|Created||July 29, 2020|
|Last modified||August 03, 2020|
Some dynamic characteristics of a small incandescent lamp. Resistance increases non-linearly with applied voltage. There is an inrush current when "cold" due to a simulated "thermal" lag.
Incandescent Lamp ("pea" bulb) simulation, with demonstration driving oscillator.
The reality is a typical 12v 0.75W bulb, about 1/4" long. The filament resistance increases with voltage due to the positive temperature coefficient of the metal coil, usually tungsten. At an operating voltage of 750mV rms the filament resistance is about right for working with IC op amps - an output swing of around +/-3v is needed. dR/dV @ 750mV is approx 30ohms/volt. A "thermal capacity" time constant in the region of 10mS is a complete guess.
"Lamp" simulation overview
Uses a behavioural voltage source, designated R1, to simulate a non-linear increase in resistance with rising rms applied voltage. A ballast resistor R2 is the basis of the cold resistance, Rcold = 17ohms. Rhot, at 3v rms is 97ohms. Operating point for the oscillator at 1kHz is 36 ohms.
A simple "thermal" lag (filament heating/cooling) is provided by leaky integrator OA1. Its output voltage appears near the end of the R1 generator function as V(lag).
A classic Wien bridge, amplitude stabilised by means of automatic gain control (AGC). Provides a varying amplitude 1kHz voltage at node 'drive'. OA2 uses the lamp resistance, together with R7, as the "resistance" side of the Wien bridge. At steady state, lamp resistance is close to 1/2 of R7. D1 and D2 are to simulate the reality of a +/- 9v psu for the op amps. At simulation start, the lamp resistance is low causing OA2 to try and oscillate at very high amplitude.
3 plots/graphs - from Time-Domain Simulation
1] V(drive), V(lag) - important control voltages for the behavioural element R1. 2] Lamp resistance - note the lag and its time constant. 3] Lamp current - note the starting inrush, with clipped peaks.
R1 is a complex element, with self-referential parameters. On 32-bit Firefox a Time-Domain simulation of Lamp+Oscillator takes 12x longer than the Oscillator alone.
Acknowledgements: CL circuit https://www.circuitlab.com/circuit/gcv8pd/non-linear-resistors-and-capacitors-rc-simulation-example/ ; Hewlett-Packard Audio Signal Generator HP-200CD.
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