📡 信號與系統工具

📡 上升時間（t_r ≈ 2.2·τ）First Order Rise 輸入一階系統時間常數 τ，按 t_r ≈ 2.2τ 估算從 10% 到 90% 的上升時間，用於 RC 電路與控制系統階躍響應的速度評估。First Order Rise - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 📡 二階系統峯值時間計算器Peak Time 2nd 二階系統峯值時間計算器：輸入阻尼比 ζ 與固有頻率 ω_n，求階躍響應達到首個峯值的時間，用於控制系統動態分析。Peak Time 2nd - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 📡 固有頻率（ω_n = √(k/m)）Natural Frequency 2nd 二階系統固有頻率計算器：輸入剛度 k 與質量 m，求 ω_n = √(k/m) 無阻尼固有角頻率，用於振動系統設計。Natural Frequency 2nd - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 📡 基頻（f₀ = 1 / T）Fourier Base 傅里葉級數基頻計算器：輸入週期 T，按 f₀ = 1/T 求週期信號基頻，用於信號頻域分解與諧波分析。Fourier Base - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 📡 增益（G = 20·log₁₀(V_out / V_in)）Gain DB 電壓增益分貝計算器：輸入輸出與輸入電壓，按 G = 20·log₁₀(V_out/V_in) 求放大器或網絡電壓增益（dB）。Gain DB - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 📡 奈奎斯特採樣（f_s ≥ 2·f_max）Nyquist Rate 輸入信號最高頻率 f_max，按 f_s ≥ 2·f_max 計算奈奎斯特最小採樣率，用於 ADC 選型與抗混疊設計，避免採樣重建失真。Nyquist Rate - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 📡 平均電壓（V_avg = D · V_cc）Pwm Average 輸入佔空比 D 與電源電壓 V_cc，按 V_avg = D·V_cc 計算 PWM 經低通濾波後的平均輸出電壓，用於 DAC、調光與電機驅動等效電壓。Pwm Average - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 📡 截止（f_c = 1 / (2π·R·C)）Rc Cutoff −3dB 截止（f_c = 1 / (2π·R·C)）Rc Cutoff - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 📡 時間常數（τ = R·C）RC Time Constant RC 時間常數計算器：輸入電阻 R 與電容 C，求 τ = R·C 決定電路充放電快慢，用於濾波與延時電路設計。RC Time Constant - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 📡 有效值（V_rms = V_pk / √2）Sine Rms 輸入正弦波峯值電壓，按 V_rms = V_pk / √2 計算有效值，用於交流測量、電源設計與功率計算的 RMS 換算。Sine Rms - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 📻 由上下邊帶求載波頻率Carrier Freq 載波頻率計算器：輸入上邊帶與下邊帶頻率，按 f_c = (f_upper + f_lower)/2 求載波頻率，用於調製信號分析。Carrier Freq - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 🎚️ 由兩功率求分貝值DB Power Ratio 功率分貝比值計算器：輸入兩功率 P1、P2，按 10·log₁₀(P1/P2) 求分貝比值，用於功率增益與損耗表達。DB Power Ratio - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 🎚️ 由兩電壓求分貝值DB Voltage Ratio 電壓分貝比值計算器：輸入兩電壓 V1、V2，按 20·log₁₀(V1/V2) 求分貝比值，用於電壓增益與衰減表達。DB Voltage Ratio - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 〰️ 由中心頻率與品質因數求帶寬Bandwidth Q 輸入諧振中心頻率 f0 與品質因數 Q，按 Δf = f0 / Q 計算 −3dB 帶寬，用於濾波器、諧振電路與射頻選頻特性的設計與分析。Bandwidth Q - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 〰️ 由中心頻率與帶寬求品質因數Q Factor 輸入中心頻率 f0 與 −3dB 帶寬 Δf，按 Q=f0/Δf 求品質因數，評估諧振系統選擇性。Q Factor - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 📈 由信號功率與噪聲功率求信噪比Snr DB 輸入信號功率 Ps 與噪聲功率 Pn，按 SNR = 10·log₁₀(Ps/Pn) 計算信噪比（dB），用於通信鏈路質量、音頻與圖像噪聲評估。Snr DB - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 🔀 由各級增益(dB)求總增益Cascade Gain DB 輸入多級（如三級）增益 dB 值，按 G_total(dB) = Σ Gᵢ 求總增益並換算為線性倍率，用於射頻級聯放大器與鏈路預算計算。Cascade Gain DB - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 🕐 由導通時間與週期求佔空比Duty Cycle 輸入導通時間 ton 與週期 T，按 D = ton / T × 100% 計算佔空比，用於 PWM 調光、電機調速與開關電源波形的佔空比參數設計。Duty Cycle - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 0️⃣ 由帶寬與電平數求最大碼率Bit Rate Nyquist 輸入信道帶寬 B 與每符號電平數 M，按 R_max = 2B·log₂(M) 求奈奎斯特最大無碼間串擾碼率，用於通信信道容量估算。Bit Rate Nyquist - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. ⚡ 由有效值與負載求功率Signal Power 輸入電壓有效值 V 與負載電阻 R，按 P = V_rms² / R 計算信號功率，用於匹配網絡、放大器輸出與傳輸線功率損耗估算。Signal Power - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. ⏱️ 由相位差與角頻率差求羣時延Group Delay 輸入相位差 Δφ（度）與角頻率差 Δω（rad/s），求羣時延 τ_g，用於濾波器與系統分析。Group Delay - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 📻 由調製波與載波幅度求調幅指數Mod Index Am 輸入調製波幅度 Am 與載波幅度 Ac，按 m = Am / Ac 計算調幅指數，判斷是否過調製，用於 AM 廣播與包絡調製的設計分析。Mod Index Am - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 📊 由採樣序列求信號能量Energy Discrete 輸入離散採樣序列（空格或逗號分隔），按 E = Σ x[n]² 計算數字信號的總能量，用於 DSP 作業、波形幅度分析與功率估計。Energy Discrete - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 📻 由頻偏與調製頻率求調頻指數Mod Index Fm 輸入最大頻偏 Δf 與調製頻率 fm，按 β = Δf / fm 計算調頻指數，用於 FM 調製深度、帶寬估算與調製方式（窄帶/寬頻）判斷。Mod Index Fm - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 📡 鎖定範圍（Δf = K_v · V_max）Pll Lock Range 輸入壓控振盪器增益 Kv 與控制電壓範圍，按 Δf = Kv·V_max 計算 PLL 鎖定（頻率牽引）範圍，用於鎖相環捕獲帶寬設計。Pll Lock Range - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 📡 階躍穩態誤差（e_ss = 1 / (1 + K_p)）Steady State Error 輸入比例增益 Kp，按 e_ss = 1/(1+Kp) 計算 0 型單位反饋系統在單位階躍輸入下的穩態誤差，用於控制系統精度分析。Steady State Error - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 📡 阻尼比（ζ = c / (2√(k·m))）Damping Ratio 二階系統阻尼比計算器：輸入阻尼係數 c、剛度 k 與質量 m，求 ζ = c/(2√(k·m))，判定系統欠阻尼、臨界阻尼或過阻尼。Damping Ratio - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 📡 頻率分辨率（Δf = f_s / N）Fft Resolution 輸入採樣率與 FFT 點數 N，按 Δf = fs / N 計算頻率分辨率，用於頻譜分析中判斷可分辨的最小頻率間隔與窗長設置。Fft Resolution - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools.