How the simulations in Curvo Studio work

The general approach

Every simulator takes the parameters you set, computes a steady-state result with a few closed-form equations, and shows it as a 3D scene, readings and curves. There is no netlist and no solver for whole circuits, so each component is driven directly by a voltage or a load you choose.

Where a motor shows a start-up curve, it is a simple exponential response drawn from the steady-state answer, not real transient dynamics.

Diodes: PN diode, Zener and LED

All three diode simulators use the Shockley equation for the forward region: I = I_s × (e^(V/(n × V_T)) − 1), with thermal voltage V_T = 25.85 mV.

PN diode: I_s and the ideality factor n come from the parameter panel (the 1N4148 preset uses 4 nA and 1.9). For reverse bias the current is −I_s until the breakdown voltage, after which a piecewise rule makes the current rise steeply with overdrive, up to a display limit of 1.5 times the rated current.

Zener diode: the forward region uses fixed I_s = 6 nA and n = 1.8. In reverse, a small leakage current grows toward the knee current as the voltage approaches V_Z, and beyond V_Z the model is linear: I = I_knee + (V − V_Z) / r_z, where r_z is the dynamic resistance.

LED: the same exponential with n = 2.1, plus a series resistance R_s for the bulk and lead resistance. Because the current appears on both sides, I = I_s × (e^((V − I × R_s)/(n × V_T)) − 1) is solved with Newton's method. I_s is back-calculated so that the LED carries its rated current at its rated forward voltage. Light output rises with current but rolls off at higher current and temperature.

MOSFET, resistor and transformer

N-channel MOSFET: a square-law model. With overdrive V_ov = V_GS − V_th, the drain current is zero below threshold, I_D = β × (V_ov × V_DS − V_DS²/2) in the linear region (V_DS < V_ov) and I_D = ½ × β × V_ov² in saturation. Gate current is zero, channel-length modulation is not modelled, and the result is clipped at the maximum drain current.

Resistor: Ohm's law and power, I = V/R and P = V × I. The colour-code display shows the bands for the chosen value, and a simple temperature estimate grows with the share of the power rating in use.

Single-phase transformer: the no-load secondary voltage is V_1 × (N_2/N_1) × k, where k is the coupling coefficient. Core flux density is B = V_1 / (4.44 × f × N_1 × A) with a fixed core area A = 0.0025 m². Above 1.6 T the core saturates and the output voltage is scaled down. Output power is capped at 94% of the VA rating, and efficiency follows a simple curve that rises with load.

Brushed DC, BLDC and PMSM motors

Brushed DC motor: V = E + I × R_a, where E is the back EMF. Torque is K_t × I, and K_t and K_e are treated as numerically equal in SI units. The load sets the current, the back EMF is what the supply leaves after the I × R_a drop, and speed follows from E / K_e. If the required current reaches V / R_a, the motor stalls.

BLDC motor: the same relations, with the supply voltage replaced by the DC bus voltage times the PWM duty cycle. PWM is represented only by its average voltage, and the drive limits current to the smaller of 4.5 times rated current and V / R.

PMSM: a synchronous machine has no slip. Speed is 120 × f / p whenever the rotor stays in step. Pull-out torque is approximated as 1.8 times rated torque, scaled by the flux ratio (voltage over frequency, capped at the rated value). If the load exceeds it, the rotor loses synchronism and the motor stalls.

Induction, stepper and servo motors

Induction motor: a slip-based steady-state model. Synchronous speed is 120 × f / p, slip rises linearly with load and grows when voltage falls, and the motor stalls when the load is too high for the voltage. The slip guide gives the details and a worked example. It is not a full equivalent-circuit model.

Stepper motor: speed is step rate × step angle / 6 in rpm. Available torque falls with step rate as T = T_0 / (1 + (f / f_c)^1.4), where the corner rate f_c grows with supply voltage headroom over the winding's rated voltage. If the requested load exceeds the available torque, the motor stalls. At standstill with power applied, the motor holds position at full holding torque.

Servo motor: the drive follows the commanded speed up to a ceiling set by the supply voltage. A proportional position loop with gain K_v leaves a steady following error of 6 × rpm / K_v degrees. Load raises current until the short-term peak torque limit of 3 times rated torque, where the axis faults instead of slowing down. The settling response is first order.

Limitations

These are lesson models. They leave out effects that matter in practice, including the temperature dependence of semiconductor parameters, parasitic capacitance and inductance, switching behaviour, motor magnetic saturation (only the transformer core is modelled) and part tolerances.

Some quantities are chosen to teach a trend rather than match a product, such as the transformer efficiency curve or the motor start-up time constants.

Do not use Curvo Studio to size a real component, select a motor or make safety decisions. Use the manufacturer's datasheet and proper design tools for that.