ETBX Bode Plot Module

Bode Plot

An EngineersToolbox Calculation Module

Background Information:

This module calculates the Bode Plot for a dynamic systems with transfer functions of the polynomial form:

The transfer function of a system is defined as the steady-state response of the system to a unit sinusoidal input signal. It can be calculated by taking the ratio of the system's output Y to an input X, where Y and X are both functions of frequency w:

Thus the transfer function H is also a function of frequency. In general, H is a complex function that consists of a real and imaginary part. Through the Euler formula, the complex function H can also be written in polar or phasor form:

Here, |H(w)| is the amplitude or magnitude (also known as the complex modulus) and q is the phase angle (also known as the complex argument).

A Bode Plot in general consists of a plot of amplitude versus frequency and a plot of phase angle versus frequency. In order to be able to view |H(w)| and q in detail at both the high end and low end of the frequency range, we use logarithmic scale for the frequency axis. If the frequency is to displayed in units of cycles per second, it is import to remember that w=2pf.

Input:

The Bode Plot module input form is shown in Figure 1. The module has two primary input fields into which the numerator and denominator polynomial coefficients are entered. The coefficients must be entered in descending order with one or more spaces between each coefficient. Input examples are shown in Table 1.

Figure 1. Bode plot module input form

Table 1: Input examples.

Input Coefficients	Polynomial
3 5 0 8 -3 1 -1 2
1 -8 5 0 0
5 0 0 -8 -6 -7 0 0 0 1

Output:

The Bode Plot module generates a bode plot for the system represented by the input coefficients. An example of the generated bode plot is shown in Figure 2. The module also creates a standard ETB text-based results report shown in Figure 3.

Figure 2. Bode plot

Figure 3. Results report

References:

Craig, R. R. (1981), Structural Dynamics, John Wiley & Sons (New York).

Ogata, K. (1997), System Dynamics, Prentice-Hall (New Jersey).

Woods, R. L., Lawrence, K. L. (1997), Modeling and Simulation of Dynamic Systems, Prentice-Hall (New Jersey).

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