PRISMORA✦
v0.1
Launch
Next-Generation Open Source Scientific Simulation & Virtual Labs
Designed & Engineered withbyAmit Singh

Explore. Experiment. Understand.

Step into verified physical apparatus, discrete micro-logic gates, RISC-V pipelined processors, and formal automata theory. Every experiment is driven by analytical closed-form equations and real-time matrix solvers.

16 Working Interactive Labs
11 Academic Disciplines
100% Client-Side Solvers
Featured Laboratory Spotlight
t: 0.00s•x: 0.0m•y: 0.0m•|v|: 22.0m/s
Speed (v₀)22 m/s
Angle (θ)50°
Gravity Field9.81 m/s²
Flagship Classical Mechanics

Analytical Projectile Motion

Investigate 2D kinematic trajectory equations with articulated drag-to-aim launcher, variable celestial gravity (Earth, Moon, Mars, Zero-G), target hit reticle, and calibrated sensor probes.

Governing Trajectory Closed-Form:y(t) = y₀ + v₀·sin(θ)·t - ½·g·t²
GRAVITY PRESETSEarth, Moon, Mars
PRECISIONZero Numerical Drift
Level: Introductory

Scientific & Engineering Disciplines

Explore verified physical models, digital micro-logic, pipelined CPU architectures, and formal automata theory.

View All Hubs
Online

Civil Engineering

Bridge Truss Statics & Stress

Enter Workspace
Online

Robotics & Automation

Planar Arm DH Kinematics

Enter Workspace
Online

Chemical Engineering

McCabe-Thiele Distillation

Enter Workspace
Online

Biotechnology

Michaelis-Menten Kinetics

Enter Workspace
Online

Physics

Kinematics & Celestial Gravity

Enter Workspace
Online

Digital Electronics

Gates, K-Maps & 4-Bit Adders

Enter Workspace
Online

Computer Architecture

RV32I 5-Stage Datapath

Enter Workspace
Online

Theory of Computation

DFA/NFA, CYK & Turing

Enter Workspace

Verified Interactive Laboratories

Fully functional browser simulations with real-time vector graphics, live instruments, and interactive parameters.

161 Labs Online
y (m)x (m)157.5h_max: 15.3mR: 61.2m45°vANALYTICAL 2D
MechanicsAvailable
x(t)=v0cos⁡(θ)tx(t) = v_0 \cos(\theta) t
Difficulty: Introductory6 tools

Ideal Projectile Motion

Scientifically validated kinematic trajectory model with articulated launcher, direct elevation drag, variable celestial gravity (Earth, Moon, Mars, Zero-G), target hit detection, data probe, and measurement tape.

Model:x(t)=v0cos⁡(θ)tx(t) = v_0 \cos(\theta) t
A:1B:0XORSUM = 1ANDCARRY = 0ABSC0000011010101101CLKSUM
Logic Gates and Boolean AlgebraAvailable
F=∑m(m0,m1,...)F = \sum m(m_0, m_1, ...)
Difficulty: Intermediate5 tools

Digital Electronics & Logic Design Workbench

Scientifically verified discrete logic laboratory featuring 7 primitive gates, interactive truth tables, Quine-McCluskey K-map minimization, 4-bit ripple adders and ALUs, sequential flip-flops (SR, JK, D, T), synchronous counters, and static 1-hazard waveforms.

Model:F=∑m(m0,m1,...)F = \sum m(m_0, m_1, ...)
RV32I RISC-V COREPC: 0x0040 • CPI: 1.14FORWARDINGIFI-CachePC+4FetchIDRegFilex1, x2ImmGenEXALUADDMEMD-CacheL1 ReadAddr/DataWBRegWritex3 <= RdRAW Forwarding Bypassx10 (a0): 0x0000002Ax1 (ra): 0x00400010x2 (sp): 0x7FFF0000Instr: add a0, a0, t0 • Opcode: 0x33 • Funct3: 0x0
CPU DatapathAvailable
CPI=Total Clock CyclesInstructions ExecutedCPI = \frac{\text{Total Clock Cycles}}{\text{Instructions Executed}}
Difficulty: Advanced6 tools

Computer Organization & Architecture (RV32I)

RISC-V 32-bit (RV32I) microarchitecture workbench with live Harvard single-cycle datapath, 5-stage classic pipeline (IF/ID/EX/MEM/WB), RAW load-use hazard bubble stall detection, forwarding unit, 32-register ABI inspection, and configurable L1 cache simulator.

Model:CPI=Total Clock CyclesInstructions ExecutedCPI = \frac{\text{Total Clock Cycles}}{\text{Instructions Executed}}
STARTq₀'a'q₁'b''a'q₂*'b'abbaaHEADL = { w | w ends with 'aa' }
DFA and NFAAvailable
M=(Q,Σ,δ,q0,F)M = (Q, \Sigma, \delta, q_0, F)
Difficulty: Advanced6 tools

Theory of Computation & Automata Studio

Formal language systems featuring interactive 5-tuple DFA and NFA execution with string stepping, powerset subset construction with state reachability pruning, Hopcroft O(n log n) DFA minimization, Thompson regex epsilon-NFA compiler, O(n³) CYK triangular parser, and 7-tuple deterministic Turing machine on bidirectional tape.

Model:M=(Q,Σ,δ,q0,F)M = (Q, \Sigma, \delta, q_0, F)
THÉVENIN REDUCTION & MAX POWERVthRthRLRLPLRL = Rthη = 50%Voc = Vth • In = Vth/Rth • P_max = Vth²/(4Rth)
Circuit Analysis and Network TheoremsAvailable
Vth=Voc=V1R1+V2R21R1+1R2+1R3V_{th} = V_{oc} = \frac{\frac{V_1}{R_1} + \frac{V_2}{R_2}}{\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}}
Difficulty: Intermediate4 tools

Network Theorems Lab: Thévenin, Norton & Maximum Power

Scientifically verified circuit reduction workbench. Compute open-circuit voltage Voc = Vth, internal de-energized resistance Rin = Rth, Norton current In = Vth/Rth, and swept load resistance dynamic power transfer curve (PL vs RL peak at RL = Rth).

Model:Vth=Voc=V1R1+V2R21R1+1R2+1R3V_{th} = V_{oc} = \frac{\frac{V_1}{R_1} + \frac{V_2}{R_2}}{\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}}
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Electrical Fundamentals and Network AnalysisAvailable
V=I⋅RV = I \cdot R
Difficulty: Intermediate6 tools

ECE Circuit Studio & Virtual Arduino Uno (TinkerCAD + PhET DC/AC)

Interactive electronic circuit designer and embedded hardware studio. Features Lifelike, Schematic, and PCB view modes, AC/DC sources, 4-band resistor color decoder, glowing filaments, spinning DC motors, SG90 servo angle sweep, and a Virtual Arduino Uno R3 ATmega328P C++ execution engine with live Serial Monitor.

Model:V=I⋅RV = I \cdot R
+-Vs: 12VR = 100ΩI = 120mAV-I LINEARITYVISlope = 100Ω
Electrical Fundamentals and Network AnalysisAvailable
V=I⋅RV = I \cdot R
Difficulty: Introductory4 tools

Ohm's Law & DC Electrical Circuits Laboratory

Explore voltage, current, and resistance in DC networks with variable bench power supply, real-time V-I scatter plotting, incandescent bulb filament glow, and digital multimeter probing.

Model:V=I⋅RV = I \cdot R
+-Vs: 12VR = 100ΩI = 120mAV-I LINEARITYVISlope = 100Ω
Electrical Fundamentals and Network AnalysisAvailable
Req=∑i=1nRiR_{eq} = \sum_{i=1}^{n} R_i
Difficulty: Introductory3 tools

Series Resistor Networks & Voltage Division

Equivalent resistance of series-connected resistors, cumulative voltage drop, and proportional voltage division.

Model:Req=∑i=1nRiR_{eq} = \sum_{i=1}^{n} R_i
+-Vs: 12VR = 100ΩI = 120mAV-I LINEARITYVISlope = 100Ω
Electrical Fundamentals and Network AnalysisAvailable
1Req=∑i=1n1Ri\frac{1}{R_{eq}} = \sum_{i=1}^{n} \frac{1}{R_i}
Difficulty: Introductory3 tools

Parallel Resistor Networks & Current Division

Equivalent conductance and current splitting across parallel resistor branches under constant node potential.

Model:1Req=∑i=1n1Ri\frac{1}{R_{eq}} = \sum_{i=1}^{n} \frac{1}{R_i}
+-Vs: 12VR = 100ΩI = 120mAV-I LINEARITYVISlope = 100Ω
Electrical Fundamentals and Network AnalysisAvailable
Difficulty: Introductory3 tools

Series-Parallel Combination Resistor Networks

Reduction of complex resistive bridge networks using successive series and parallel equivalence transformations.

Verified Scientific Model
+-Vs: 12VR = 100ΩI = 120mAV-I LINEARITYVISlope = 100Ω
Electrical Fundamentals and Network AnalysisAvailable
∑k=1nIk=0\sum_{k=1}^{n} I_k = 0
Difficulty: Introductory3 tools

Kirchhoff's Current Law (KCL) Junction Analysis

Conservation of electric charge at electrical circuit nodes where algebraic sum of all currents equals zero.

Model:∑k=1nIk=0\sum_{k=1}^{n} I_k = 0
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Electrical Fundamentals and Network AnalysisAvailable
∑k=1mVk=0\sum_{k=1}^{m} V_k = 0
Difficulty: Introductory3 tools

Kirchhoff's Voltage Law (KVL) Closed Loop Analysis

Conservation of energy along any closed loop in a circuit, confirming total potential rise equals total potential drop.

Model:∑k=1mVk=0\sum_{k=1}^{m} V_k = 0
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Electrical Fundamentals and Network AnalysisAvailable
Difficulty: Introductory3 tools

Voltage Divider Circuits & Potentiometer Loading

Loaded vs unloaded voltage dividers, potentiometer wiper control, and finite input impedance loading effects.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Electrical Fundamentals and Network AnalysisAvailable
Difficulty: Introductory2 tools

Current Divider Circuits & Shunt Resistors

Current division between parallel branches and design of ammeter shunt resistors for range extension.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Electrical Fundamentals and Network AnalysisAvailable
P=V⋅I=I2R=V2RP = V \cdot I = I^2 R = \frac{V^2}{R}
Difficulty: Introductory3 tools

Electrical Power, Energy Dissipation & Joule Heating

Power dissipation in resistors, Joules law thermal heating, kilowatt-hour accumulation, and component wattage ratings.

Model:P=V⋅I=I2R=V2RP = V \cdot I = I^2 R = \frac{V^2}{R}
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Electrical Fundamentals and Network AnalysisAvailable
Difficulty: Intermediate3 tools

Thevenin's Theorem & Equivalent Circuit Extraction

Transforming any linear bilateral two-terminal resistive network into an equivalent voltage source V_th in series with R_th.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Electrical Fundamentals and Network AnalysisAvailable
Difficulty: Intermediate3 tools

Norton's Theorem & Dual Current Equivalent

Reduction of two-terminal linear circuits to a single Norton current source I_N in parallel with Norton resistance R_N.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Electrical Fundamentals and Network AnalysisAvailable
Difficulty: Intermediate3 tools

Superposition Theorem in Multi-Source DC Networks

Analyzing linear circuits with multiple independent voltage and current sources by summing individual responses.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Electrical Fundamentals and Network AnalysisAvailable
Pmax=Vth24Rth(when RL=Rth)P_{max} = \frac{V_{th}^2}{4 R_{th}} \quad (\text{when } R_L = R_{th})
Difficulty: Intermediate3 tools

Maximum Power Transfer Theorem in DC Circuits

Condition for maximum power transfer from source to load (R_L = R_th) and efficiency vs power trade-off.

Model:Pmax=Vth24Rth(when RL=Rth)P_{max} = \frac{V_{th}^2}{4 R_{th}} \quad (\text{when } R_L = R_{th})
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Electrical Fundamentals and Network AnalysisAvailable
Difficulty: Intermediate2 tools

Source Transformation (Thevenin to Norton Dual)

Equivalence between practical voltage source (V_s in series with R_s) and practical current source (I_s in parallel with R_s).

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Electrical Fundamentals and Network AnalysisAvailable
Difficulty: Intermediate3 tools

Mesh Current Analysis & Planar Loop Equations

Formulating and solving matrix equations for planar circuits using fictitious circulating mesh currents.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Electrical Fundamentals and Network AnalysisAvailable
Difficulty: Intermediate2 tools

Nodal Voltage Analysis & Conductance Matrix

Modified Nodal Analysis (MNA) using reference ground and node voltages to solve arbitrary circuit graphs.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Electrical Fundamentals and Network AnalysisAvailable
Rx=R3⋅R2R1R_x = R_3 \cdot \frac{R_2}{R_1}
Difficulty: Intermediate3 tools

Wheatstone Bridge & Precision Resistance Measurement

Null-deflection measurement of unknown resistors using balanced four-arm bridge topology.

Model:Rx=R3⋅R2R1R_x = R_3 \cdot \frac{R_2}{R_1}
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Electrical Fundamentals and Network AnalysisAvailable
Difficulty: Intermediate2 tools

Delta-Wye (Pi-T) Network Transformation

Transformation between 3-terminal Delta (triangle) and Star (Y) resistor topologies to simplify non-bridge networks.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Electrical Fundamentals and Network AnalysisAvailable
Z=R+j(ωL−1ωC)Z = R + j(\omega L - \frac{1}{\omega C})
Difficulty: Intermediate3 tools

AC Impedance, Phasors & Complex Reactance

Complex impedance Z = R + jX, inductive reactance X_L = 2pi*f*L, capacitive reactance X_C = 1/(2pi*f*C), and rotating phasors.

Model:Z=R+j(ωL−1ωC)Z = R + j(\omega L - \frac{1}{\omega C})
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Electrical Fundamentals and Network AnalysisAvailable
Difficulty: Intermediate3 tools

AC Power, Power Factor & Reactive Compensation

Active power (P), reactive power (Q), apparent power (S), power factor (cos phi), and capacitor power factor correction.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Electrical Fundamentals and Network AnalysisAvailable
f0=12πLCf_0 = \frac{1}{2\pi \sqrt{LC}}
Difficulty: Intermediate3 tools

Series & Parallel RLC Resonance (Q-Factor & Bandwidth)

Resonant frequency f_0 = 1/(2pi*sqrt(LC)), impedance minimum/maximum, quality factor Q, and -3dB half-power bandwidth.

Model:f0=12πLCf_0 = \frac{1}{2\pi \sqrt{LC}}
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Electrical Fundamentals and Network AnalysisAvailable
vC(t)=Vs(1−e−t/RC)v_C(t) = V_s (1 - e^{-t / RC})
Difficulty: Introductory3 tools

RC Circuit Transient Charging & Discharging Response

First-order transient exponential charging and discharging curves with time constant tau = R*C and step response.

Model:vC(t)=Vs(1−e−t/RC)v_C(t) = V_s (1 - e^{-t / RC})
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Electrical Fundamentals and Network AnalysisAvailable
Difficulty: Intermediate3 tools

RL Circuit Transient Inductor Current Response

Inductor current continuity, back-EMF spikes during disconnection, and exponential settling with time constant tau = L/R.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Electrical Fundamentals and Network AnalysisAvailable
s1,2=−α±α2−ω02s_{1,2} = -\alpha \pm \sqrt{\alpha^2 - \omega_0^2}
Difficulty: Advanced3 tools

RLC Transient Damping (Overdamped, Critical, Underdamped)

Second-order differential equation response with variable damping ratio zeta: underdamped oscillations, critical damping, and overdamped decay.

Model:s1,2=−α±α2−ω02s_{1,2} = -\alpha \pm \sqrt{\alpha^2 - \omega_0^2}
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Electrical Fundamentals and Network AnalysisAvailable
Difficulty: Introductory2 tools

Practical Voltage and Current Measurements (Meter Loading)

Internal resistance of practical voltmeters and ammeters, insertion errors, and measurement correction factors.

Verified Scientific Model
PN JUNCTION ENERGY BAND DIAGRAMEfEcEv
Basic Electronics and Semiconductor DevicesAvailable
ID=Is(eVDηVT−1)I_D = I_s \left( e^{\frac{V_D}{\eta V_T}} - 1 \right)
Difficulty: Introductory4 tools

PN-Junction Diode I-V Characteristics & Knee Voltage

Forward and reverse DC bias characteristics of Silicon and Germanium diodes, Shockley equation modeling, knee voltage (0.7V / 0.3V), and dynamic resistance.

Model:ID=Is(eVDηVT−1)I_D = I_s \left( e^{\frac{V_D}{\eta V_T}} - 1 \right)
PN JUNCTION ENERGY BAND DIAGRAMEfEcEv
Basic Electronics and Semiconductor DevicesAvailable
Difficulty: Introductory2 tools

Forward and Reverse Diode Bias Dynamics

Depletion region width modulation, majority carrier diffusion under forward bias, and drift current saturation under reverse bias.

Verified Scientific Model
Vin 12VACVd: 0.7VC=470µFRL=1kΩCH1: Vin ACCH2: Vdc
Basic Electronics and Semiconductor DevicesAvailable
Vdc=Vm−VFπV_{dc} = \frac{V_m - V_F}{\pi}
Difficulty: Introductory3 tools

Half-Wave Rectifier Circuit with Dual-Trace Scope

AC to DC conversion using single-diode half-wave rectifier, peak output voltage, DC average calculation, and dual-channel waveform observation.

Model:Vdc=Vm−VFπV_{dc} = \frac{V_m - V_F}{\pi}
PN JUNCTION ENERGY BAND DIAGRAMEfEcEv
Basic Electronics and Semiconductor DevicesAvailable
Vdc=2(Vm−VF)πV_{dc} = \frac{2(V_m - V_F)}{\pi}
Difficulty: Intermediate2 tools

Full-Wave Center-Tapped Transformer Rectifier

Two-diode full-wave rectifier using center-tapped secondary winding, producing 2*f_in ripple frequency and higher DC efficiency.

Model:Vdc=2(Vm−VF)πV_{dc} = \frac{2(V_m - V_F)}{\pi}
PN JUNCTION ENERGY BAND DIAGRAMEfEcEv
Basic Electronics and Semiconductor DevicesAvailable
Vdc=2(Vm−2VF)πV_{dc} = \frac{2(V_m - 2V_F)}{\pi}
Difficulty: Intermediate3 tools

Full-Wave Bridge Rectifier (4-Diode Diamond Topology)

Four-diode bridge rectifier delivering full-wave DC output without center-tapped transformer, 2*V_F forward drop, and PIV = V_m.

Model:Vdc=2(Vm−2VF)πV_{dc} = \frac{2(V_m - 2V_F)}{\pi}
PN JUNCTION ENERGY BAND DIAGRAMEfEcEv
Basic Electronics and Semiconductor DevicesAvailable
Vr(pp)=Vmf⋅RL⋅CV_{r(pp)} = \frac{V_m}{f \cdot R_L \cdot C}
Difficulty: Intermediate3 tools

Capacitor-Filtered Rectifier & DC Smoothing

Shunt capacitor filter across rectifier load, ripple voltage reduction, conduction angle narrowing, and surge current spikes.

Model:Vr(pp)=Vmf⋅RL⋅CV_{r(pp)} = \frac{V_m}{f \cdot R_L \cdot C}
PN JUNCTION ENERGY BAND DIAGRAMEfEcEv
Basic Electronics and Semiconductor DevicesAvailable
Difficulty: Intermediate2 tools

Ripple Factor & Rectification Efficiency Analysis

Systematic comparison of unfiltered vs LC vs Pi-filter networks on DC power supply quality.

Verified Scientific Model
PN JUNCTION ENERGY BAND DIAGRAMEfEcEv
Basic Electronics and Semiconductor DevicesAvailable
Vout=VZV_{out} = V_Z
Difficulty: Intermediate3 tools

Zener Diode Voltage Regulation & Line/Load Regulation

Zener reverse breakdown voltage clamping, series current-limiting resistor design, line regulation, and load regulation limits.

Model:Vout=VZV_{out} = V_Z
PN JUNCTION ENERGY BAND DIAGRAMEfEcEv
Basic Electronics and Semiconductor DevicesAvailable
Difficulty: Intermediate3 tools

Diode Clipper Circuits (Positive, Negative, Biased Shunt)

Waveform shaping using series and shunt diode clippers with DC reference bias voltages to truncate voltage peaks.

Verified Scientific Model
PN JUNCTION ENERGY BAND DIAGRAMEfEcEv
Basic Electronics and Semiconductor DevicesAvailable
Difficulty: Intermediate2 tools

Diode Clamping Circuits (DC Level Restorers)

Capacitor-diode clamping networks that shift AC signals to a new positive or negative DC reference level without altering peak-to-peak amplitude.

Verified Scientific Model
PN JUNCTION ENERGY BAND DIAGRAMEfEcEv
Basic Electronics and Semiconductor DevicesAvailable
Rseries=VCC−VFIFR_{series} = \frac{V_{CC} - V_F}{I_F}
Difficulty: Introductory3 tools

Light Emitting Diode (LED) Current Limiting & Efficiency

Forward voltage drop across various LED colors (Red, Green, Blue, White), luminous intensity, and series ballast resistor calculation.

Model:Rseries=VCC−VFIFR_{series} = \frac{V_{CC} - V_F}{I_F}
PN JUNCTION ENERGY BAND DIAGRAMEfEcEv
Basic Electronics and Semiconductor DevicesAvailable
Difficulty: Intermediate2 tools

BJT Common-Emitter Input Characteristics (I_B vs V_BE)

NPN Bipolar Junction Transistor base-emitter junction input family curves with collector-emitter voltage parameter V_CE.

Verified Scientific Model
PN JUNCTION ENERGY BAND DIAGRAMEfEcEv
Basic Electronics and Semiconductor DevicesAvailable
IC=βIB+ICEOI_C = \beta I_B + I_{CEO}
Difficulty: Intermediate2 tools

BJT Common-Emitter Output Characteristics (I_C vs V_CE)

Collector characteristic curves with base current parameter I_B, highlighting Cutoff, Active, and Saturation regions.

Model:IC=βIB+ICEOI_C = \beta I_B + I_{CEO}
PN JUNCTION ENERGY BAND DIAGRAMEfEcEv
Basic Electronics and Semiconductor DevicesAvailable
Difficulty: Intermediate2 tools

BJT Operating Regions & DC Load Line Analysis

Q-point biasing, DC load line slope -1/R_C, maximum undistorted output voltage swing, and thermal stability.

Verified Scientific Model
PN JUNCTION ENERGY BAND DIAGRAMEfEcEv
Basic Electronics and Semiconductor DevicesAvailable
Av=−gm(RC∥RL)1+gmREA_v = -\frac{g_m (R_C \parallel R_L)}{1 + g_m R_E}
Difficulty: Intermediate3 tools

BJT Common-Emitter Small-Signal Voltage Amplifier

Voltage gain A_v = -g_m * (R_C || R_L), 180-degree phase inversion, input/output impedance, and emitter bypass capacitor effects.

Model:Av=−gm(RC∥RL)1+gmREA_v = -\frac{g_m (R_C \parallel R_L)}{1 + g_m R_E}
PN JUNCTION ENERGY BAND DIAGRAMEfEcEv
Basic Electronics and Semiconductor DevicesAvailable
Difficulty: Advanced2 tools

BJT Common-Base High-Frequency Amplifier

Unity current gain, non-inverting high voltage gain, low input impedance, and absence of Miller effect for RF amplification.

Verified Scientific Model
PN JUNCTION ENERGY BAND DIAGRAMEfEcEv
Basic Electronics and Semiconductor DevicesAvailable
Difficulty: Intermediate2 tools

BJT Common-Collector (Emitter Follower) Buffer

Unity voltage gain, high input impedance, low output impedance, and impedance matching buffer applications.

Verified Scientific Model
PN JUNCTION ENERGY BAND DIAGRAMEfEcEv
Basic Electronics and Semiconductor DevicesAvailable
Difficulty: Introductory2 tools

BJT Digital Switching & Saturated Inverter

Cutoff to saturation transitions, storage time delay, turn-on/turn-off times, and relay/load driver interfacing.

Verified Scientific Model
PN JUNCTION ENERGY BAND DIAGRAMEfEcEv
Basic Electronics and Semiconductor DevicesAvailable
ID=12μnCoxWL(VGS−Vth)2I_D = \frac{1}{2} \mu_n C_{ox} \frac{W}{L} (V_{GS} - V_{th})^2
Difficulty: Intermediate2 tools

N-Channel MOSFET Drain & Transfer Characteristics

Enhancement-mode MOSFET drain curves (I_D vs V_DS), threshold voltage V_th, transconductance g_m, and pinch-off saturation.

Model:ID=12μnCoxWL(VGS−Vth)2I_D = \frac{1}{2} \mu_n C_{ox} \frac{W}{L} (V_{GS} - V_{th})^2
PN JUNCTION ENERGY BAND DIAGRAMEfEcEv
Basic Electronics and Semiconductor DevicesAvailable
Difficulty: Advanced2 tools

Power MOSFET Fast Switching & Gate Charge Dynamics

Gate capacitance charging, Miller plateau voltage, R_DS(on) conduction losses, and high-side/low-side driver circuits.

Verified Scientific Model
PN JUNCTION ENERGY BAND DIAGRAMEfEcEv
Basic Electronics and Semiconductor DevicesAvailable
NML=VIL−VOLNM_L = V_{IL} - V_{OL}
Difficulty: Intermediate3 tools

CMOS Inverter Transfer Characteristics & Noise Margins

Complementary NMOS and PMOS pair, static power dissipation near zero, voltage transfer characteristic (VTC), and noise margins NM_H/NM_L.

Model:NML=VIL−VOLNM_L = V_{IL} - V_{OL}
PN JUNCTION ENERGY BAND DIAGRAMEfEcEv
Basic Electronics and Semiconductor DevicesAvailable
Pdynamic=CL⋅VDD2⋅fP_{dynamic} = C_L \cdot V_{DD}^2 \cdot f
Difficulty: Advanced2 tools

CMOS Dynamic Switching Power & Parasitic Capacitances

Charging and discharging of load capacitance C_L, dynamic power P = C_L * V_DD^2 * f, and short-circuit crowbar current.

Model:Pdynamic=CL⋅VDD2⋅fP_{dynamic} = C_L \cdot V_{DD}^2 \cdot f
PN JUNCTION ENERGY BAND DIAGRAMEfEcEv
Basic Electronics and Semiconductor DevicesAvailable
Difficulty: Intermediate2 tools

Semiconductor Energy Band Diagrams & Fermi Level

Conduction band, valence band, bandgap energy E_g, intrinsic vs extrinsic doping, and Fermi level positioning.

Verified Scientific Model
PN JUNCTION ENERGY BAND DIAGRAMEfEcEv
Basic Electronics and Semiconductor DevicesAvailable
Vbi=VTln⁡(NANDni2)V_{bi} = V_T \ln\left(\frac{N_A N_D}{n_i^2}\right)
Difficulty: Advanced2 tools

PN-Junction Depletion Region & Built-in Potential

Space charge density distribution, electric field profile, built-in potential barrier V_bi, and junction capacitance.

Model:Vbi=VTln⁡(NANDni2)V_{bi} = V_T \ln\left(\frac{N_A N_D}{n_i^2}\right)
PN JUNCTION ENERGY BAND DIAGRAMEfEcEv
Basic Electronics and Semiconductor DevicesAvailable
Difficulty: Intermediate2 tools

Temperature Effects on Semiconductor Device Parameters

Thermal generation of electron-hole pairs, temperature coefficient of diode forward drop (-2mV/degC), and thermal runaway.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Analog Electronics and Integrated CircuitsAvailable
Av=−RfRinA_v = -\frac{R_f}{R_{in}}
Difficulty: Introductory3 tools

Inverting Operational Amplifier (Gain A_v = -R_f / R_in)

Virtual ground concept, negative feedback stabilization, inverting voltage amplification, and gain-bandwidth trade-offs.

Model:Av=−RfRinA_v = -\frac{R_f}{R_{in}}
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Analog Electronics and Integrated CircuitsAvailable
Av=1+RfR1A_v = 1 + \frac{R_f}{R_1}
Difficulty: Introductory2 tools

Non-Inverting Operational Amplifier (A_v = 1 + R_f / R_1)

High input impedance non-inverting amplification, zero phase shift, and negative feedback gain stabilization.

Model:Av=1+RfR1A_v = 1 + \frac{R_f}{R_1}
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Analog Electronics and Integrated CircuitsAvailable
Difficulty: Introductory2 tools

Op-Amp Voltage Follower (Unity Gain Buffer)

Zero loading buffer circuit with A_v = 1, infinite input impedance, and low output impedance for sensor isolation.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Analog Electronics and Integrated CircuitsAvailable
Vout=−Rf(V1R1+V2R2+V3R3)V_{out} = -R_f \left(\frac{V_1}{R_1} + \frac{V_2}{R_2} + \frac{V_3}{R_3}\right)
Difficulty: Intermediate2 tools

Summing Amplifier (Analog Audio Mixer)

Weighted analog addition of multiple input voltages using inverting summing junction.

Model:Vout=−Rf(V1R1+V2R2+V3R3)V_{out} = -R_f \left(\frac{V_1}{R_1} + \frac{V_2}{R_2} + \frac{V_3}{R_3}\right)
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Analog Electronics and Integrated CircuitsAvailable
CMRR=20log⁡10∣AdAcm∣CMRR = 20 \log_{10}\left|\frac{A_d}{A_{cm}}\right|
Difficulty: Intermediate2 tools

Difference Amplifier & Common-Mode Rejection Ratio (CMRR)

Differential voltage amplification V_out = (R_2/R_1)*(V_2 - V_1) and rejection of common-mode environmental noise.

Model:CMRR=20log⁡10∣AdAcm∣CMRR = 20 \log_{10}\left|\frac{A_d}{A_{cm}}\right|
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Analog Electronics and Integrated CircuitsAvailable
Av=(1+2R1Rgain)R3R2A_v = \left(1 + \frac{2 R_1}{R_{gain}}\right)\frac{R_3}{R_2}
Difficulty: Advanced2 tools

Three Op-Amp Precision Instrumentation Amplifier (In-Amp)

Buffered differential amplifier with single resistor gain adjustment R_gain, ultra-high CMRR, and microvolt-level sensor amplification.

Model:Av=(1+2R1Rgain)R3R2A_v = \left(1 + \frac{2 R_1}{R_{gain}}\right)\frac{R_3}{R_2}
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Analog Electronics and Integrated CircuitsAvailable
Vout(t)=−1RC∫0tVin(τ)dτ+V0V_{out}(t) = -\frac{1}{R C}\int_0^t V_{in}(\tau) d\tau + V_0
Difficulty: Intermediate2 tools

Op-Amp Integrator Circuit (Square to Triangle Converter)

Capacitive feedback integration V_out = -1/(R*C) * integral(V_in dt), frequency response rolloff (-20dB/dec), and DC drift saturation.

Model:Vout(t)=−1RC∫0tVin(τ)dτ+V0V_{out}(t) = -\frac{1}{R C}\int_0^t V_{in}(\tau) d\tau + V_0
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Analog Electronics and Integrated CircuitsAvailable
Vout(t)=−RCdVin(t)dtV_{out}(t) = -R C \frac{d V_{in}(t)}{dt}
Difficulty: Intermediate2 tools

Op-Amp Differentiator Circuit & Noise Suppression

Capacitive input differentiation V_out = -R*C * (dV_in / dt), high-frequency noise sensitivity, and practical series resistor stabilization.

Model:Vout(t)=−RCdVin(t)dtV_{out}(t) = -R C \frac{d V_{in}(t)}{dt}
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Analog Electronics and Integrated CircuitsAvailable
Difficulty: Introductory3 tools

Open-Loop Voltage Comparator & Zero-Crossing Detector

Open-loop high gain switching, rail-to-rail saturation, reference voltage thresholding, and zero-crossing detection.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Analog Electronics and Integrated CircuitsAvailable
VUTP=Vsat+R1R1+R2V_{UTP} = V_{sat}^+ \frac{R_1}{R_1 + R_2}
Difficulty: Intermediate2 tools

Schmitt Trigger (Inverting & Non-Inverting with Hysteresis)

Positive feedback comparator creating upper (V_UTP) and lower (V_LTP) trigger thresholds, eliminating noise chattering.

Model:VUTP=Vsat+R1R1+R2V_{UTP} = V_{sat}^+ \frac{R_1}{R_1 + R_2}
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Analog Electronics and Integrated CircuitsAvailable
fc=12πR1R2C1C2f_c = \frac{1}{2\pi \sqrt{R_1 R_2 C_1 C_2}}
Difficulty: Intermediate2 tools

Active First-Order & Second-Order Low-Pass Filter (Sallen-Key)

Butterworth low-pass filter response, cutoff frequency f_c = 1/(2pi*R*C), -20dB/-40dB per decade rolloff, and zero passband loading.

Model:fc=12πR1R2C1C2f_c = \frac{1}{2\pi \sqrt{R_1 R_2 C_1 C_2}}
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Analog Electronics and Integrated CircuitsAvailable
Difficulty: Intermediate2 tools

Active High-Pass Filter (First & Second Order)

Active HPF topology passing high frequencies while attenuating DC and low-frequency hum.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Analog Electronics and Integrated CircuitsAvailable
Difficulty: Advanced2 tools

Active Band-Pass Filter (Multiple Feedback Topology)

Center frequency f_0, bandwidth B, and quality factor Q selection for selective audio and radio frequency tuning.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Analog Electronics and Integrated CircuitsAvailable
Difficulty: Advanced2 tools

Active Twin-T Notch Filter (Hum Eliminator)

Deep attenuation notch at 50Hz/60Hz to eliminate interference while preserving adjacent signal harmonics.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Analog Electronics and Integrated CircuitsAvailable
f0=12πRC6f_0 = \frac{1}{2\pi R C \sqrt{6}}
Difficulty: Advanced3 tools

RC Phase-Shift Oscillator (Sinusoidal Wave Generator)

Barkhausen criterion, 3-stage RC feedback ladder each providing 60-degree phase shift (total 180 deg), and inverting amplifier gain A_v >= 29.

Model:f0=12πRC6f_0 = \frac{1}{2\pi R C \sqrt{6}}
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Analog Electronics and Integrated CircuitsAvailable
f0=12πRCf_0 = \frac{1}{2\pi R C}
Difficulty: Advanced3 tools

Wien-Bridge Oscillator with Non-Linear Amplitude Stabilization

Lead-lag network providing zero phase shift at f_0 = 1/(2pi*R*C), required gain A_v = 3, and automatic gain control (AGC) lamp/diode stabilization.

Model:f0=12πRCf_0 = \frac{1}{2\pi R C}
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Analog Electronics and Integrated CircuitsAvailable
Difficulty: Advanced2 tools

LC Tank Oscillators (Colpitts & Hartley RF Generators)

High-frequency LC resonant tank circuits, capacitive tapped divider (Colpitts) vs inductive tapped divider (Hartley) feedback.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Analog Electronics and Integrated CircuitsAvailable
GBWP=AOL⋅fb=ACL⋅fCLGBWP = A_{OL} \cdot f_b = A_{CL} \cdot f_{CL}
Difficulty: Intermediate2 tools

Op-Amp Open-Loop & Closed-Loop Frequency Response

Internal compensation dominant pole, unity-gain bandwidth product (GBWP), open-loop gain rolloff, and closed-loop bandwidth expansion.

Model:GBWP=AOL⋅fb=ACL⋅fCLGBWP = A_{OL} \cdot f_b = A_{CL} \cdot f_{CL}
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Analog Electronics and Integrated CircuitsAvailable
SR=dVoutdt∣maxSR = \left.\frac{dV_{out}}{dt}\right|_{max}
Difficulty: Advanced2 tools

Op-Amp Slew Rate & Large-Signal Distortion

Internal compensation capacitor charging rate limit SR = dV/dt, triangular distortion of high-frequency sine waves, and full-power bandwidth.

Model:SR=dVoutdt∣maxSR = \left.\frac{dV_{out}}{dt}\right|_{max}
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Analog Electronics and Integrated CircuitsAvailable
Difficulty: Advanced2 tools

Negative Feedback Stability, Phase Margin & Nyquist Criterion

Loop gain T = A*beta, gain margin, phase margin, Barkhausen instability, and capacitive load compensation.

Verified Scientific Model
A:1B:0XORSUM = 1ANDCARRY = 0ABSC0000011010101101CLKSUM
Digital Electronics and Logic DesignAvailable
Difficulty: Introductory3 tools

Discrete Logic Gates Explorer (AND, OR, NOT, XOR, NAND, NOR, XNOR)

Interactive discrete logic gates, truth table evaluation, toggle switch inputs, output LEDs, and Boolean algebraic identity proofs.

Verified Scientific Model
A:1B:0XORSUM = 1ANDCARRY = 0ABSC0000011010101101CLKSUM
Digital Electronics and Logic DesignAvailable
Difficulty: Introductory2 tools

Universal Gate Realization (NAND & NOR Completeness)

Construct NOT, AND, OR, and XOR functions exclusively using universal NAND or NOR gate topologies.

Verified Scientific Model
A=1B=1Cin=0XORANDXORORSUM = 0CARRY = 1BINARY ADDITION: 1 + 1 + 0 = 10₂ (SUM=0, CARRY=1)
Digital Electronics and Logic DesignAvailable
S=A⊕B⊕CinS = A \oplus B \oplus C_{in}
Difficulty: Introductory4 tools

Half Adder & Full Adder 2D Circuit Laboratory

Interactive 2D circuit editor for binary addition: Half Adder (XOR + AND), Full Adder (2 HAs + OR), automated truth-table verification, and multi-channel logic analysis.

Model:S=A⊕B⊕CinS = A \oplus B \oplus C_{in}
A=1B=1Cin=0XORANDXORORSUM = 0CARRY = 1BINARY ADDITION: 1 + 1 + 0 = 10₂ (SUM=0, CARRY=1)
Digital Electronics and Logic DesignAvailable
D=A⊕B⊕BinD = A \oplus B \oplus B_{in}
Difficulty: Introductory2 tools

Half Subtractor & Full Subtractor Binary Arithmetic

Binary subtraction, Difference bit D = A xor B xor Bin, Borrow bit B_out, and 2s complement equivalence.

Model:D=A⊕B⊕BinD = A \oplus B \oplus B_{in}
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Digital Electronics and Logic DesignAvailable
Difficulty: Introductory2 tools

Multiplexers (MUX 2:1, 4:1, 8:1) & Demultiplexers

Data selection, address line decoding, digital steering, and arbitrary Boolean function implementation using MUX chips.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Digital Electronics and Logic DesignAvailable
Difficulty: Intermediate2 tools

Binary Encoders, Priority Encoders & BCD Decoders

Converting active input lines to binary codes, priority resolution for concurrent inputs, and 3-to-8 line address decoders.

Verified Scientific Model
REFLECTED GRAY CODE SHAFT ENCODERXOR LADDER:G3 = B3 = 1G2 = B3 ⊕ B2 = 1G1 = B2 ⊕ B1 = 0G0 = B1 ⊕ B0 = 1Hamming Distance H = 1
Digital Electronics and Logic DesignAvailable
Difficulty: Introductory2 tools

Binary-to-Gray and Gray-to-Binary Code Converters

Single-bit transition Gray code encoding for rotary shaft encoders, mechanical debounce, and XOR ladder converters.

Verified Scientific Model
4-BIT MAGNITUDE COMPARATOR (7485)A = 1100 (12)B = 1001 (9)74LS854-BIT COMPCASCADEDA > B: 1A = B: 0A < B: 0
Digital Electronics and Logic DesignAvailable
Difficulty: Introductory2 tools

Digital Magnitude Comparators (4-Bit A > B, A = B, A < B)

Bitwise equality and magnitude comparison, cascading multiple 4-bit comparators for 8-bit word evaluation.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Digital Electronics and Logic DesignAvailable
Difficulty: Introductory2 tools

Parity Bit Generators & Error Detection Checkers

Even and odd parity tree synthesis with XOR gate trees, single-bit error detection across transmission channels.

Verified Scientific Model
BISTABLE LATCH & FLIP-FLOP MEMORYR=0NOR 1S=1NOR 2Q = 1 (SET)Q̄ = 0
Digital Electronics and Logic DesignAvailable
Difficulty: Introductory2 tools

SR Latch & Clocked SR Flip-Flop (Race Condition Analysis)

Bistable multivibrator cross-coupled NAND/NOR gates, transparent latch operation, clock gating, and invalid S=1, R=1 state.

Verified Scientific Model
BISTABLE LATCH & FLIP-FLOP MEMORYR=0NOR 1S=1NOR 2Q = 1 (SET)Q̄ = 0
Digital Electronics and Logic DesignAvailable
Difficulty: Introductory2 tools

Edge-Triggered D Flip-Flop & Master-Slave Register

Positive/negative edge triggering, setup time t_su, hold time t_h, and multi-bit data register latching.

Verified Scientific Model
BISTABLE LATCH & FLIP-FLOP MEMORYR=0NOR 1S=1NOR 2Q = 1 (SET)Q̄ = 0
Digital Electronics and Logic DesignAvailable
Difficulty: Intermediate2 tools

JK Flip-Flop & Master-Slave Race-Around Prevention

Elimination of invalid state using feedback to inputs, Toggle mode when J=1, K=1, and Master-Slave isolation.

Verified Scientific Model
BISTABLE LATCH & FLIP-FLOP MEMORYR=0NOR 1S=1NOR 2Q = 1 (SET)Q̄ = 0
Digital Electronics and Logic DesignAvailable
Difficulty: Introductory2 tools

T Flip-Flop & Binary Frequency Dividers

Toggle flip-flop, binary ripple counting, cascaded frequency divider stages, and clock prescalers.

Verified Scientific Model
4-BIT SIPO SHIFT REGISTER (74164)SIN=1FF01FF10FF21FF31PARALLEL BUS [Q3..Q0]:1011 (0xB)
Digital Electronics and Logic DesignAvailable
Difficulty: Intermediate2 tools

Universal Shift Registers (SISO, SIPO, PISO, PIPO)

Serial-in serial-out, serial-in parallel-out, parallel-in serial-out, bidirectional shifting, and serial communication serialization.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Digital Electronics and Logic DesignAvailable
Difficulty: Intermediate2 tools

Ring Counters and Twisted Johnson Counters

Circulating one-hot shift ring counters, self-starting logic, and 2N-state Johnson mobius counters with decoding logic.

Verified Scientific Model
RIPPLE SKEW & TRANSIENT DECODING GLITCHCLKQ0 (10ns)Q1 (20ns)Q2 (30ns)TRANSIENT GLITCH SPIKE
Digital Electronics and Logic DesignAvailable
Difficulty: Intermediate2 tools

Asynchronous Ripple Counters & Propagation Skew

Modulo-N ripple counters, cumulative flip-flop propagation delay, clock skew, and transient decoding glitches.

Verified Scientific Model
RIPPLE SKEW & TRANSIENT DECODING GLITCHCLKQ0 (10ns)Q1 (20ns)Q2 (30ns)TRANSIENT GLITCH SPIKE
Digital Electronics and Logic DesignAvailable
Difficulty: Intermediate2 tools

Synchronous Up/Down Counters with Common Clock

Zero cumulative clock skew using parallel clocked flip-flops, lookahead carry logic, and programmable count sequences.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Digital Electronics and Logic DesignAvailable
Difficulty: Advanced3 tools

Finite State Machine (FSM) Sequence Detectors (Mealy vs Moore)

Design of Mealy and Moore state machines detecting overlapping bit sequences (e.g. 1011), state transition tables, and state minimization.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Digital Electronics and Logic DesignAvailable
Difficulty: Advanced2 tools

Timing Diagrams, Static Hazards & Glitch Elimination

Static-1 and static-0 hazards caused by unequal path propagation delays, and elimination via consensus terms on K-maps.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Digital Electronics and Logic DesignAvailable
Difficulty: Advanced3 tools

4-Bit Arithmetic Logic Unit (ALU 74181 Architecture)

Construction of 4-bit ALU performing 16 arithmetic operations (Add, Sub, Inc) and 16 logic operations (AND, OR, XOR, NOT) with status flags (Z, C, V, N).

Verified Scientific Model
DISCRETE TIME SIGNAL x[n] & FFT
Signals and SystemsAvailable
Difficulty: Introductory2 tools

Standard Continuous and Discrete Time Signals

Impulse (Dirac delta), Unit Step, Ramp, Exponential, and Sinc functions in continuous and discrete domains.

Verified Scientific Model
DISCRETE TIME SIGNAL x[n] & FFT
Signals and SystemsAvailable
y(t)=∫−∞∞x(τ)h(t−τ)dτy(t) = \int_{-\infty}^{\infty} x(\tau) h(t - \tau) d\tau
Difficulty: Intermediate2 tools

Continuous and Discrete Convolution (LTI Systems)

Graphical convolution: flip, shift, multiply, and integrate y(t) = x(t) * h(t) for arbitrary input signals and impulse responses.

Model:y(t)=∫−∞∞x(τ)h(t−τ)dτy(t) = \int_{-\infty}^{\infty} x(\tau) h(t - \tau) d\tau
DISCRETE TIME SIGNAL x[n] & FFT
Signals and SystemsAvailable
fs≥2fmaxf_s \ge 2 f_{max}
Difficulty: Intermediate3 tools

Nyquist-Shannon Sampling Theorem & Aliasing Demonstration

Sampling continuous signals at rate f_s, Nyquist criterion f_s >= 2*f_max, spectrum replication, and audio aliasing distortion.

Model:fs≥2fmaxf_s \ge 2 f_{max}
DISCRETE TIME SIGNAL x[n] & FFT
Signals and SystemsAvailable
x(t)=a0+∑n=1∞[ancos⁡(nω0t)+bnsin⁡(nω0t)]x(t) = a_0 + \sum_{n=1}^{\infty} \left[a_n \cos(n \omega_0 t) + b_n \sin(n \omega_0 t)\right]
Difficulty: Intermediate2 tools

Fourier Series Synthesis of Periodic Waveforms

Decomposition of square, triangle, and sawtooth waves into harmonic sine and cosine series, Gibbs phenomenon at discontinuities.

Model:x(t)=a0+∑n=1∞[ancos⁡(nω0t)+bnsin⁡(nω0t)]x(t) = a_0 + \sum_{n=1}^{\infty} \left[a_n \cos(n \omega_0 t) + b_n \sin(n \omega_0 t)\right]
DISCRETE TIME SIGNAL x[n] & FFT
Signals and SystemsAvailable
Difficulty: Advanced3 tools

Laplace Transform, Pole-Zero Plots & System Stability

S-plane pole and zero locations, region of convergence (ROC), impulse response decay, and BIBO stability criteria in the left half plane.

Verified Scientific Model
DISCRETE TIME SIGNAL x[n] & FFT
Signals and SystemsAvailable
Difficulty: Advanced2 tools

Z-Transform, Unit Circle & Discrete System Frequency Response

Mapping from s-plane to z-plane z = e^(sT), unit circle stability (|p_i| < 1), and discrete transfer function H(z) evaluation.

Verified Scientific Model
DISCRETE TIME SIGNAL x[n] & FFT
Digital Signal ProcessingAvailable
Difficulty: Intermediate3 tools

Discrete Fourier Transform (DFT) & Fast Fourier Transform (FFT)

Radix-2 Cooley-Tukey FFT algorithm, O(N log N) computational efficiency, frequency bin resolution, and spectral leakage.

Verified Scientific Model
DISCRETE TIME SIGNAL x[n] & FFT
Digital Signal ProcessingAvailable
Difficulty: Advanced2 tools

Windowing Functions (Rectangular, Hanning, Hamming, Blackman)

Spectral leakage reduction using non-rectangular window functions, main lobe width vs side lobe suppression trade-offs.

Verified Scientific Model
DISCRETE TIME SIGNAL x[n] & FFT
Digital Signal ProcessingAvailable
Difficulty: Advanced3 tools

Finite Impulse Response (FIR) Filter Design (Window Method)

Linear phase digital filter synthesis, ideal sinc impulse response truncation, windowing design method, and tap coefficient generation.

Verified Scientific Model
DISCRETE TIME SIGNAL x[n] & FFT
Digital Signal ProcessingAvailable
Difficulty: Advanced2 tools

Infinite Impulse Response (IIR) Filter Design (Bilinear Transform)

Butterworth and Chebyshev IIR digital filters via Bilinear Transform, frequency warping compensation, and feedback stability.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Analog and Digital CommunicationAvailable
sAM(t)=Ac[1+mcos⁡(ωmt)]cos⁡(ωct)s_{AM}(t) = A_c [1 + m \cos(\omega_m t)] \cos(\omega_c t)
Difficulty: Intermediate3 tools

Amplitude Modulation (AM) & Envelope Detection

Double Sideband Full Carrier (DSB-FC), modulation index m, overmodulation distortion, sideband power distribution, and diode envelope detector.

Model:sAM(t)=Ac[1+mcos⁡(ωmt)]cos⁡(ωct)s_{AM}(t) = A_c [1 + m \cos(\omega_m t)] \cos(\omega_c t)
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Analog and Digital CommunicationAvailable
B=2(Δf+fm)=2fm(β+1)B = 2 (\Delta f + f_m) = 2 f_m (\beta + 1)
Difficulty: Advanced3 tools

Frequency Modulation (FM) & Carson Bandwidth Rule

Frequency deviation delta_f, modulation index beta, Bessel function sideband distribution, Carson bandwidth rule, and phase-locked loop (PLL) demodulation.

Model:B=2(Δf+fm)=2fm(β+1)B = 2 (\Delta f + f_m) = 2 f_m (\beta + 1)
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Analog and Digital CommunicationAvailable
Difficulty: Advanced3 tools

Digital Modulation Schemes (BPSK, QPSK, 16-QAM Constellations)

I/Q constellation diagrams, phase shifts, bit mapping, symbol rate, carrier recovery, and Additive White Gaussian Noise (AWGN) channel degradation.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Analog and Digital CommunicationAvailable
Difficulty: Advanced3 tools

Eye Diagrams & Intersymbol Interference (ISI)

Overlaid oscilloscope traces of digital pulse stream, eye height (noise margin), eye width (timing jitter), zero-crossing jitter, and raised cosine Nyquist pulse shaping.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Embedded Systems and MicrocontrollersAvailable
Difficulty: Introductory3 tools

Microcontroller Digital GPIO Interfacing & Button Debouncing

Push-pull vs open-drain outputs, internal pull-up/pull-down resistors, mechanical switch contact bounce, and software debouncing algorithms.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Embedded Systems and MicrocontrollersAvailable
Vavg=tonTVCC=D⋅VCCV_{avg} = \frac{t_{on}}{T} V_{CC} = D \cdot V_{CC}
Difficulty: Introductory3 tools

Pulse-Width Modulation (PWM) Duty Cycle & Motor Control

Timer-driven PWM generation, duty cycle modulation, average voltage delivery, H-bridge DC motor speed and direction control, and LED brightness regulation.

Model:Vavg=tonTVCC=D⋅VCCV_{avg} = \frac{t_{on}}{T} V_{CC} = D \cdot V_{CC}
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Embedded Systems and MicrocontrollersAvailable
Difficulty: Intermediate3 tools

UART Serial Protocol Framing & Baud Rate Synchronization

Asynchronous serial data framing: start bit, 8 data bits, parity bit, stop bit, baud rate clock mismatch tolerance, and FIFO buffer overflow.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Embedded Systems and MicrocontrollersAvailable
Difficulty: Advanced2 tools

Synchronous Serial Buses (SPI vs I2C Two-Wire Protocol)

Comparison of 4-wire high-speed SPI (MOSI, MISO, SCK, CS) and 2-wire open-drain I2C (SDA, SCL with ACK/NACK and slave 7-bit addressing).

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
RF, Antennas and Wireless CommunicationAvailable
L=λ2=c2fL = \frac{\lambda}{2} = \frac{c}{2 f}
Difficulty: Intermediate3 tools

Half-Wave Dipole Antenna & 3D Radiation Pattern

Resonant length lambda/2, current and voltage standing waves along antenna arms, radiation resistance (73 Ohm), and 3D toroidal donut radiation pattern.

Model:L=λ2=c2fL = \frac{\lambda}{2} = \frac{c}{2 f}
ANALYTICAL CIRCUIT SCHEMATICZ(s)
RF, Antennas and Wireless CommunicationAvailable
PrPt=GtGr(λ4πd)2\frac{P_r}{P_t} = G_t G_r \left(\frac{\lambda}{4\pi d}\right)^2
Difficulty: Intermediate2 tools

Friis Transmission Equation & Free-Space Path Loss

Inverse-square law power density decay, transmit/receive antenna gains, link budget calculations, and received power P_r in dBm.

Model:PrPt=GtGr(λ4πd)2\frac{P_r}{P_t} = G_t G_r \left(\frac{\lambda}{4\pi d}\right)^2
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Information and Coding TheoryAvailable
Difficulty: Intermediate3 tools

Hamming Code (7,4) Single Error Correction & Double Detection

Generator matrix G, parity-check matrix H, syndrome decoding vector, and automatic single-bit error localization and correction.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Information and Coding TheoryAvailable
C=Blog⁡2(1+SN)C = B \log_2\left(1 + \frac{S}{N}\right)
Difficulty: Advanced2 tools

Shannon Entropy & Channel Capacity Limit (Shannon-Hartley)

Information entropy H(X) = -sum(p_i * log2 p_i), channel capacity C = B * log2(1 + SNR), and theoretical bandwidth-power trade-offs.

Model:C=Blog⁡2(1+SN)C = B \log_2\left(1 + \frac{S}{N}\right)
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Electronic Instrumentation and MeasurementsAvailable
Difficulty: Introductory3 tools

Virtual Digital Multimeter (Voltage, Current, Resistance, Continuity)

Comprehensive 4.5-digit benchtop digital multimeter with auto-ranging, DC/AC voltage, current shunts, resistance bridge, and continuity beeper.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Electronic Instrumentation and MeasurementsAvailable
Difficulty: Intermediate3 tools

Dual-Trace Digital Storage Oscilloscope (DSO & X-Y Lissajous)

Dual-channel oscilloscope with calibrated timebase, volts/division dials, trigger edge/level controls, automated V_pp/frequency measurements, and X-Y Lissajous figures.

Verified Scientific Model
ANALYTICAL CIRCUIT SCHEMATICZ(s)
Electronic Instrumentation and MeasurementsAvailable
Difficulty: Introductory3 tools

Precision Benchtop Function Generator (Sine, Square, Triangle)

Direct digital synthesis (DDS) waveform generator with frequency range from 0.1Hz to 1MHz, variable amplitude, DC offset, and duty cycle.

Verified Scientific Model
m=2kgx(t) = Ae^(-ζωt)cos(ωt)DAMPED RESONANCE CURVEω (rad/s)ω₀ Peak
Waves and OscillationsAvailable
mx¨+cx˙+kx=F0cos⁡(ωt)m \ddot{x} + c \dot{x} + k x = F_0 \cos(\omega t)
Difficulty: Intermediate4 tools

Damped Harmonic Oscillator & Mechanical Resonance

Mass-spring-damper oscillator with viscous dashpot, harmonic forcing excitation, phase-space state portrait (x vs v), and resonant frequency magnification factor sweep.

Model:mx¨+cx˙+kx=F0cos⁡(ωt)m \ddot{x} + c \dot{x} + k x = F_0 \cos(\omega t)
∇ × F = 2ẑ • ∇ • F = 0
Geometry and VectorsAvailable
v⃗(x,y)=P(x,y)i^+Q(x,y)j^\vec{v}(x, y) = P(x, y)\hat{i} + Q(x, y)\hat{j}
Difficulty: Advanced4 tools

Prismora Studio: Calculus, Linear Maps & Vector Fields

Interactive mathematical computing environment featuring function derivative tangents, Riemann sums, 2D matrix transformations with basis vector warping, and autonomous vector fields with RK4 integration.

Model:v⃗(x,y)=P(x,y)i^+Q(x,y)j^\vec{v}(x, y) = P(x, y)\hat{i} + Q(x, y)\hat{j}
WAVE OPTICS: DOUBLE SLIT INTERFERENCELASERd = 0.25mmw = λD/dλ = 632.8nm • I(θ) = I₀ · (sinα/α)² · cos²β
OpticsAvailable
I(θ)=I0(sin⁡αα)2cos⁡2(β)I(\theta) = I_0 \left( \frac{\sin\alpha}{\alpha} \right)^2 \cos^2(\beta)
Difficulty: Intermediate4 tools

Wave Optics: Young's Double-Slit Interference & Diffraction

Virtual optical bench with multi-wavelength laser sources (Red 633nm, Green 532nm, Blue 450nm, Violet 405nm), double-slit aperture slide, real-time spatial irradiance profile I(x), photodetector probe, and missing orders analysis.

Model:I(θ)=I0(sin⁡αα)2cos⁡2(β)I(\theta) = I_0 \left( \frac{\sin\alpha}{\alpha} \right)^2 \cos^2(\beta)
pH TITRATION CURVE1470Equivalence Point (pH=7)
Acid-Base EquilibriumAvailable
pH=−log⁡10[H+]\text{pH} = -\log_{10}[\text{H}^+]
Difficulty: Intermediate4 tools

Acid-Base Neutralization & Buffer Titration Curves

Digital automatic burette titration apparatus. Titrate strong/weak acids (HCl, CH3COOH) with standard base (NaOH), record continuous dynamic pH sigmoidal curves, observe first derivative inflection peaks (dpH/dV), and simulate indicator color transitions.

Model:pH=−log⁡10[H+]\text{pH} = -\log_{10}[\text{H}^+]
P = 60kNWarren Bridge Truss • Method of Joints • m + r = 2j
Structural AnalysisAvailable
∑Fx=0,∑Fy=0\sum F_x = 0, \quad \sum F_y = 0
Difficulty: Intermediate4 tools

Planar Bridge Truss Structural Mechanics

Method of joints matrix solution for architectural bridge trusses, tension-compression distribution, safety factors, and node load deflection.

Model:∑Fx=0,∑Fy=0\sum F_x = 0, \quad \sum F_y = 0
Robotics Kinematics • DH Matrix [T] • det(J) = l₁l₂·sinθ₂
RoboticsAvailable
i−1Ti=Rotz(θi)Transz(di)Transx(ai)Rotx(αi)^{i-1}T_i = \text{Rot}_z(\theta_i) \text{Trans}_z(d_i) \text{Trans}_x(a_i) \text{Rot}_x(\alpha_i)
Difficulty: Advanced4 tools

Planar & Spatial Robotic Arm Kinematics

Denavit-Hartenberg (DH) homogeneous transformation matrices, forward kinematics, closed-form analytical inverse kinematics, and Jacobian singularity detection.

Model:i−1Ti=Rotz(θi)Transz(di)Transx(ai)Rotx(αi)^{i-1}T_i = \text{Rot}_z(\theta_i) \text{Trans}_z(d_i) \text{Trans}_x(a_i) \text{Rot}_x(\alpha_i)
McCabe-Thiele • VLE Equilibrium • R = L/D • N_trays
Separation ProcessesAvailable
y=RR+1x+xDR+1y = \frac{R}{R+1} x + \frac{x_D}{R+1}
Difficulty: Advanced4 tools

McCabe-Thiele Binary Distillation Column

Continuous fractional distillation column simulation. Adjust reflux ratio R, feed thermal condition q, distillate and bottoms purity to step off theoretical trays.

Model:y=RR+1x+xDR+1y = \frac{R}{R+1} x + \frac{x_D}{R+1}
V_maxMichaelis-Menten Kinetics • v₀ = V_max[S] / (K_m + [S])
Enzyme KineticsAvailable
v0=Vmax[S]Km+[S]v_0 = \frac{V_{max} [S]}{K_m + [S]}
Difficulty: Intermediate4 tools

Enzyme Kinetics: Michaelis-Menten Studio

Initial velocity rate assays, Lineweaver-Burk double reciprocal plots, and reversible inhibition kinetics (competitive, non-competitive, uncompetitive).

Model:v0=Vmax[S]Km+[S]v_0 = \frac{V_{max} [S]}{K_m + [S]}
VENTURIMETER & BERNOULLI THEOREMh₁h₂v₁ (low)v₂ (high)P₁ + ½ρv₁² = P₂ + ½ρv₂² • Q = C_d · A₁A₂√(2gΔh / (A₁²-A₂²))
Fluid MechanicsAvailable
P1+12ρv12=P2+12ρv22P_1 + \frac{1}{2}\rho v_1^2 = P_2 + \frac{1}{2}\rho v_2^2
Difficulty: Intermediate4 tools

Bernoulli's Theorem & Venturimeter Flow Measurement

Fluid mechanics testbench. Measure piezometric pressure heads h1..h7 across converging-diverging venturi pipe, compute theoretical discharge, and determine discharge coefficient Cd.

Model:P1+12ρv12=P2+12ρv22P_1 + \frac{1}{2}\rho v_1^2 = P_2 + \frac{1}{2}\rho v_2^2
UTM TENSILE TEST & STRESS-STRAINStrain εStress σ (MPa)σ_y (Yield)UTS = 460MPaFractureE = σ/ε (Young's Modulus) • Mild Steel • Yield: 250 MPa • Elongation: 26%
Mechanics of MaterialsAvailable
σ=PA0,ϵ=ΔLL0\sigma = \frac{P}{A_0}, \quad \epsilon = \frac{\Delta L}{L_0}
Difficulty: Intermediate4 tools

Universal Testing Machine (UTM) Tensile Test & Stress-Strain Curve

Uniaxial tensile loading of mild steel, aluminium 6061, and brass specimens. Observe linear Hookean elasticity, yield plateau, plastic strain hardening, necking, and fracture.

Model:σ=PA0,ϵ=ΔLL0\sigma = \frac{P}{A_0}, \quad \epsilon = \frac{\Delta L}{L_0}
BEAM BENDING & SFD / BMD DIAGRAMSP = 20 kN+V-VM_max = PL/4M/I = σ/y = E/R • Simply Supported • L = 6m • EI d²y/dx² = M(x)
Structural AnalysisAvailable
V(x)=dMdx,M(x)=∫V(x)dxV(x) = \frac{dM}{dx}, \quad M(x) = \int V(x) dx
Difficulty: Intermediate4 tools

Beam Bending Mechanics: Shear Force & Bending Moment Diagrams

Structural mechanics workbench for simply supported and cantilever beams. Apply point loads and distributed loads to plot real-time SFD V(x), BMD M(x), and deflection delta(x).

Model:V(x)=dMdx,M(x)=∫V(x)dxV(x) = \frac{dM}{dx}, \quad M(x) = \int V(x) dx
TRANSFORMER EQUIVALENT CIRCUIT & OC/SCΦ(t)N₁N₂OC Test: R_c || X_mSC Test: R_eq + jX_eqη_max = 98.4%V₁/V₂ = N₁/N₂ • P_core = V_oc² / R_c • P_cu = I_sc² R_eq • %VR
Electrical MachinesAvailable
Rc=V02W0,Xm=V0I0sin⁡ϕ0R_c = \frac{V_0^2}{W_0}, \quad X_m = \frac{V_0}{I_0 \sin\phi_0}
Difficulty: Intermediate4 tools

Single-Phase Transformer Open & Short Circuit Tests

Electrical machines laboratory. Perform no-load O.C. test and full-load S.C. test to extract core loss resistance Rc, magnetizing reactance Xm, equivalent impedance, and efficiency curve.

Model:Rc=V02W0,Xm=V0I0sin⁡ϕ0R_c = \frac{V_0^2}{W_0}, \quad X_m = \frac{V_0}{I_0 \sin\phi_0}
SERIES RLC RESONANCE & QUALITY FACTOR~V_sRLCFreq fCurrent If₀BW = f₀/Qf₀ = 1 / (2π√LC) • Z_min = R • Q = ω₀L/R • Bandwidth Δf = R / (2πL)
Circuits and ElectronicsAvailable
f0=12πLCf_0 = \frac{1}{2\pi\sqrt{LC}}
Difficulty: Intermediate4 tools

Series RLC Circuit AC Resonance & Frequency Response

AC circuit resonance testbench. Sweep frequency from 100 Hz to 1500 Hz to observe resonance peak, minimum impedance Z = R, Quality Factor Q, and phasor phase angles.

Model:f0=12πLCf_0 = \frac{1}{2\pi\sqrt{LC}}
CHEMICAL REACTOR KINETICS (CSTR VS PFR)CSTRPFRτ (s)Conv X_APFRCSTRτ_CSTR = C_A0 X_A / (-r_A) • τ_PFR = C_A0 ∫ dX_A / (-r_A) • Damköhler Da
Reaction EngineeringAvailable
XCSTR=Da1+Da,XPFR=1−e−DaX_{CSTR} = \frac{Da}{1 + Da}, \quad X_{PFR} = 1 - e^{-Da}
Difficulty: Advanced4 tools

Chemical Reaction Engineering: CSTR vs PFR Performance

Reaction engineering laboratory. Compare isothermal performance of Continuous Stirred Tank Reactor (CSTR) vs Plug Flow Reactor (PFR) for first-order reaction kinetics.

Model:XCSTR=Da1+Da,XPFR=1−e−DaX_{CSTR} = \frac{Da}{1 + Da}, \quad X_{PFR} = 1 - e^{-Da}
MICROBIAL BATCH FERMENTATION PHASESTime t (h)ln(Cell Density X)LagExponentialStationaryDeathSubstrate [S]Monod: μ = μ_max·S / (K_s + S) • dX/dt = μX • Doubling Time t_d = ln(2)/μ
Bioprocess EngineeringAvailable
μ=μmaxSKs+S\mu = \mu_{max} \frac{S}{K_s + S}
Difficulty: Intermediate4 tools

Microbial Growth & Monod Kinetics Batch Fermentation

Bioprocess engineering laboratory. Simulate bacterial growth curves through lag, exponential log, stationary, and death phases under Monod substrate limitation.

Model:μ=μmaxSKs+S\mu = \mu_{max} \frac{S}{K_s + S}
EINSTEIN PHOTOELECTRIC EFFECT & WORK FUNCTIONCathodeAnodeFreq νK_max (eV)ν₀Slope = hK_max = hν - Φ = e·V₀ • Planck Constant h = 6.626×10⁻³⁴ J·s • Work Function Φ
Modern PhysicsAvailable
eVs=hν−Φ=hcλ−Φe V_s = h\nu - \Phi = \frac{hc}{\lambda} - \Phi
Difficulty: Intermediate4 tools

Einstein's Photoelectric Effect & Planck's Constant

Modern physics laboratory. Irradiate metal targets with monochromatic light, adjust retarding voltage, record I-V curves, and determine stopping potential Vs and Planck's constant h.

Model:eVs=hν−Φ=hcλ−Φe V_s = h\nu - \Phi = \frac{hc}{\lambda} - \Phi
CLOSED-LOOP PID TUNING & STEP TRANSIENTPIDG(s)r(t)=1M_p = 18%u(t) = K_p·e(t) + K_i ∫ e(τ)dτ + K_d · de/dt • Ziegler-Nichols Rules
Control SystemsAvailable
u(t)=Kpe(t)+Ki∫e(τ)dτ+Kdde(t)dtu(t) = K_p e(t) + K_i \int e(\tau) d\tau + K_d \frac{de(t)}{dt}
Difficulty: Advanced4 tools

Closed-Loop PID Controller Tuning & Dynamic Step Response

Control systems and robotics workbench. Tune proportional Kp, integral Ki, and derivative Kd gains to eliminate steady-state error and optimize transient step response.

Model:u(t)=Kpe(t)+Ki∫e(τ)dτ+Kdde(t)dtu(t) = K_p e(t) + K_i \int e(\tau) d\tau + K_d \frac{de(t)}{dt}
DARCY-WEISBACH PIPE FRICTION & LOSSESh₁h₂f vs ReLaminarRe > 4000h_f = f(L/D)(v²/2g) • f_laminar = 64/Re • Swamee-Jain Colebrook
Fluid MechanicsAvailable
hf=fLDv22gh_f = f \frac{L}{D} \frac{v^2}{2g}
Difficulty: Intermediate4 tools

Darcy-Weisbach Major & Minor Pipe Friction Losses

Investigate frictional pressure drops in fluid pipes across laminar, transition, and turbulent flow regimes, Moody chart, and manometer head loss.

Model:hf=fLDv22gh_f = f \frac{L}{D} \frac{v^2}{2g}
TORSION TEST & SHEAR MODULUS (G)T (N·m)Twist θ = 4.2°T/J = τ/r = Gθ/L • J = πD⁴/32 • G = TL / (Jθ) • τ_max = Tr/J
Mechanics of SolidsAvailable
TJ=τr=GθL\frac{T}{J} = \frac{\tau}{r} = \frac{G \theta}{L}
Difficulty: Intermediate4 tools

Torsion Testing of Circular Shaft & Shear Modulus (G)

Determine torsional stiffness, polar moment of inertia J, maximum surface shear stress, and modulus of rigidity G of solid and hollow shafts.

Model:TJ=τr=GθL\frac{T}{J} = \frac{\tau}{r} = \frac{G \theta}{L}
FOUR-BAR PLANAR MECHANISM (GRASHOF)Grashof: s + l ≤ p + q • Crank-Rocker • Transmission Angle μ = 62°
Theory of MachinesAvailable
s+l≤p+qs + l \le p + q
Difficulty: Intermediate4 tools

Four-Bar Planar Mechanism Kinematics (Grashof Criterion)

Synthesize planar four-bar linkages, classify mechanisms using the Grashof criterion (s+l <= p+q), compute transmission angles, and trace coupler curves.

Model:s+l≤p+qs + l \le p + q
EULER COLUMN BUCKLING & SLENDERNESSP_crδ_maxλ = L_eff / rSlenderness > 100Elastic RegimeP_cr = π²EI / (KL)² • Both Ends Pinned (K=1.0) • σ_cr = π²E / λ²
Structural MechanicsAvailable
Pcr=π2EILe2P_{cr} = \frac{\pi^2 E I}{L_e^2}
Difficulty: Intermediate4 tools

Euler Column Buckling & Critical Slenderness Ratio

Investigate elastic stability of slender structural columns under axial compression, effective length factors K, and Rankine-Gordon transition.

Model:Pcr=π2EILe2P_{cr} = \frac{\pi^2 E I}{L_e^2}
DIRECT SHEAR TEST & MOHR-COULOMB (SOIL)σ_nτσ_nτc (Cohesion)φ = 32°τ_f = c + σ_n · tan(φ) • Shear Strength of Soils • Peak vs Residual
Geotechnical EngineeringAvailable
τf=c+σntan⁡ϕ\tau_f = c + \sigma_n \tan\phi
Difficulty: Intermediate4 tools

Soil Direct Shear Test & Mohr-Coulomb Failure Envelope

Determine soil shear strength parameters: internal friction angle phi and effective cohesion c using laboratory shear box data.

Model:τf=c+σntan⁡ϕ\tau_f = c + \sigma_n \tan\phi
OPEN CHANNEL WEIR FLOW & HYDRAULICSHDischarge QRectangular: Q = ⅔ C_d b √(2g) H^(3/2) • V-Notch (90°): Q = 8/15 C_d √(2g) tan(θ/2) H^(5/2)
HydraulicsAvailable
Qrect=23Cdb2gH3/2Q_{rect} = \frac{2}{3} C_d b \sqrt{2g} H^{3/2}
Difficulty: Introductory4 tools

Open Channel Flow Discharge over Notches & Sharp-Crested Weirs

Calibrate rectangular, triangular (V-notch), and trapezoidal (Cipolletti) weirs for flow measurement in open hydraulic channels.

Model:Qrect=23Cdb2gH3/2Q_{rect} = \frac{2}{3} C_d b \sqrt{2g} H^{3/2}
DC SHUNT MOTOR TORQUE-SPEED DYNAMICSNSω (rad/s)Torque TSpeed N (RPM)N₀ (No Load)Rated LoadE_b = V - I_a R_a = k_e Φ ω • T = k_t Φ I_a • Speed N = (V - I_a R_a) / kΦ
Electrical MachinesAvailable
N=V−IaRakΦN = \frac{V - I_a R_a}{k \Phi}
Difficulty: Intermediate4 tools

DC Shunt Motor Speed Control & Torque-Speed Characteristics

Simulate speed control of DC shunt motors via armature voltage variation and field flux weakening, back-EMF, and torque-speed regulation.

Model:N=V−IaRakΦN = \frac{V - I_a R_a}{k \Phi}
TWO-WATTMETER 3-PHASE POWER MEASUREMENTRYBW₁W₂V_RV_YV_BP_total = W₁ + W₂ • tan φ = √3 (W₁ - W₂) / (W₁ + W₂) • PF = cos φ
Electrical MeasurementsAvailable
P=W1+W2=3VLILcos⁡ϕP = W_1 + W_2 = \sqrt{3} V_L I_L \cos\phi
Difficulty: Intermediate4 tools

3-Phase Power & Power Factor Measurement by Two-Wattmeter Method

Measure total active power and load power factor across balanced 3-phase star/delta AC systems using two electrodynamometer wattmeters.

Model:P=W1+W2=3VLILcos⁡ϕP = W_1 + W_2 = \sqrt{3} V_L I_L \cos\phi
SYNCHRONOUS ALTERNATOR REGULATION (OCC & SCC)Field Current I_fV_oc / I_scOCCSCCLagging: +%VRUnity: ~5%Leading: -%VRZ_s = V_oc / I_sc%VR = (E₀ - V_rated)/V_rated × 100 • Synchronous Impedance Method
AC MachinesAvailable
Zs=VocIscZ_s = \frac{V_{oc}}{I_{sc}}
Difficulty: Advanced4 tools

Alternator Voltage Regulation by Synchronous Impedance Method

Determine synchronous impedance Zs from Open-Circuit (OCC) and Short-Circuit (SCC) tests, and calculate percentage voltage regulation.

Model:Zs=VocIscZ_s = \frac{V_{oc}}{I_{sc}}
LIQUID-LIQUID EXTRACTION (TERNARY EQUILIBRIUM)Solute (A)Carrier (B)Solvent (S)Plait PointTernary Phase Diagram • Extract vs Raffinate Phases • Distribution Coeff K_d
Separation ProcessesAvailable
K=yExRK = \frac{y_E}{x_R}
Difficulty: Intermediate4 tools

Liquid-Liquid Extraction (LLE) & Ternary Phase Equilibrium

Simulate cross-current liquid-liquid extraction, ternary binodal solubility dome, partition coefficient K, and solute recovery percentage.

Model:K=yExRK = \frac{y_E}{x_R}
SHELL & TUBE HEAT EXCHANGER (LMTD)T_h,inT_h,outT_c,inT_c,outHot StreamCold StreamQ = U·A·ΔT_lm • ΔT_lm = (ΔT₁ - ΔT₂) / ln(ΔT₁/ΔT₂) • NTU Method
Heat TransferAvailable
Q=UAΔTlmQ = U A \Delta T_{lm}
Difficulty: Intermediate4 tools

Double-Pipe & Shell-and-Tube Heat Exchanger Performance

Thermal performance of concentric double-pipe heat exchangers in counter-current and co-current flows, LMTD, and effectiveness-NTU analysis.

Model:Q=UAΔTlmQ = U A \Delta T_{lm}
GAS ABSORPTION & PACKED TOWER (NTU / HTU)Liquid LGas Gx (Liq mole)y (Gas mole)Equil y*Oper L/GZ = H_OG × N_OG • Height of Transfer Unit • Henry's Law y = H·x
Mass TransferAvailable
A=LmGA = \frac{L}{m G}
Difficulty: Advanced4 tools

Gas Absorption in Packed Bed Column & Number of Transfer Units

Design packed absorption columns for gas-liquid mass transfer, Colburn equation, Number of Transfer Units N_OG, and bed height Z.

Model:A=LmGA = \frac{L}{m G}
BIOREACTOR AERATION & K_La OXYGEN TRANSFERTime t (s)DO (% Saturation)C* (100% Sat)dC_L/dt = k_La (C* - C_L) • Dynamic Gassing-Out Method • Aerobic Cultures
Bioprocess EngineeringAvailable
dCLdt=KLa(C∗−CL)\frac{dC_L}{dt} = K_L a (C^* - C_L)
Difficulty: Intermediate4 tools

Volumetric Oxygen Transfer Coefficient (KLa) in Bioreactors

Measure volumetric oxygen transfer coefficient KLa in benchtop fermenters using the dynamic gassing-out method under variable RPM and aeration.

Model:dCLdt=KLa(C∗−CL)\frac{dC_L}{dt} = K_L a (C^* - C_L)
GEL FILTRATION CHROMATOGRAPHY (COLUMN RESOLUTION)Retention t_R (min)A₂₈₀ (UV)Peak 1Peak 2R_s = 2(t_R2 - t_R1)/(W₁ + W₂) • Theoretical Plates N = 16(t_R/W)²
Downstream ProcessingAvailable
Kav=Ve−V0Vt−V0K_{av} = \frac{V_e - V_0}{V_t - V_0}
Difficulty: Intermediate4 tools

Size Exclusion / Gel Filtration Chromatography (SEC)

Separate protein mixtures based on hydrodynamic molecular size through dextran bead matrices, void volume V0, and calibration curves.

Model:Kav=Ve−V0Vt−V0K_{av} = \frac{V_e - V_0}{V_t - V_0}
REAL-TIME QPCR AMPLIFICATION & C_T KINETICSCycles: 95°→55°→72°CDenatAnnealExtCycle #Fluorescence (Rn)C_t lineN_n = N₀ · (1 + E)^n • Threshold Cycle C_t • Taq Polymerase 5'→3'
Molecular BiologyAvailable
N=N0(1+E)nN = N_0 (1 + E)^n
Difficulty: Introductory4 tools

Polymerase Chain Reaction (PCR) Amplification Kinetics

Model real-time quantitative PCR (qPCR) amplification curves, 3-step thermal cycling, cycle threshold Ct, and enzyme efficiency.

Model:N=N0(1+E)nN = N_0 (1 + E)^n
NEWTON'S RINGS INTERFERENCE & LENS RADIUSλ = 589nmAir Wedge FilmD_n² = 4n·λ·R • Dark Ring Condition • Radius of Curvature R = (D_(n+p)² - D_n²) / 4pλ
Wave OpticsAvailable
Dn2=4nλRD_n^2 = 4 n \lambda R
Difficulty: Intermediate4 tools

Newton's Rings Interference & Wavelength Determination

Measure monochromatic sodium D-line wavelength and liquid refractive indices using circular thin-film interference fringes.

Model:Dn2=4nλRD_n^2 = 4 n \lambda R
DIFFRACTION GRATING & SPECTRAL DISPERSIONd = 1/Nm = 0m = +1m = -1(a + b) sin θ = m λ • Grating Equation • Resolving Power R = λ/Δλ = m·N
Optics & SpectroscopyAvailable
dsin⁡θ=mλd \sin\theta = m \lambda
Difficulty: Intermediate4 tools

Plane Diffraction Grating Spectrometer & Angular Dispersion

Calibrate optical spectrometers, determine ruling element d = 1/N, resolve spectral lines of Mercury and Sodium doublet separation.

Model:dsin⁡θ=mλd \sin\theta = m \lambda
COUPLED OSCILLATORS (BEATS & NORMAL MODES)m₁m₂k_cBeats: ω_b = |ω₁ - ω₂|Mode 1 (In-phase): ω₁ = √(g/L) • Mode 2 (Anti-phase): ω₂ = √(g/L + 2k_c/m)
Mechanics & WavesAvailable
ωs=km,ωa=k+2kcm\omega_s = \sqrt{\frac{k}{m}}, \quad \omega_a = \sqrt{\frac{k + 2k_c}{m}}
Difficulty: Intermediate4 tools

Coupled Harmonic Oscillators, Normal Modes & Beats

Explore energy transfer between coupled mechanical masses, in-phase symmetric mode w1, out-of-phase antisymmetric mode w2, and beat periods.

Model:ωs=km,ωa=k+2kcm\omega_s = \sqrt{\frac{k}{m}}, \quad \omega_a = \sqrt{\frac{k + 2k_c}{m}}
DIFFERENTIAL DRIVE ROBOT (ODOMETRY & ICC)v_Lv_RICCR = L(v_R+v_L)/2(v_R-v_L)ω = (v_R - v_L) / L • v = (v_R + v_L)/2 • Non-holonomic Constraint: ẏ cos θ - ẋ sin θ = 0
Mobile RoboticsAvailable
v=vR+vL2,ω=vR−vLLv = \frac{v_R + v_L}{2}, \quad \omega = \frac{v_R - v_L}{L}
Difficulty: Intermediate4 tools

Differential Drive Mobile Robot Kinematics & Odometry

Simulate forward kinematics and dead-reckoning odometry of two-wheeled mobile robots, instantaneous center of curvature, and 2D trajectory tracking.

Model:v=vR+vL2,ω=vR−vLLv = \frac{v_R + v_L}{2}, \quad \omega = \frac{v_R - v_L}{L}
INVERTED PENDULUM CART (STATE-SPACE & LQR)θ = 2.4°u(t)(M + m)ẍ + ml θ̈ cos θ - ml θ̇² sin θ = u • (I + ml²)θ̈ + ml ẍ cos θ = mgl sin θ
State Space ControlAvailable
x˙=Ax+Bu\dot{\mathbf{x}} = A \mathbf{x} + B u
Difficulty: Advanced4 tools

Inverted Pendulum on a Cart: State-Space LQR Stabilization

Stabilize an inherently unstable non-linear inverted pendulum using linearized 4-state state-space full state feedback LQR control.

Model:x˙=Ax+Bu\dot{\mathbf{x}} = A \mathbf{x} + B u
BODE PLOT (GAIN & PHASE MARGINS)0dBω_gc-180°PM = 48°GM = -20 log|G(jω_pc)| • PM = 180° + ∠G(jω_gc) • Asymptotic Stability
Frequency Domain ControlAvailable
MdB=20log⁡10∣G(jω)∣M_{dB} = 20 \log_{10} |G(j\omega)|
Difficulty: Advanced4 tools

Bode Plot Frequency Response: Stability, Gain & Phase Margins

Construct logarithmic magnitude and phase frequency response curves, locate gain/phase crossover frequencies, and verify Nyquist stability margins.

Model:MdB=20log⁡10∣G(jω)∣M_{dB} = 20 \log_{10} |G(j\omega)|
BJT NPN TRANSISTOR OUTPUT CHARACTERISTICSBCEV_CE (V)I_C (mA)I_B=40μAI_B=30μAI_B=20μASatI_C = β·I_B • Early Effect V_A • Active, Saturation & Cutoff Regions
Semiconductor DevicesAvailable
IC=βIB(1+VCEVA)I_C = \beta I_B \left(1 + \frac{V_{CE}}{V_A}\right)
Difficulty: Intermediate4 tools

BJT Common Emitter (CE) Input & Output Characteristics

Plot input and output family of characteristic curves of BJT in common emitter configuration, Early voltage VA, and small-signal parameters.

Model:IC=βIB(1+VCEVA)I_C = \beta I_B \left(1 + \frac{V_{CE}}{V_A}\right)
OP-AMP INVERTING AMPLIFIER & FREQUENCY RESPONSE-+R_inR_fV_outV_in (1V)V_out (-5V)A_v = -R_f / R_in • Virtual Ground V⁻ ≈ V⁺ = 0V • Slew Rate SR = dV/dt
Analog ElectronicsAvailable
Vout=−RfRinVinV_{out} = -\frac{R_f}{R_{in}} V_{in}
Difficulty: Intermediate4 tools

Operational Amplifiers: Inverting, Non-Inverting, Summing & Integrator

Verify linear operational amplifier circuit topologies, virtual ground concept, closed-loop voltage gain, summing nodes, and integrator waveforms.

Model:Vout=−RfRinVinV_{out} = -\frac{R_f}{R_{in}} V_{in}

Curriculum Roadmap & Scientific Concepts

Carefully previewed conceptual models aligned with undergraduate engineering and physics syllabi.

0 Concepts

The Prismora Scientific Architecture

Decoupled, zero-dependency mathematical models operating directly in browser memory.

Prismora Explore

Kinematics, dynamics, and celestial gravity simulations with verified analytical models.

Prismora ECE Lab

Nodal circuit analysis, virtual breadboards, oscilloscopes, and DMM instrumentation.

Prismora Micro & TOC

RISC-V 5-stage CPU pipelining, associative caches, DFA/NFA powerset, and Turing machines.

Prismora Studio

Continuous function manifolds, coordinate geometry, vector fields, and reproducible reports.

PRISMORA✦

Explore. Experiment. Understand. • Open-Source Virtual Laboratories

Licensed under MIT License • Free and accessible for universities, students, and researchers worldwide