Everything about Time constant
Characteristic time in a system
In physics and engineering, the time constant, usually denoted by the Greek letter τ (tau), is the parameter characterizing the response to a step input of a first-order, linear time-invariant (LTI) system. The time constant is the main characteristic unit of a first-order LTI system. It gives speed of the response. For example, in a simple RC circuit driven by a step change in voltage, the time constant τ = RC sets how quickly the capacitor voltage charges toward its new steady-state value. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Time constantA 5-minute orientation
- Skim a recent paper: Time-Efficient Constant-Space-Overhead Fault-Tolerant Quantum ComputationInfluential work since 2022
- Pick up a classic book: Foundations of electonicsThe most-reprinted book on the subject
- Read the landmark paper: Liquid Time-constant NetworksCited 293 times
- Go sideways: Linear time-invariant systemA closely related topic
- Go sideways: Step responseA closely related topic
đź“– Definitions
Noun A characteristic of an exponential function, represented by Ď„ in the function:
Noun The time in which a physical system's response to a step-wise change in an external variable reaches approximately 63% of its final (asymptotic) value.
Noun For radioactivity: the decay constant.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Liquid Time-constant Networks
Median Filtering in Constant Time
Membrane Time Constant of Motoneurons
Time-Multiplexed Multiple-Constant Multiplication
Constant-Time Discrete Gaussian Sampling
CTIDH: faster constant-time CSIDH
Cosmological constant and time delay
Constant time modular inversion
🆕 Influential since 2022
Time-Efficient Constant-Space-Overhead Fault-Tolerant Quantum Computation
Late-time interacting cosmologies and the Hubble constant tension
Photonic Physical Reservoir Computing with Tunable Relaxation Time Constant
Adaptive histogram equalization in constant time
A General Approach to Sampled-Data Modeling for Ripple-Based Control—Part II: Constant ON-Time and Constant OFF-Time Control
đź“š Books worth reading
Foundations of electonicsRussell L. Meade · 2006- 📕Examination of a practical aerobraking guidance algorithmS. W. Evans · 1995
- 📕The IAU resolutions on astronomical reference systems, time scales, and earth rotation modelsGeorge H. Kaplan · 2005
Curvature CosmologyDavid, F. Crawford · 2006
Introduction to the Z80 microcomputerAdi J. Khambata · 1987
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
- Linear time-invariant system In system analysis, among other fields of study, a linear time-invariant (LTI) system is a system that produces an output signal from any input signal…
- Step response The step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions…
- RC circuit A resistor–capacitor circuit (RC circuit), or RC filter or RC network, is an electric circuit composed of resistors and capacitors. It may be driven by…
- RC time constant The RC time constant, denoted τ (lowercase tau), the time constant of a resistor–capacitor circuit (RC circuit), is equal to the product of the circuit…
- RL circuit A resistor–inductor circuit (RL circuit), or RL filter or RL network, is an electric circuit composed of resistors and inductors driven by a voltage or…
- Low-pass filter A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher…
- Exponential decay A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by…
- Harmonic oscillator In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force F proportional…