時定数 計算ツール
RC/RL過渡応答
Required Parameters
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Quick Answer
The time constant (τ) determines how fast an RC or RL circuit responds to a step change. RC: τ = R×C. RL: τ = L/R. After 5τ, the circuit has settled to 99.3% of its final value.
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RC鏅傚畾鏁癭n
tau = R x C
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| 鏅傞枔 | 鍏呴浕鐜? | 娈嬨倞 |
|---|---|---|
| 1 tau | 63.2% | 36.8% |
| 2 tau | 86.5% | 13.5% |
| 3 tau | 95.0% | 5.0% |
| 4 tau | 98.2% | 1.8% |
| 5 tau | 99.3% | 0.7% |
RL鏅傚畾鏁癭n
tau = L / R
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Design Notes
The time constant connects two fundamental domains: time response and frequency response. A circuit with τ = 1ms has a bandwidth of fc = 1/(2πτ) = 159 Hz. This means slower circuits (larger τ) filter more noise but respond more sluggishly to input changes. In digital design, minimizing parasitic RC (stray capacitance × trace resistance) is critical for achieving fast rise times: t_rise ≈ 2.2τ.
Common Mistakes
- 1
Forgetting that RL and RC time constants have opposite dependencies on R — increasing R makes RC slower but RL faster.
- 2
Assuming the circuit reaches final value after one time constant. One τ only reaches 63.2% — you need 5τ for practical completion.
- 3
Not accounting for source impedance when calculating the time constant of an RC network driven by a non-ideal source.
Engineering Handbox
1. τ = R × C = 10,000 × 47 × 10⁻⁶ = 0.47 seconds 2. Time to 95%: 3τ = 1.41 seconds 3. Time to 99.3%: 5τ = 2.35 seconds 4. Cutoff frequency: fc = 1/(2π × 0.47) = 0.339 Hz
Knowledge Base
時定数（τ）とは？
RC/RL回路が最終値の63.2%に達する時間。RC: τ = R×C、RL: τ = L/R。
完全充電まで何τ必要？
1τ=63.2%、2τ=86.5%、3τ=95%、5τ=99.3%。5τで実用上「完全」とみなします。
充電時の電圧方程式は？
V(t) = V最終 × (1 - e^(-t/τ))（充電）、V(t) = V初期 × e^(-t/τ)（放電）。
カットオフ周波数との関係は？
fc = 1/(2πτ)。時定数が長いほどカットオフ周波数は低くなります。
チャタリング防止での重要性は？
機械スイッチは1〜10msバウンスします。τ=5〜10ms（例：10kΩ+1µF）でチャタリングを除去。
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