Frequency Response Tool
The JAVA applet below shows the relationship between frequency response and step response. The selection box allows you to choose one of:
You can select between these by pressing the "Change Parameters" button, which also allows you to change the transfer function of the system being examined, and the scale of the graph. The two sets of numbers represent the transfer function of the system. The top row represents the coefficients in the numerator, with the first one being the coefficient of s4, the second one being the coefficient of s3, and so on. Similarly, the second row represents the denominator of the transfer function. For example, the array of numbers
represents the transfer function
The vertical scale of the step response graph can be changed (with ymin being the lower axis limit and ymax the upper limit). The horizontal scale of this graph always starts at 0 seconds (since this is when the step occurs). The vertical scale of the magnitude plot is measured in decibels (dB). The horizontal scales of the Bode plots are logarithmic, and choosing a value of -1 (for either wmax or wmin) means that the frequency limit is 10-1 = 0.1.
Depending on the speed of your computer, it may take a few seconds to calculate the data for the plot.
I suggest that you experiment with the following transfer functions:
Low pass filtersNote the difference in bandwidth between the following 2 low pass filters:
High pass filtersNote the difference in bandwidth between the following 2 high pass filters:
Resonant systemNote the effect of changing the damping constant a in the following transfer function:
Try a = 0, 0.5, 1 and note the height of the resonant peak in the frequency response and the corresponding step response.
Note that you should choose the time scale appropriately - a large time scale for a fast response will produce an unstable result even if the system is stable because the sampling interval in the step response simulation is proportional to the time scale. A guide is to choose your time scale to be no more than 100 times the response time.
Note that this sort of analysis is normally done in MATLAB. The point of this tool is merely to give you some insight as to how the frequency response of a system affects its step response.