Circuit Dynamics: Design-Oriented Analysis, Dennis L. Feucht, Innovatia (www.innovatia.com), first printing: OCT 2016, 86 pages, 6 × 9 inch, glossy softcover, $25 US.
This short book is a systematic, detailed treatment of dynamic circuit analysis from a design-oriented viewpoint, and fills in more of the theoretical basis of dynamics than in my recently-published book, Transistor Amplifiers. It starts by introducing the big picture of the methods of dynamic circuit analysis from a historic development perspective on page 1, as shown below.
This flowchart summarizes what is essentially in the book. The general goal is to start with a circuit diagram, find its transfer function in the complex-frequency domain of the form
and determine from it the poles and zeros of the circuit. Then some properties of the transfer function, such as bandwidth and risetime, are approximated from the transfer function.
One challenge is factorization of the polynomials of the numerator and denominator. If they are cubic (with an s3 term) or higher, factorization is not attempted, though there is a math formula for finding the roots of cubic polynomials. It does not inspire much intuitive understanding of dynamics, however! Not all is lost in that circuits constrain polynomials to have some properties that aid in determining where their poles and zeros are, approximately. These various methods comprise about half of the analysis, with the Cochrun-Grabel method, Extra Element Theorem, nEET, and others listed in the above chart and developed in the book. They are ways of avoiding high-degree polynomial factorization. Central to this effort is the quest for the open-circuit time constants (OCTCs), and this can often be done by inspection of the circuit. (Christophe Basso’s recent book, Linear Circuit Transfer Functions, (Wiley), Book Review: Linear Circuit Transfer Functions, reviewed on Planet Analog, covers the topic using the EET, with detailed examples.)
About a third of the book finds OCTCs from general circuits such as the common-emitter (CE) and common-base (CB) amplifier stages. Undergraduate active-circuits textbooks invariably work out the CE circuit with grounded emitter, though in actual engineering, emitter resistance, RE, is often present. This floats the base-emitter junction from ground, making the analysis more difficult. Happily, once the OCTCs are found for general circuits, their formulas form with them a template for further use, thereby avoiding having to work out tedious formulas multiple times. OCTCs of the general, single-stage BJT amplifier stage, with base, emitter, and collector series resistors as shown below, is one circuit template.
The OCTCs are derived for the two capacitances of the BJT T model, Cc (or C
) across the b-c junction, and Ce (or Cπ) across the b-e junction. (The results of BJT analysis also apply to FETs with a change of notation.) The textbook CE stage (RE = 0
) is worked out as a starting exercise leading to the generalized single-stage amplifier and cascaded CE stages.
In the section “OCTCs and the Base Node Time Constant”, a commonly-occurring yet often misleading approximation of the Cc time constant, usually dominated by the Miller Effect, is not based on the resistance across the base-collector nodes but at the base node to ground. The nodal resistance is not the open-circuit b-c resistance, and leads to an error in the pole location. In some cases, it is not in error by much, but conceptually it can mislead students into thinking that it is the nodal and not the open-circuit port resistances that lead to pole determination.