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First order LTI systems are characterized by the differential equation + = where τ represents the exponential decay constant and V is a function of time t = (). The right-hand side is the forcing function f(t) describing an external driving function of time, which can be regarded as the system input, to which V(t) is the response, or system output.
The RC time constant, denoted τ (lowercase tau), the time constant (in seconds) of a resistor–capacitor circuit (RC circuit), is equal to the product of the circuit resistance (in ohms) and the circuit capacitance (in farads):
An oscilloscope, (formerly known as an oscillograph), (informally scope or O-scope) is a type of electronic test instrument that graphically displays varying voltages of one or more signals as a function of time. Their main purpose is capturing information on electrical signals for debugging, analysis, or characterization.
An increase in this variable means the higher pole is further above the corner frequency. The y-axis is the ratio of the OCTC (open-circuit time constant) estimate to the true time constant. For the lowest pole use curve T_1; this curve refers to the corner frequency; and for the higher pole use curve T_2. The worst agreement is for τ 1 = τ 2.
The RC time constants are adjusted to match. For example, the 9 megohm series resistor is shunted by a 12.2 pF capacitor for a time constant of 110 microseconds. The cable capacitance of 90 pF in parallel with the scope input of 20 pF (total capacitance 110 pF) and 1 megohm also gives a time constant of 110 microseconds.
One example of this would be 30 ps/ms in the Coherent Model FR-103 scanning autocorrelator, which suggests that a 30 ps pulse autocorrelation width would produce a 1 ms FWHM trace when viewed on an oscilloscope. Time Resolution-- related to the time constant of the PMT, an estimate can be made by multiplying the time constant with the ...
The second order time constant, , is simply the time constant associated with the reactive element (where subscript always denotes the index of the element in question), when element is infinite valued. In this notation, the superscript always denotes the index of the element (or elements) being infinite valued, with superscript zero implying ...
A spectrum analyzer from 2005 A modern real time spectrum analyzer from 2019. A spectrum analyzer measures the magnitude of an input signal versus frequency within the full frequency range of the instrument. The primary use is to measure the power of the spectrum of known and unknown signals.