He assumes students have been exposed to the theory of

linear circuits, differential equations, and linear algebra; and that after this course they will take courses in control, communication, or digital signal processing.

Anyway, once real active elements are used, this advantageous feature is valid only for

linear circuits or non-linear circuits operated in the frequency areas much below the value of fT.

In the 70s, Liou developed a closed-form solution for the complete frequency-domain response of periodically switched

linear circuits [4].

Those equations [6, 7] have been applied in dynamic programming [8-13], neural network [10, 14, 15], economic modeling [10, 16], population biology [17], quantum calculus [18], geometric analysis [19], real-time communication networks [20], intelligent robotic control [21], adaptive sampling [22], approximation theory [13], financial engineering [12] on time scales, and switched

linear circuits [23] among others.

When we work with problem formulations for

linear circuits with tolerance-affected electrical parameters which lead to systems of linear interval equations.

Section 3 tests the effectiveness of theories of Section 2 in some representative

linear circuits. In Section 4, we draw the corresponding comments and conclusions.

Readers are assumed to have knowledge of

linear circuits, microelectronics, and digital logic design, but this book has been designed deliberately to be useful to an eclectic audience.

The differential equations are implemented using basic

linear circuits with op--amps e.g.

RCCs, though, have drawbacks that prevented them from displacing

linear circuits;

Although the measurement of S-parameters by VNAs is invaluable to the microwave designer for modeling and measuring

linear circuits, these measurements are oftentimes inadequate for nonlinear circuits operating at large-signal conditions, since nonlinearities transfer energy from the stimulus frequency to products at new frequencies.

Cirrus Logic Cirrus Logic is a premier supplier of precision

linear circuits and advanced mixed-signal system-level chip solutions, the latter which demand high-performance mixed-signal processing, embedded DSP, algorithms and firmware.