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| """ | |
| Calculate electron drift speed and relate it to transistor switching (tick) rate for a modern GPU. | |
| Assume: We want to simulate 900 quintillion (9e20) transistor switches per second (B200 scale). | |
| """ | |
| # Physical constants | |
| ELEM_CHARGE = 1.602e-19 # Coulombs | |
| ELECTRON_MASS = 9.109e-31 # kg | |
| VACUUM_PERMITTIVITY = 8.854e-12 # F/m | |
| SILICON_MOBILITY = 0.14 # m^2/(V·s) (typical for electrons in Si at room temp) | |
| # Example parameters (can be tuned for realism) | |
| VOLTAGE = 0.7 # V (typical for advanced nodes) | |
| CHANNEL_LENGTH = 5e-9 # 5 nm process | |
| ELECTRIC_FIELD = VOLTAGE / CHANNEL_LENGTH # V/m | |
| # Calculate drift velocity (v = μE) | |
| drift_velocity = SILICON_MOBILITY * ELECTRIC_FIELD # m/s | |
| # Calculate time for electron to cross channel (t = L / v) | |
| transit_time = CHANNEL_LENGTH / drift_velocity # seconds | |
| # Calculate max theoretical switching frequency (f = 1 / t) | |
| max_switch_freq = 1 / transit_time # Hz | |
| # For 900 quintillion switches/sec, but with 600 billion transistors | |
| TARGET_SWITCHES_PER_SEC = 9e20 | |
| TRANSISTORS_ON_CHIP = 6e11 # 600 billion | |
| transistors_needed = TARGET_SWITCHES_PER_SEC / max_switch_freq | |
| required_switch_freq_per_transistor = TARGET_SWITCHES_PER_SEC / TRANSISTORS_ON_CHIP | |
| # Speed of light in silicon (approx 2/3 c) | |
| SPEED_OF_LIGHT_VACUUM = 3e8 # m/s | |
| SILICON_REFRACTIVE_INDEX = 3.5 | |
| speed_of_light_silicon = SPEED_OF_LIGHT_VACUUM / SILICON_REFRACTIVE_INDEX | |
| if __name__ == "__main__": | |
| print(f"Electron drift velocity: {drift_velocity:.2e} m/s") | |
| print(f"Channel transit time: {transit_time:.2e} s") | |
| print(f"Max transistor switching frequency: {max_switch_freq:.2e} Hz") | |
| print(f"To achieve {TARGET_SWITCHES_PER_SEC:.1e} switches/sec:") | |
| print(f"- You'd need {transistors_needed:.2e} transistors switching at max speed in parallel.") | |
| print(f"- For a chip with 600B transistors, each must switch at {required_switch_freq_per_transistor:.2e} Hz.") | |
| print(f"- Electron drift speed: {drift_velocity:.2e} m/s vs. speed of light in silicon: {speed_of_light_silicon:.2e} m/s") | |
| print(f"- Electron drift is ~{(drift_velocity/speed_of_light_silicon)*100:.2f}% the speed of light in silicon (photon speed).") | |
| # --- SR, D, JK, T Flip-Flop Physics/Timing Summary --- | |
| print("\n--- Flip-Flop Types and Switching Physics ---") | |
| print("SR Flip-Flop: Set-Reset, basic memory, built from NAND/NOR gates.") | |
| print("D Flip-Flop: Data/Delay, synchronizes input to clock, used in registers.") | |
| print("JK Flip-Flop: Universal, toggles or sets/resets based on inputs.") | |
| print("T Flip-Flop: Toggle, divides clock, used in counters.") | |
| print("All flip-flops are built from logic gates, so their switching speed is limited by the gate delay (set by electron drift and channel length).\n") | |
| # Example: Calculate flip-flop switching time (assuming 4 gate delays per flip-flop) | |
| GATE_DELAY = transit_time # seconds, from above | |
| FF_GATE_COUNT = 4 # typical for basic flip-flop | |
| flip_flop_delay = FF_GATE_COUNT * GATE_DELAY | |
| flip_flop_max_freq = 1 / flip_flop_delay | |
| print(f"Estimated flip-flop delay: {flip_flop_delay:.2e} s (for {FF_GATE_COUNT} gates)") | |
| print(f"Max flip-flop switching frequency: {flip_flop_max_freq:.2e} Hz") | |