a manner consistent with the way they are designed to be applied. Most LVDTs require a higher frequency AC source (higher than that available in the receptacle on the wall in the building) to operate properly.
If it's just design information you are looking for, there is tons of it on the Internet. Rahul P. Sharma also provided some good links.
Amazingly enough, there are also MANY videos about LVDTs on YouTube (I continue to be amazed at what can be found on YouTube).
But, if you have a turbine control systems employing LVDTs then it's a pretty safe bet that the way it's been designed is to provide the necessary excitation (power--voltage and frequency) for the LVDT to work properly.
If you're having specific LVDT problems, we can try to answer those.