Question

Draw the constructional diagram of LVDT. State its working principle. What is residual voltage? Explain with a neat diagram.

Answer 1

### Constructional Diagram of LVDT

A Linear Variable Differential Transformer (LVDT) is a type of electrical transformer used for measuring linear displacement. Here's a typical constructional diagram of an LVDT:

```
        +---------+---------+
        |   Core   |   Core   |
        |  Inside  |   Outside |
        +---------+---------+
            |         |
           +-+-------+-+
           |     |     |
           |     |     |
           |     |     |
         +-+-----+-----+-+
         |      Secondary Coils    |
         |           (2 coils)          |
         +--------------------+
                |         |
               +-+-------+-+
               |      Primary Coil      |
               +------------------+
```

### Working Principle of LVDT

1. **Construction**: An LVDT consists of three main parts:
   - **Primary Coil**: This coil is connected to an AC power supply.
   - **Two Secondary Coils**: These coils are placed symmetrically around the primary coil.
   - **Movable Core**: This core is placed inside the coils and moves with the displacement being measured.

2. **Operation**:
   - When an AC voltage is applied to the primary coil, it generates an alternating magnetic field.
   - This magnetic field induces voltages in the two secondary coils, which are located on either side of the primary coil.
   - The induced voltage in each secondary coil depends on the position of the movable core.
   - When the core is centered, the induced voltages in the secondary coils are equal and out of phase, resulting in no net voltage (differential voltage) between the secondary coils.
   - When the core moves from the center position, it causes a change in the magnetic coupling between the primary coil and each secondary coil. This results in a difference in the induced voltages in the secondary coils, producing a differential voltage.

3. **Signal Output**:
   - The differential voltage output of the LVDT is proportional to the displacement of the core from the center position. The direction of the core movement (left or right) affects whether the differential voltage is positive or negative.

### Residual Voltage

**Residual voltage** in the context of an LVDT refers to the small voltage that remains in the secondary coils even when there is no displacement of the core. This residual voltage is essentially the result of imperfections or inherent asymmetries in the LVDT's construction or electronic circuit.

**Residual Voltage Explanation**:
- **Ideal Case**: In a perfectly balanced LVDT with the core exactly at the center, the output voltage from both secondary coils should be equal and opposite, resulting in a net differential output of zero.
- **Practical Case**: In practice, due to manufacturing tolerances, imperfections, or external factors, there might be a small residual voltage even when the core is at the central position. This voltage is a result of slight mismatches in the secondary coils or small asymmetries in the core.

**Diagram of Residual Voltage Effect**:

```
                 +----+-------+----+
    Core Center:  |   V1   |   V2   |
                 +----+-------+----+
                       |       |   
                       |       |  
           Residual Voltage: V_residual
                       |
                       |
                 +-----+-----+
                 | Differential |
                 | Voltage Output |
                 +-------------+
```

- **V1** and **V2** are the voltages induced in the two secondary coils.
- **V_residual** is the small voltage difference even when the core is ideally at the center.

In summary, the LVDT measures linear displacement by producing a differential voltage proportional to the core's position. Residual voltage is an inherent small voltage that remains due to non-ideal conditions, affecting the accuracy of the measurement.

Answer 2

### Constructional Diagram of LVDT (Linear Variable Differential Transformer)

#### Constructional Diagram
The Linear Variable Differential Transformer (LVDT) is a type of electromechanical transducer used to measure linear displacement. Here's a simplified constructional diagram of an LVDT:

```
        +-------------------+
        |                   |
        |      Core          |
        |                   |
        +---------+---------+
                  |
                  |
                  |
+---------+       +---------+
| Primary |-------| Secondary|
| Winding |-------| Winding  |
| 1       |       | 1       |
+---------+       +---------+
                  |
                  |
+---------+       +---------+
| Primary |-------| Secondary|
| Winding |-------| Winding  |
| 2       |       | 2       |
+---------+       +---------+
```

- **Core**: The core is a ferromagnetic rod that moves within the LVDT.
- **Primary Windings (Winding 1 and Winding 2)**: These are typically positioned in a single plane and are energized with an AC signal.
- **Secondary Windings (Winding 1 and Winding 2)**: These are positioned symmetrically around the primary windings and are used to sense the position of the core.

#### Working Principle

1. **AC Excitation**: An AC voltage is applied to the primary windings. This generates a magnetic field that induces voltages in the secondary windings.
2. **Core Movement**: As the core moves within the LVDT, the magnetic coupling between the primary and secondary windings changes.
3. **Differential Output**: The LVDT produces a differential output voltage between the two secondary windings. The amplitude and phase of this output voltage are proportional to the position of the core.

The output voltage is a function of the core position relative to the center of the winding assembly. When the core is centered, the output voltage is at its maximum, and as the core moves away from the center, the output voltage decreases. The direction of the core movement can be inferred from the phase of the output voltage.

#### Residual Voltage

**Residual Voltage** refers to the small amount of voltage that remains in a system or device even when it is supposed to be zero or turned off. In the context of an LVDT or similar measurement systems, residual voltage can be an unwanted offset that affects the accuracy of the measurement.

**Explanation with a Diagram**

Consider the following simplified diagram showing an LVDT output characteristic:

```
+---------------------+
|     Output Voltage  |
|      (V_out)        |
|                     |
|                     |   Residual Voltage
|                     |       (V_res)
|                     |
|        |            |
|        |            |
|        |            |
|--------|------------|-----------+-----------------------> Core Position
        Center Position           Full Displacement
```

- **Residual Voltage (V_res)**: This is the voltage present when the core is in the center position or when no displacement is applied. Ideally, it should be zero, but practical LVDTs may have a small residual voltage due to imperfections in the windings or other factors.

**Impact of Residual Voltage**: Residual voltage can affect the accuracy of displacement measurements by introducing an offset. Calibration procedures are often used to compensate for residual voltage and improve measurement accuracy.

### Summary

- **LVDT Construction**: Consists of a core and three windings (two primary and two secondary).
- **Working Principle**: Measures displacement based on changes in induced voltages due to core movement.
- **Residual Voltage**: The small offset voltage that remains in the system and can affect measurement accuracy.

If you have any more questions or need further details, feel free to ask!