1.4 Limitations of the lumped circuit abstraction

• Third postulate of lumped matter discipline requires signal speed to be significantly lower than the speed of electromagnetic waves
• Electromagnetic waves travel at 15 cm per nanosecond in insulator with 4x dielectric constant of vacuum
• Electromagnetic waves propagation delay across a 1-cm chip is about 1/15 ns
• When signal speeds are comparable to speed of electromagnetic waves, lumped matter discipline is violated, and therefore cannot use lumped circuit abstraction. ( resolve through distributed circuit model)
• Capacitive & inductive effects on lumped elements (resistors, wires) resulting from electric fields and magnetic fluxes generated by high frequency oscillator will violate lumped matter discipline ( resolve through separate these effects into new lumped element-capacitor & inductor)