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where resistance in ohms and capacitance in farads yields the time constant in seconds or the cutoff frequency in hertz (Hz). The cutoff frequency when expressed as an angular frequency ( ω c = 2 π f c ) {\displaystyle (\omega _{c}{=}2\pi f_{c})} is simply the reciprocal of the time constant.
In order to increase accuracy (and decrease speed), the most common methods are: Lumped C. The entire wire capacitance is applied to the gate output, and the delay through the wire itself is ignored. Elmore delay [5] is a simple approximation, often used where speed of calculation is important but the delay through the wire itself cannot be ...
In the frequency domain (for example, looking at the Fourier transform of the step response, or using an input that is a simple sinusoidal function of time) the time constant also determines the bandwidth of a first-order time-invariant system, that is, the frequency at which the output signal power drops to half the value it has at low ...
In general, capacitance is a function of frequency. At high frequencies, capacitance approaches a constant value, equal to "geometric" capacitance, determined by the terminals' geometry and dielectric content in the device. A paper by Steven Laux [27] presents a review of numerical techniques for capacitance calculation.
Position vectors r and r′ used in the calculation. Retarded time t r or t′ is calculated with a "speed-distance-time" calculation for EM fields.. If the EM field is radiated at position vector r′ (within the source charge distribution), and an observer at position r measures the EM field at time t, the time delay for the field to travel from the charge distribution to the observer is |r ...
The natural frequency (that is, the frequency at which it will oscillate when isolated from any other system, as described above) is determined by the capacitance and inductance values. In most applications the tuned circuit is part of a larger circuit which applies alternating current to it, driving continuous oscillations.
Propagation delay is equal to d / s where d is the distance and s is the wave propagation speed. In wireless communication, s=c, i.e. the speed of light. In copper wire, the speed s generally ranges from .59c to .77c. [3] [4] This delay is the major obstacle in the development of high-speed computers and is called the interconnect bottleneck in ...
That form may be a simple analytic parallel plate capacitance equation or may involve a full numerical solution for a complex 3D geometry with wave propagation. In layout extraction , analytic formulas for simple or simplified geometry can be used where accuracy is less important than speed.