# Bode plot magnitude and phase pdf

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*Unit circle is now apparent, and this is the usual kind of scale chosen for Nyquist plots of the Loop Gain. When the green curve of the Nyquist plot crosses the unit circle, the phase of the system above degrees angle of vector with the negative real axis can be measured. Bode Plots - Free download as Powerpoint Presentation.*

## Bode Plot Examples

In this section we examine the response of resistors, capacitors and inductors to an applied sinusoidal voltage. In each case we will consider the effect of the sinusoidal signal:. We begin our discussion with the simplest of the three components - the resistor. The impedance response of the circuit is presented in the animation below using, time, phasor and bode plots. The observed behaviour can be explained since the current at any point on the voltage curve is predicted by Ohms law, so the current is always proportional to the magnitude of the voltage.

In Phasor representation this result gives a single point on the real axis corresponding to the resistance R at any frequency. The Bode plot shows the same information with the phase angle equal to zero and the magnitude of the impedance equal to R for the whole frequency range.

Next let us consider a single capacitor of capacitance C , here the relationship between the current flow and applied voltage is given by. The impedance response for a circuit containing a single capacitor is shown in time, phasor and bode notations below. To explain this behaviour we need to understand how the capacitor resists the passage of current.

This quantity Xc has both magnitude and phase and calculated using. Finally we consider the response of an inductor with an inductance L. Here the relationship between the current flow and applied voltage is given by.

The impedance response of a circuit containing a single inductor is shown below in time phasor and bode forms. In an analogous manner to the capacitor the 'resistance' to current flow is given by the inductive reactance Xl which has both a magnitude and phase:.

We now have the basic information required to analyse circuits containing combinations of the above components in series or parallel. As the majority of circuits of interest in electrochemical analysis are combinations of resistors and capacitors we will only consider these in the later sections, although the extension to examine inductive circuits requires no further developments. Search site. International students Continuing education Executive and professional education Courses in education.

Research at Cambridge. Why study Chemical Engineering? Why study Chemical Engineering at Cambridge? Entry requirements Finances and funding How do I apply? Single: Capacitor, Resistor or Inductor Circuits.

Introduction In this section we examine the response of resistors, capacitors and inductors to an applied sinusoidal voltage. Capacitor Circuits Next let us consider a single capacitor of capacitance C , here the relationship between the current flow and applied voltage is given by unlike the resistor, the current flow is proportional to the voltage gradient with respect to time and consequently this introduces a phase shift between the two.

Inductor Circuits Finally we consider the response of an inductor with an inductance L. Here the relationship between the current flow and applied voltage is given by like the capacitor, the current can be seen to be out of phase with the voltage.

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## Bode diagrams and 2-port networks

Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. Use of this web site signifies your agreement to the terms and conditions. A Bode Plot Characterization of All Stabilizing Controllers Abstract: In this technical note, we consider continuous-time control systems and present a new characterization of the Nyquist criterion in terms of Bode plots of the plant and the controller. This gives a nonparametric, and model independent characterization of arbitrary order stabilizing controllers. The result shows that the frequency response of any stabilizing controller must satisfy constraints on its magnitude, phase, and rate of change of phase at certain frequencies that are imposed by the frequency response of the inverse plant. Article :.

A Bode plot is a graph of the magnitude (in dB) or phase of the transfer function versus frequency. Of course we can easily program the transfer function into a.

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In this section we examine the response of resistors, capacitors and inductors to an applied sinusoidal voltage. In each case we will consider the effect of the sinusoidal signal:. We begin our discussion with the simplest of the three components - the resistor. The impedance response of the circuit is presented in the animation below using, time, phasor and bode plots.

The plot can be used to interpret how the input affects the output in both magnitude and phase overfrequency. Each of these individual terms is very easy to show on a logarithmic plot. The entire Bode log magnitude plthe result of the superposition of all the straight line terms. This means with a little practice, we can quicklythe effect of each term and quickly find the overall effect.

Documentation Help Center Documentation. The plot displays the magnitude in dB and phase in degrees of the system response as a function of frequency. All systems must have the same number of inputs and outputs. If w is a vector of frequencies, then bode plots the response at each specified frequency.