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## Control Systems/Bode Plots

Once the straight-line graph is determined, the actual Bode plot is a smooth curve that follows the straight lines, and travels through the breakpoints. From Wikibooks, open books for tutorila open world. Because the gain value is constant, and is not dependent on the frequency, we know that the value of the magnitude graph is constant at all places on dowlnoad graph. For instance, on a standard Bode plot, the values of the markers go from 0.

Step 6 At a zero breakpoint, the value of the actual graph differs from the value of the straight-line graph by 3dB. Policies and guidelines Contact us.

There are 2 pending changes awaiting review. The Bode magnitude and phase plots can be quickly and easily approximated by using a blde of straight lines.

Bode phase plots are plots of the phase pd to an input waveform dependent on the frequency characteristics of the system input. In other languages Add links. The Magnitude plot is typically on the top, and the Phase plot is typically on the bottom of the set.

A Decibel is a ratio between two numbers on a logarithmic scale.

These approximate graphs can be generated by following a few short, simple rules listed below. If we convert both sides to decibels, the logarithms from the decibel calculations convert multiplication of the arguments into additions, and the divisions into subtractions:. Step 2 Find the frequency response from the Transfer function. The frequency of the bode plots are plotted against a logarithmic frequency axis.

Here are some boce. Luckily, our decibel calculation tutoriall in handy. Double, triple, or higher amounts of repeat poles and zeros affect the gain by multiplicative amounts.

Let’s say we have a frequency response defined as a fraction with numerator and denominator polynomials defined as:. We now have the slope of the line, and a point that it intersects, and we can draw the graph: Step 5 The locations of every pole and every zero are called break points. Notice that the “length” of a decade decreases as you move to the right on the graph.

## Bode Tutorial

Again, the Laplace transform does not account for the phase shift characteristics of the system, but the Fourier Transform can. These are the values where the Bode plots experience the largest change in direction. An example of a Bode magnitude and phase plot set. Because each tickmark is a power of 10, they are referred to as a decade. From here, we can say that our frequency response is a composite of two parts, a real part R and an imaginary part X:.

### Rules for Drawing Bode Diagrams

Views Read Latest draft Edit View history. Draw the bode plot of an amplifier system, with a constant gain increase of 6dB. Step 7 Sketch the actual bode plot bodr a smooth-curve that follows the straight lines of the previous point, and travels through the breakpoints.

Every tickmark on the frequency axis represents a power of 10 times the previous value. The line is straight until it reaches the next break point. If we have a system transfer function T swe can separate it into a numerator polynomial N s and a denominator polynomial D s. Retrieved from ” https: We say that the values for all z n and p m are called break points of the Bode plot.

We can draw the graph as a straight, horizontal line at 6dB:. Draw the bode plot of a perfect integrator system given by the transfer function: To get the magnitude gain plot, we must first transit the transfer function into the frequency response by using the change of variables:.

And calculating out the gain of each term and adding them together will give the gain of the system at that frequency. There are no break points, so the slope of the graph never changes.