Piezoelectric ceramics are a special type of material that can convert electrical energy into mechanical energy and vice versa. Since the invention of the first piezoelectric ceramic, barium titanate, in 1942, it has been widely applied in various fields. The applications of piezoelectric ceramics are mainly divided into two categories: one is as tuning devices, such as piezoelectric resonators; the other is for quasi-static applications involving energy conversion.

1. Piezoelectric Vibrators and Their Working Principle:
   - After polarization treatment, piezoelectric ceramics are called piezoelectric vibrators, which have an inherent vibration frequency determined by their dimensions.
   - When the frequency of the applied voltage matches the inherent frequency of the piezoelectric vibrator, resonance occurs, and the amplitude significantly increases.
   - In this process, the electric field generates strain through the inverse piezoelectric effect, and the strain generates current through the direct piezoelectric effect, achieving efficient conversion between electrical and mechanical energy.
   - Utilizing these characteristics, various filters and resonators can be manufactured, which have the advantages of low cost, small size, non-hygroscopicity, long life, good frequency stability, higher quality factor compared to LC filters, wide applicable frequency range, and high precision. Especially in communication and measurement equipment, these devices have improved anti-interference capabilities, having replaced many electromagnetic oscillators and filters.

2. Piezoelectric Transformers and Their Working Principle:
   - Piezoelectric transformers use the piezoelectric effect to convert electrical energy into mechanical energy and then back into electrical energy.
   - They consist of two parts, the input end and the output end, with the input end polarized in the thickness direction. When an alternating current voltage is applied, it produces longitudinal vibration, which in turn generates high-voltage output at the output end.
   - These transformers are a new type of solid-state electronic device, mainly used as AC-DC, DC-DC power devices, and high-voltage devices, such as cold cathode tubes, neon lamp tubes, laser tubes, etc.

3. Piezoelectric Ultrasonic Motors and Their Working Principle:
   - Piezoelectric transducers convert electrical energy into acoustic energy and vice versa through the piezoelectric effect and the inverse piezoelectric effect.
   - They are one of the underwater acoustic devices for emitting and receiving ultrasonic waves. In industry, piezoelectric transducers are widely used in navigation, marine water body detection, precision measurement, ultrasonic cleaning, solid detection, and medical imaging, ultrasonic diagnosis, ultrasonic treatment, etc.
   - Another application of piezoelectric transducers is in telemetry and remote control systems, such as piezoelectric ceramic buzzers, piezoelectric igniters, ultrasonic microscopes, etc.

In short, due to their unique energy conversion capabilities, piezoelectric ceramics play an increasingly important role in modern technology.