Time constant - Wikipedia
Rise time (tr) is a function of bandwidth (BW). An approximate The relation that youprovided seems to be not reasonable. In fact for a 2 Ghz. Reading time (words). The frequency of a waveform is the number of times it repeats (cycles) in one second. A sine wave of Hz (many. Oscilloscope in action. O-scopes are . The rise time of a scope is very closely related to the bandwidth. It can be calculated as Rise Time = / Bandwidth.
Almost all switching devices follow a switching pattern similar to that shown by the rising line in Figure 1, but they may differ significantly in the very first or last portions of their switching pattern. Switching devices might have quite different switching patterns in the very beginning or ending stages of their switching range, but usually all have quite similar patterns during their main transition. There is no necessary relationship between rise time and frequency See Figure 2.
There is an exception to this rule in the very special case of a well formed signal.
From a practical standpoint for those of us in the PCB design business, a sine or cosine waveform is the one I believe exception. The sine and square waves have the same frequency but much different rise times. But consider a square wave whose frequency is Hz. If the rise and fall times are linear but not zerothen the waveform is not strictly square, but it is trapezoidal. In any event, we can know nothing about the rise time of an approximately square waveform without at least some other information.
These two measurements, frequency and rise time, can be quite important to us, but in quite different ways. Frequency is inherently related to timing and information.
This has implications for the sequencing of operations as a clock signal controls the sequence of a controller circuit. It also can be directly related to information — an audio signal is a perfect example. As long as frequencies remain undistorted, we can predict what will happen in the various circuits we design.
A circuit must have a fast enough rise time to accommodate the signal being processed. If it does not, information in the waveform or circuit timing may be lost or distorted. But here is the clincher: Faster is not necessarily better.
What relation exists between rise/fall time and frequency?
In one sense, we have opposite feelings about these measures. Faster frequencies are good. Just ask any computer operator!
But faster rise times are bad. In contrast, when measuring action potentials in nerve axons, which are much more rapidly changing events, a sampling rate of kHz is required. However, for a signal of given frequency content, increasing the sampling rate beyond a certain point does not significantly increase the fidelity with which the signal is rendered. In addition, the cost of an ADC increases as higher sampling rates are desired.
Finally, more computer processing time and storage space in memory or disk are needed to process the larger number of data points produced when the sampling rate is increased.
Thus there is a tradeoff between fidelity of reproduction on the one hand, and computer storage space, computing time, and cost on the other. Filtering Any ADC has a maximum sampling rate.
In some circumstances, this maximum sampling rate is not high enough to satisfy the Nyquist conditions mentioned above.
In that case, one can pass the analogue signal through a low-pass filter before sending it on to the ADC. This filter acts to remove some of the high-frequency content of the signal that would otherwise alias down in frequency, producing spurious low-frequency content along the lines illustrated above. Note that this anti-alias filtering could remove high frequency information of physiological importance to the phenomenon under investigation.
If it is important to retain these higher frequencies, one has no choice but to use a better data acquisition system that has a higher sampling rate.
A biological signal can be broken down into fundamental frequencies, with each frequency having its own intensity. Display of the intensities at all frequencies is a power spectrum.
Usually we are interested in signals of a particular frequency range or bandwidth.
Rise Time vs. Frequency: What's the Relationship?
The bandwidth is determined by filters, which are devices that alter the frequency composition of the signal. There are three types of filter: Low frequency or in old terminology high pass. High frequency or in old terminology low pass.
Filters one frequency, usually 60 Hz. Real filters or hardware filters alter the frequency composition of the signal. It means after filtering the signal, we cannot recover the frequencies that have been filtered. Digital filters change the frequency of the signal by performing calculations on the data.
It means you can record all the frequency components of your signal and by digitally filtering it, eliminate the unwanted frequencies. Any unwanted signal that modifies the desired signal is noise. It can have multiple sources.BANDWIDTH OF SIGNAL
It is interesting to note that you can dither add white noise: Narrowband noise confines itself to a relatively small portion of the overall signal bandwidth as defined by Nyquist. Broadband noise occupies a significant portion of the Nyquist bandwidth.