Approximations and Filter Circuits

In the first part of this chapter we will consider a graphical representation of the transfer function in terms of its frequency response \(H(j\omega ) = \left| {H(j\omega )} \right|e^{\angle H(j\omega )}\). Bode diagrams or plots consist of two separate plots, the amplitude \(\left| {H(j\omega )} \right|\) and the phase angle \(\angle H(j\omega )\), with respect to the frequency \(\omega\) on a logarithmic scale. These plots are named after Bode, in recognition of his pioneering work Bode (1945). Bode’s basic work was based upon approximate representation of amplitude and phase response plots of a communication system. Wide range of frequencies of interest in a communication system dictated the use of the logarithmic frequency scale. Bode plots use the asymptotic behavior of the amplitude and the phase responses of simple functions by straight-line segments and are then approximated by smooth plots with ease and accuracy. Bode plots can be created by using computer software, such as MATLAB. The topic is mature and can be found in most circuits, systems, and control books. For example, see Melsa and Schultz (1969), Lathi (1998), Close (1966), Nilsson and Riedel (1966), and many others.