The battery energizes an electronic oscillator circuit, which uses the piezoelectric properties of quartz to keep the crystal vibrating at its natural frequency. A divider circuit repeatedly halves 32,768 Hz until it produces one electrical pulse each second: 32,768 / 2^15 = 1 Hz. Each pulse drives a stepper motor, turning its rotor by a small fixed angle.
A gear train reduces and transfers this motion so the second, minute, and hour hands move at their required rates.
Key Facts
- Quartz is piezoelectric: mechanical stress produces voltage, and an applied voltage can produce mechanical vibration.
- A common watch crystal frequency is f = 32,768 Hz.
- 32,768 = 2^15, so binary divider circuits can reduce the signal exactly to 1 Hz.
- Frequency division follows f_out = f_in / 2^n.
- For a 15-stage divider, 32,768 Hz / 2^15 = 1 pulse/s.
- The stepper motor converts each 1 Hz electrical pulse into a small, controlled mechanical step.
Vocabulary
- Quartz crystal
- A precisely shaped piece of quartz that vibrates at a stable natural frequency when driven electrically.
- Piezoelectric effect
- The ability of certain materials, including quartz, to convert mechanical deformation and electrical voltage into each other.
- Oscillator
- An electronic system that produces a repeating electrical signal at a controlled frequency.
- Frequency divider
- A digital circuit that lowers an input frequency by producing an output pulse after a fixed number of input cycles.
- Stepper motor
- A motor that rotates through small fixed angles in response to individual electrical pulses.
Common Mistakes to Avoid
- Thinking the battery determines the watch's timing. The battery provides energy, while the quartz crystal's resonant vibration provides the timing reference.
- Saying that 32,768 Hz means the second hand moves 32,768 times per second. The divider circuit reduces this frequency to one pulse per second before the motor is driven.
- Dividing 32,768 by 15 to find the one-second signal. The circuit halves the frequency 15 times, so the correct calculation is 32,768 / 2^15.
- Assuming quartz watches are perfectly accurate forever. Temperature changes, crystal aging, and electronic tolerances can cause small timing errors.
Practice Questions
- 1 A quartz crystal vibrates at 32,768 Hz. How many complete vibrations does it make in 5.0 s?
- 2 A divider circuit halves a 32,768 Hz signal 15 times. Calculate the output frequency in hertz.
- 3 Explain why a quartz watch uses both a high-frequency crystal oscillator and a gear train instead of connecting the crystal directly to the watch hands.