numapplied.com

Category: Calculators

  • Boolean Algebra Circuits tool

    Boolean_Algebra_Simulator

    Numerically Applied – Boolean_Algebra_Simulator

    How it works: Select number of inputs (A–E). Add columns (layers) → add/edit/delete gates inside columns. Each gate wires to any previous-layer signal via dropdown. Gates in same column are parallel (no intra-column wiring). Select any signal as F. Truth table always evaluates correctly from gate types + connections. Expressions update on edit; use “Rebuild Expressions” after changing upstream gates. Final output shows both symbolic and traditional Boolean algebra form ( * = AND, + = OR, ! = NOT ).

    Build your circuit, edit gates as needed, select output F, then Generate Truth Table.

    All data stored internally as CSV-ready structures. Export downloads .txt with expression (symbolic + algebraic) + truth table CSV.

  • Circuits 1 Calculator

    circuits_equation_calculator.html

    Numerically Applied

    circuits_equation_calculator.html

    Enter values in consistent SI units. Calculations auto-log to CSV (persisted in browser).

    Basic Circuit Laws

    1. Ohm’s Law — V = IR

    Solves for any one variable when the other two are known. Fundamental starting equation.

    2. Power in Resistor — P = VI / I²R / V²R

    Computes power using any available pair. Derived from Ohm’s law substitutions.

    Inductors & Capacitors — Basic Relations

    3. Inductor Voltage — v = L di/dt

    Voltage induced by changing current. Provide numeric di/dt at the instant of interest.

    4. Capacitor Current — i = C dv/dt

    Current due to changing voltage across capacitor.

    5. Energy in Inductor — w_L = ½ L I²

    Magnetic energy stored. Often used with i_L(0) initial condition.

    6. Energy in Capacitor — w_C = ½ C V²

    Electric energy stored. Dual of inductor energy.

    First-Order RC & RL Circuits — Natural & Step Responses

    7. RC Time Constant — τ = RC

    Governs speed of exponential transients in RC circuits.

    8. RL Time Constant — τ = L/R

    Governs speed of exponential transients in RL circuits.

    9. RC Natural Response — v(t) = V₀ e^(-t/τ)

    Source-free capacitor voltage decay (t ≥ 0). Vss = 0. Find V₀ from DC analysis at t=0−. Matches source sheet algorithm.

    10. RC Step Response — v(t) = Vss + (V₀ − Vss) e^(-t/τ)

    Complete response when DC source is applied. Find Vss (t→∞, cap open) and V₀ (t=0−) first per PDF 5-step method.

    11. RL Natural Response — i(t) = I₀ e^(-(R/L)t)

    Source-free inductor current decay. I₀ from t=0− (inductor current continuous).

    12. RL Step Response — i(t) = Iss + (I₀ − Iss) e^(-(R/L)t)

    Complete response for RL circuit with DC source. Iss found with inductor as short-circuit (t→∞).

    Second-Order RLC Circuits — Parameters & Transient Response Forms

    13. RLC Parameters — α, ω₀, Damping Type, Roots / ωd

    First step for any RLC analysis. Computes Neper frequency α and resonant frequency ω₀. Classifies overdamped / critically damped / underdamped and gives s1,s2 or ωd. Use exact formulas from source sheet step 5.

    14. Overdamped RLC Response — r(t) = rss + A₁e^{s₁t} + A₂e^{s₂t}

    For α > ω₀. Supply A1/A2 (solved from initial conditions i_L(0), v_C(0) per PDF) and s1/s2 from Parameters calculator. rss usually 0 for natural response.

    15. Critically Damped RLC Response — r(t) = rss + (A₁ + A₂ t) e^{-α t}

    For α = ω₀ (repeated root). Form includes linear t multiplier. Obtain α from Parameters calculator.

    16. Underdamped RLC Response — r(t) = rss + e^{-αt} (A₁ cos(ωd t) + A₂ sin(ωd t))

    For α < ω₀ (ringing case). Most common. Supply ωd and α from Parameters calculator. A1/A2 from initial conditions.

    Calculation Log — CSV Data Store

    Every successful calculation is automatically recorded here and saved in browser localStorage (persists across refreshes). Data is stored internally as a CSV structure. Use Export to download as .txt file (CSV content).

    Timestamp Equation Inputs Result
    Standalone HTML • Dark theme #212121 • Green accents #22c55e • No rounded corners • Data export .txt (CSV)