##### From Wideband Amplifier Design

In the early days of analog design there were no computers, only slide rules. The thinking was that the best way to understand analog design was to obtain closed-form algebraic solutions to various parameters of interest. Many of the circuits described in this book were originally analyzed by tedious hand solutions to the algebra; the inventors deserve great credit for their achievements.

With the advent of digital computers and good software simulators, earlier techniques began to fade away since the new tools were capable of solving complex problems that were simply not amenable to brain-derived algebra. While these tools made a dramatic difference in the number of circuits that could be designed and built, they offered numerical solutions only.

Something was lost in the process. Using simulators alone did not furnish the same level of "gut" understanding that actually working out those algebraic equations did for the original wizards of analog design. In fact, it was these circuit-design pioneers who derived maximum benefit from these tools building on their already great understanding of analog design from having had to solve all those algebraic equations by hand. Before SPICE, Barrie Gilbert invented the gain cell by hand. Bob Ross and Thor Hallen, both from Tektronix, invented different versions of the T-coil by hand (an astounding accomplishment given the complexity of these equations). Carl Battjes invented the *f _{t}* doubler circuit by hand (he also invented many of the simplified models and how to use them that I have described in...

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The f t of a transistor is given by the following equation, (A.1) where C jc is the collector base junction capacitance, C je is the emitter base junction capacitance, R c is the collector bulk...

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Chapter List Chapter 1: Polynomials Chapter 2: Representations of Polynomial Ideals Chapter 3: Polynomials with Coefficients of Limited Accuracy Chapter 4: Approximate Numerical Computation...

When a set of algebraic equations is nonlinear, there are no general uniqueness and existence criteria, and solution can be quite difficult, even for sets of equations that appear simple. This chapter...