Electrical Engineer

Fundamental Laws

Kirchhoff's Voltage Law (KVL)

Around any closed loop, the sum of voltage drops equals zero:

V_battery - I·R_internal - V_driver_drop - I·R_armature - V_backEMF = 0

Solving for motor current:

I_motor = (V_terminal - V_backEMF) / R_armature
V_terminal = V_battery - I_total·R_internal - V_driver_drop
V_backEMF = K_e · ω

Kirchhoff's Current Law (KCL)

At any node, current in equals current out:

I_battery = I_motor_left + I_motor_right + I_sensors

The total current drawn from the battery must equal the sum of all branch currents.

Circuit Topology Rules

Complete Circuit Requirement

No current flows without a complete path. For a motor to operate:

Battery V_OUT → Driver VCC → Driver OUT_x → Motor POWER → (return path implicit)

If ANY link in this chain is missing, that motor receives zero power.

Validation Checklist

Power Path Validation

interface CircuitError {
  severity: 'error' | 'warning';
  component: string;
  message: string;
}

// Example errors:
// { severity: 'error', component: 'motor-left', message: 'No power connection: driver OUT_A is not wired to motor-left POWER' }
// { severity: 'error', component: 'driver', message: 'No power supply: battery V_OUT is not wired to driver VCC' }
// { severity: 'warning', component: 'driver', message: 'ENA pin not connected — channel A will remain disabled' }

Motor Electrical Model

DC Motor Equivalent Circuit

V_terminal = I · R_a + K_e · ω + L · (dI/dt)

For our simulation (no inductance, quasi-static):

V_terminal = I · R_a + K_e · ω
I = (V_terminal - K_e · ω) / R_a

Electromechanical Coupling

The same constant K links electrical and mechanical domains:

V_backEMF = K_e · ω        (generator effect)
τ_motor = K_t · I           (motor effect)
K_e ≈ K_t                   (in SI units, for ideal motor)

Torque from Terminal Voltage

τ = K_t · (V_terminal - K_e · ω) / R_a

This replaces the "linear torque-speed" approximation with a physically grounded model. The linear model is an approximation valid only at nominal voltage.

Motor Parameters (from datasheet)

H-Bridge Driver Models

L298N Truth Table

Driver Voltage Drop

Each driver has a characteristic voltage drop that reduces the voltage available to the motor:

V_motor = V_battery - V_driver_drop

Current Limiting

When present (e.g. DRV8833 at 1.5A), the driver clamps motor current:

if I_motor > I_limit:
  I_motor = I_limit
  τ_motor = K_t · I_limit    (torque is also limited)

Battery Model

Terminal Voltage

V_terminal = V_OCV(SoC) - I_total · R_effective

Open-Circuit Voltage (OCV)

Piecewise linear approximation of the discharge curve:

SoC  → V_fraction
1.00 → 1.00
0.90 → 0.98
0.20 → 0.90
0.10 → 0.80
0.05 → 0.60
0.00 → 0.00

V_OCV = V_nominal × V_fraction

Internal Resistance Scaling

At low SoC, internal resistance increases:

R_effective = R_nominal × (1 + max(0, (0.2 - SoC)) × 5)

This models the increased impedance as the battery depletes.

State-of-Charge Update

capacity_remaining -= I_total × (dt / 3600)    // Ah
SoC = capacity_remaining / capacity_total

Power Budget

Per-Step Energy Balance

P_battery = V_terminal × I_total
P_driver_loss = V_driver_drop × I_total
P_motor_copper = Σ(I_motor² × R_a)            // resistive loss
P_motor_mechanical = Σ(τ_motor × ω_motor)     // useful work
P_total_loss = P_driver_loss + P_motor_copper

// Conservation check:
P_battery ≈ P_motor_mechanical + P_total_loss

If P_battery < P_motor_mechanical + P_total_loss, the model has a leak.

Wiring Validation Rules

Before Simulation Starts

1. For each motor in the component map, verify a wire path from driver output to motor power pin exists
2. For each driver, verify a wire path from battery V_OUT to driver VCC exists
3. For each driver control pin (ENA, IN1, etc.), check if an MCU wire exists — warn if not
4. Report all errors to the user before allowing play()

During Simulation

• If hasPowerConnection() is false → supplyVoltage = 0 → nothing moves
• If isMotorConnected(pin, motorId) is false → that motor gets no driver output → zero torque
• These checks must use the ACTUAL wiring topology, not hardcoded assumptions

Anti-Patterns (NEVER do these)

• Assuming power exists without checking the wire topology
• Using nominal voltage instead of actual terminal voltage
• Ignoring driver voltage drop (it matters: 1.4V of 6V = 23% loss)
• Allowing current to flow without a complete circuit path
• Hardcoding component IDs ('driver', 'battery') — derive from wiring
• Treating motor current and torque as independent (they are coupled via K_t)