Timing & Oscillators Formulas
Timing and oscillator formulas convert RC and crystal values into frequency, period, and duty cycle. These calculators help you design 555 timers, clocks, and pulse generators with predictable output. They are central to any circuit that needs a stable time base.
Timing & Oscillators Formula Calculators
- 555 Timer Astable f = 1.44 / ((R1 + 2×R2) × C) R1 100 Ω, R2 0.22 kΩ, Capacitance 100 pF → Frequency = 26.67 MHz
- 555 Timer Monostable t = 1.1 × R × C Resistance 100 Ω, Capacitance 100 nF → Pulse Width = 11 µs
- Crystal Load Capacitance CL = (C1×C2)/(C1+C2) + Cstray C1 1 pF, C2 2.2 pF, Stray Capacitance 4.7 pF → CL = 5.388 pF
- RC Oscillator Frequency f = 1 / (2πRC) Resistance 100 Ω, Capacitance 100 pF → Frequency = 15.92 MHz
- Crystal Frequency Stability Δf = f0 × ppm × 1e-6 Nominal Frequency 100 kHz, Stability (ppm) 0.025 → Frequency Deviation = 0.0025 Hz
- PLL Lock Time t ≈ 2π / (ωn × ζ) Natural Frequency 0.1 rad/s, Damping Ratio 0.025 → Lock Time = 0.6981 h
- VCO Tuning Sensitivity KVCO = Δf / ΔV Frequency Change 0.22 MHz, Tuning Voltage Change 0.33 V → VCO Gain = 666700 Hz/V
- Jitter from Phase Noise Tj = √(2 × ∫L(f)df) / (2πf0) Integrated Phase Noise (rad² rms) 0.025, Carrier Frequency 100 kHz → RMS Jitter = 0.3559 µs
- SPI Maximum Clock Frequency fmax = 1 / (tsetup + thold + tprop) Setup Time 100 ps, Hold Time 0.22 ns, Propagation Delay 0.47 ns → Max Clock Frequency = 1.266 GHz
- CAN Bus Termination Resistor Rterm = Z0 / 2 Cable Impedance 2.2 Ω → Termination Resistor = 1.1 Ω
- PLL Output Frequency fout = fref × N / R Reference Frequency 0.22 MHz, Feedback Divider (N) 0.025, Reference Divider (R) 0.055 → Output Frequency = 100 kHz
- Delay-Matched Trace Length Δl = vp × Δt Propagation Velocity 0.025, Skew Requirement 1 ps → Length Difference = 2.5 × 10⁻¹¹ mm
- PWM Resolution (Bits) bits = log2(fclk / fpwm) Timer Clock 100 kHz, PWM Frequency 100 Hz → Resolution (bits) = 9.966
- Wien Bridge Oscillator Frequency f = 1 / (2π · R · C) Resistance 100 Ω, Capacitance 100 pF → Frequency = 15.92 MHz
- Wien Bridge Gain Resistor Rf = 2 · Rg (for Av = 3) Ground Resistor 0.22 kΩ → Feedback Resistor = 0.44 kΩ
- RC Phase-Shift Oscillator Frequency f = 1 / (2π · R · C · √6) Resistance 100 Ω, Capacitance 100 pF → Frequency = 6.497 MHz
- Colpitts Oscillator Frequency f = 1 / (2π√(L · Cs)), Cs = C1·C2/(C1+C2) Inductance 100 nH, Capacitor C1 100 pF, Capacitor C2 0.22 nF → Frequency = 60.7 MHz
- Hartley Oscillator Frequency f = 1 / (2π√((L1+L2) · C)) Inductor L1 100 nH, Inductor L2 0.22 µH, Tank Capacitor 100 pF → Frequency = 28.13 MHz
- Clapp Oscillator Frequency f = 1/(2π√(L·Cs)), 1/Cs = 1/C1+1/C2+1/C3 Inductance 100 nH, Capacitor C1 100 pF, Capacitor C2 0.22 nF, Capacitor C3 0.47 nF → Frequency = 64.99 MHz
- DDS Output Frequency fout = M · fclk / 2ᴺ Tuning Word 0.025, Clock Frequency 100 kHz, Accumulator Bits 0.055 → Output Frequency = 2.406 kHz
- DDS Frequency Resolution Δf = fclk / 2ᴺ Clock Frequency 100 kHz, Accumulator Bits 0.025 → Frequency Step = 98.28 kHz
Worked result for every Timing & Oscillators formula
| Formula | Expression | Worked result |
|---|---|---|
| 555 Timer Astable | f = 1.44 / ((R1 + 2×R2) × C) | R1 100 Ω, R2 0.22 kΩ, Capacitance 100 pF → Frequency = 26.67 MHz |
| 555 Timer Monostable | t = 1.1 × R × C | Resistance 100 Ω, Capacitance 100 nF → Pulse Width = 11 µs |
| Crystal Load Capacitance | CL = (C1×C2)/(C1+C2) + Cstray | C1 1 pF, C2 2.2 pF, Stray Capacitance 4.7 pF → CL = 5.388 pF |
| RC Oscillator Frequency | f = 1 / (2πRC) | Resistance 100 Ω, Capacitance 100 pF → Frequency = 15.92 MHz |
| Crystal Frequency Stability | Δf = f0 × ppm × 1e-6 | Nominal Frequency 100 kHz, Stability (ppm) 0.025 → Frequency Deviation = 0.0025 Hz |
| PLL Lock Time | t ≈ 2π / (ωn × ζ) | Natural Frequency 0.1 rad/s, Damping Ratio 0.025 → Lock Time = 0.6981 h |
| VCO Tuning Sensitivity | KVCO = Δf / ΔV | Frequency Change 0.22 MHz, Tuning Voltage Change 0.33 V → VCO Gain = 666700 Hz/V |
| Jitter from Phase Noise | Tj = √(2 × ∫L(f)df) / (2πf0) | Integrated Phase Noise (rad² rms) 0.025, Carrier Frequency 100 kHz → RMS Jitter = 0.3559 µs |
| SPI Maximum Clock Frequency | fmax = 1 / (tsetup + thold + tprop) | Setup Time 100 ps, Hold Time 0.22 ns, Propagation Delay 0.47 ns → Max Clock Frequency = 1.266 GHz |
| CAN Bus Termination Resistor | Rterm = Z0 / 2 | Cable Impedance 2.2 Ω → Termination Resistor = 1.1 Ω |
| PLL Output Frequency | fout = fref × N / R | Reference Frequency 0.22 MHz, Feedback Divider (N) 0.025, Reference Divider (R) 0.055 → Output Frequency = 100 kHz |
| Delay-Matched Trace Length | Δl = vp × Δt | Propagation Velocity 0.025, Skew Requirement 1 ps → Length Difference = 2.5 × 10⁻¹¹ mm |
| PWM Resolution (Bits) | bits = log2(fclk / fpwm) | Timer Clock 100 kHz, PWM Frequency 100 Hz → Resolution (bits) = 9.966 |
| Wien Bridge Oscillator Frequency | f = 1 / (2π · R · C) | Resistance 100 Ω, Capacitance 100 pF → Frequency = 15.92 MHz |
| Wien Bridge Gain Resistor | Rf = 2 · Rg (for Av = 3) | Ground Resistor 0.22 kΩ → Feedback Resistor = 0.44 kΩ |
| RC Phase-Shift Oscillator Frequency | f = 1 / (2π · R · C · √6) | Resistance 100 Ω, Capacitance 100 pF → Frequency = 6.497 MHz |
| Colpitts Oscillator Frequency | f = 1 / (2π√(L · Cs)), Cs = C1·C2/(C1+C2) | Inductance 100 nH, Capacitor C1 100 pF, Capacitor C2 0.22 nF → Frequency = 60.7 MHz |
| Hartley Oscillator Frequency | f = 1 / (2π√((L1+L2) · C)) | Inductor L1 100 nH, Inductor L2 0.22 µH, Tank Capacitor 100 pF → Frequency = 28.13 MHz |
| Clapp Oscillator Frequency | f = 1/(2π√(L·Cs)), 1/Cs = 1/C1+1/C2+1/C3 | Inductance 100 nH, Capacitor C1 100 pF, Capacitor C2 0.22 nF, Capacitor C3 0.47 nF → Frequency = 64.99 MHz |
| DDS Output Frequency | fout = M · fclk / 2ᴺ | Tuning Word 0.025, Clock Frequency 100 kHz, Accumulator Bits 0.055 → Output Frequency = 2.406 kHz |
| DDS Frequency Resolution | Δf = fclk / 2ᴺ | Clock Frequency 100 kHz, Accumulator Bits 0.025 → Frequency Step = 98.28 kHz |
Variables used across Timing & Oscillators formulas
- f — Output frequency (Hz)
- R1 — Timing resistor between Vcc and discharge pin (Ω)
- R2 — Timing resistor between discharge and threshold pins (Ω)
- C — Timing capacitor (F)
- t — Output pulse duration (s)
- R — Timing resistor (Ω)
- CL — Effective load capacitance seen by the crystal (F)
- C1 — Load capacitor on one crystal pin (F)
- C2 — Load capacitor on the other crystal pin (F)
- Cstray — Stray capacitance from PCB traces and IC pins (F)
- Δf — Frequency deviation from nominal (Hz)
- f0 — Nominal crystal frequency (Hz)
- ppm — Stability specification in parts per million
- ωn — Loop natural frequency (rad/s)
- ζ — Damping ratio (dimensionless)
- KVCO — VCO tuning sensitivity (Hz/V)
- ΔV — Tuning voltage change (V)
- Tj — RMS timing jitter (s)
- ∫L(f)df — Integrated SSB phase noise power (rad² rms)
- f_max — Maximum achievable clock frequency (Hz)
- t_setup — Setup time required by the receiver (s)
- t_hold — Hold time required by the receiver (s)
- t_prop — Total propagation delay, driver + PCB + receiver (s)
- R_term — Termination resistor value at each bus end (Ω)
- Z₀ — Characteristic impedance of the CAN bus cable (Ω)
- f_out — PLL output frequency (Hz)
- f_ref — Reference oscillator frequency (Hz)
- N — Feedback divider ratio (integer)
- Δl — Maximum trace length difference (m)
- v_p — Propagation velocity (m/s)
- Δt — Maximum allowable timing skew (s)
- bits — PWM duty cycle resolution in bits
- f_clk — Timer clock frequency (Hz)
- f_PWM — PWM output frequency (Hz)
- Rf — Feedback resistor (Ω)
- Rg — Resistor from inverting input to ground (Ω)
- L — Tank inductance (H)
- C1, C2 — The two tank capacitors (F)
- Cs — Series combination C1·C2/(C1+C2)
- L1, L2 — The two inductor sections (H)
- C3 — Series tuning capacitor (F)
- fout — Output frequency (Hz)
- M — Frequency tuning word (integer)
- fclk — Reference clock frequency (Hz)
Questions people ask about Timing & Oscillators
- Crystal load capacitance calculation — Crystal Load Capacitance
- Crystal load capacitance calculator — Crystal Load Capacitance
- Rc oscillator frequency formula — RC Oscillator Frequency
- Vco tuning sensitivity — VCO Tuning Sensitivity
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