This type of signal is called a step function. The jump from the lower to the higher amplitude must happen faster than the system can respond. The minimum rise time for a system can be found using an input signal that is first steady at one amplitude and then abruptly steady at a higher amplitude. How can a system's rise time be measured? If the input signal includes features whose amplitudes change faster than the system can respond, those features will be smoother and broader in the output signal than in the input signal. When the rise time of a system is specified, it describes the fastest response a system can make to an amplitude change in an input signal. The points are often located 10% and 90% up the rising edge of the curve, but sometimes other points on the curve are chosen. Rise time ( r) is the time separating two points on the rising edge of a signal. Points located 10% and 90% up the curve are commonly used, although other points are sometimes chosen. This Lab Fact uses the RC low-pass filter model to derive the relationship,įigure 1: Rise time is the time separating two points on the rising edge of a curve. The inversely proportional relationship between rise time and 3 dB bandwidth can be derived by considering the time and frequency response of an ideal RC low-pass filter, which consists of a resistor and capacitor in series. The 3 dB bandwidth is found by referencing the system's frequency response. Rise time is the time separating two points on the rising edge of the signal output in response to an input step function. Rise time is measured with respect to time, while 3 dB bandwidth is measured with respect to electrical frequency. Depending on the function of the system and the requirements of the application, it may be most convenient to reference one parameter, the other, or both. Having a mathematical expression relating the two is useful, since it is possible that only one of these parameters is known or can be found using available resources. Rise time and 3 dB bandwidth are inversely proportional, with a proportionality constant of ~0.35 when the system's response resembles that of an RC low-pass filter. Rise time and 3 dB bandwidth are two closely-related parameters used to describe the limit of a system's ability to respond to abrupt changes in an input signal. How are rise time and 3 dB bandwidth related?
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