📡 信号与系统工具

📡 上升时间（t_r ≈ 2.2·τ）First Order Rise 输入一阶系统时间常数 τ，按 t_r ≈ 2.2τ 估算从 10% 到 90% 的上升时间，用于 RC 电路与控制系统阶跃响应的速度评估。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. 📡 二阶系统峰值时间计算器Peak Time 2nd 二阶系统峰值时间计算器：输入阻尼比 ζ 与固有频率 ω_n，求阶跃响应达到首个峰值的时间，用于控制系统动态分析。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. 📡 固有频率（ω_n = √(k/m)）Natural Frequency 2nd 二阶系统固有频率计算器：输入刚度 k 与质量 m，求 ω_n = √(k/m) 无阻尼固有角频率，用于振动系统设计。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. 📡 基频（f₀ = 1 / T）Fourier Base 傅里叶级数基频计算器：输入周期 T，按 f₀ = 1/T 求周期信号基频，用于信号频域分解与谐波分析。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 电压增益分贝计算器：输入输出与输入电压，按 G = 20·log₁₀(V_out/V_in) 求放大器或网络电压增益（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. 📡 奈奎斯特采样（f_s ≥ 2·f_max）Nyquist Rate 输入信号最高频率 f_max，按 f_s ≥ 2·f_max 计算奈奎斯特最小采样率，用于 ADC 选型与抗混叠设计，避免采样重建失真。Nyquist Rate - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 📡 平均电压（V_avg = D · V_cc）Pwm Average 输入占空比 D 与电源电压 V_cc，按 V_avg = D·V_cc 计算 PWM 经低通滤波后的平均输出电压，用于 DAC、调光与电机驱动等效电压。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. 📡 时间常数（τ = R·C）RC Time Constant RC 时间常数计算器：输入电阻 R 与电容 C，求 τ = R·C 决定电路充放电快慢，用于滤波与延时电路设计。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 输入正弦波峰值电压，按 V_rms = V_pk / √2 计算有效值，用于交流测量、电源设计与功率计算的 RMS 换算。Sine Rms - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 📻 由上下边带求载波频率Carrier Freq 载波频率计算器：输入上边带与下边带频率，按 f_c = (f_upper + f_lower)/2 求载波频率，用于调制信号分析。Carrier Freq - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 🎚️ 由两功率求分贝值DB Power Ratio 功率分贝比值计算器：输入两功率 P1、P2，按 10·log₁₀(P1/P2) 求分贝比值，用于功率增益与损耗表达。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. 🎚️ 由两电压求分贝值DB Voltage Ratio 电压分贝比值计算器：输入两电压 V1、V2，按 20·log₁₀(V1/V2) 求分贝比值，用于电压增益与衰减表达。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. 〰️ 由中心频率与品质因数求带宽Bandwidth Q 输入谐振中心频率 f0 与品质因数 Q，按 Δf = f0 / Q 计算 −3dB 带宽，用于滤波器、谐振电路与射频选频特性的设计与分析。Bandwidth Q - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 〰️ 由中心频率与带宽求品质因数Q Factor 输入中心频率 f0 与 −3dB 带宽 Δf，按 Q=f0/Δf 求品质因数，评估谐振系统选择性。Q Factor - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 📈 由信号功率与噪声功率求信噪比Snr DB 输入信号功率 Ps 与噪声功率 Pn，按 SNR = 10·log₁₀(Ps/Pn) 计算信噪比（dB），用于通信链路质量、音频与图像噪声评估。Snr DB - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 🔀 由各级增益(dB)求总增益Cascade Gain DB 输入多级（如三级）增益 dB 值，按 G_total(dB) = Σ Gᵢ 求总增益并换算为线性倍率，用于射频级联放大器与链路预算计算。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. 🕐 由导通时间与周期求占空比Duty Cycle 输入导通时间 ton 与周期 T，按 D = ton / T × 100% 计算占空比，用于 PWM 调光、电机调速与开关电源波形的占空比参数设计。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 由带宽与电平数求最大码率Bit Rate Nyquist 输入信道带宽 B 与每符号电平数 M，按 R_max = 2B·log₂(M) 求奈奎斯特最大无码间串扰码率，用于通信信道容量估算。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. ⚡ 由有效值与负载求功率Signal Power 输入电压有效值 V 与负载电阻 R，按 P = V_rms² / R 计算信号功率，用于匹配网络、放大器输出与传输线功率损耗估算。Signal Power - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. ⏱️ 由相位差与角频率差求群时延Group Delay 输入相位差 Δφ（度）与角频率差 Δω（rad/s），求群时延 τ_g，用于滤波器与系统分析。Group Delay - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 📻 由调制波与载波幅度求调幅指数Mod Index Am 输入调制波幅度 Am 与载波幅度 Ac，按 m = Am / Ac 计算调幅指数，判断是否过调制，用于 AM 广播与包络调制的设计分析。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. 📊 由采样序列求信号能量Energy Discrete 输入离散采样序列（空格或逗号分隔），按 E = Σ x[n]² 计算数字信号的总能量，用于 DSP 作业、波形幅度分析与功率估计。Energy Discrete - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 📻 由频偏与调制频率求调频指数Mod Index Fm 输入最大频偏 Δf 与调制频率 fm，按 β = Δf / fm 计算调频指数，用于 FM 调制深度、带宽估算与调制方式（窄带/宽带）判断。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. 📡 锁定范围（Δf = K_v · V_max）Pll Lock Range 输入压控振荡器增益 Kv 与控制电压范围，按 Δf = Kv·V_max 计算 PLL 锁定（频率牵引）范围，用于锁相环捕获带宽设计。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. 📡 阶跃稳态误差（e_ss = 1 / (1 + K_p)）Steady State Error 输入比例增益 Kp，按 e_ss = 1/(1+Kp) 计算 0 型单位反馈系统在单位阶跃输入下的稳态误差，用于控制系统精度分析。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 二阶系统阻尼比计算器：输入阻尼系数 c、刚度 k 与质量 m，求 ζ = c/(2√(k·m))，判定系统欠阻尼、临界阻尼或过阻尼。Damping Ratio - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools. 📡 频率分辨率（Δf = f_s / N）Fft Resolution 输入采样率与 FFT 点数 N，按 Δf = fs / N 计算频率分辨率，用于频谱分析中判断可分辨的最小频率间隔与窗长设置。Fft Resolution - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Signals & Systems tools.