555

Do you mean the 555 timer IC? If so, here’s a quick refresher (handy for exams):

Pinout (common version)

• 1 GND
• 2 TRIG
• 3 OUT
• 4 RESET
• 5 CTRL
• 6 THR
• 7 DISCH
• 8 VCC

Astable (continuous oscillation)

• Thigh = 0.693 × (R1 + R2) × C
• Tlow = 0.693 × R2 × C
• Period T = Thigh + Tlow = 0.693 × (R1 + 2R2) × C
• Frequency f = 1 / T = 1 / [0.693 × (R1 + 2R2) × C]
• Duty cycle D = (R1 + R2) / (R1 + 2R2)

Monostable (one-shot)

• Triggered by a low on TRIG (< 1/3 VCC)
• Output goes high for t = 1.1 × R × C
• After t, output returns to low (assuming RESET is high)

Example design

• Want ~1 kHz square wave
  • Pick C = 100 nF, R2 = 10 kΩ, R1 = 2 kΩ
  • Thigh = 0.693 × (2k + 10k) × 100 nF ≈ 0.824 ms
  • Tlow = 0.693 × 10k × 100 nF ≈ 0.693 ms
  • f ≈ 1 / (0.824 + 0.693) ms ≈ 0.96 kHz
  • Duty ≈ (2k + 10k) / (2k + 2×10k) ≈ 12/22 ≈ 54.5%

If you meant something else by “555” (a math problem, another topic, etc.), tell me and I’ll tailor it. Would you like a step-by-step design exercise or a couple of practice problems on 555 timer circuits?