This chapter will naturally expand upon the ideas in Chap. 1 and discuss black boxes that have more than two terminals. We will first discuss characterization of a multi-terminal black box, followed by a discussion of the two-port representation technique. We will then talk about resistive, inductive (including transformers), and capacitive three-terminal elements. Circulators and opamps are next discussed. After this, we discuss the family of two-port scalors, rotators, reflectors, and gyrators. A current feedback opamp-based implementation approach is used for studying mutators.
Two-terminal piecewise linear negative resistor, synthesized using a multi-terminal opamp
This is especially true for the transistor, where the characteristic curves can be more accurately, and more easily, measured if a particular terminal (called emitter for npn junction transistors) is chosen to be the ground terminal.
2.
Diamond-shaped symbol for controlled sources was used for the first time in [3].
3.
This section was added after a discussion on June 6th 2017, with Dr. Yuping Huang from the Stevens Institute of Technology. His group uses circulators in optical quantum computing applications.
4.
We could also apply Tellegen’s theorem.
5.
Unless otherwise stated, we will assume that all opamp circuits operate at low enough frequencies so the ideal opamp model is valid.
6.
Although we cover circuit simulation in QUCS in Chap. 3 lab, the reader should be able to use their “native intelligence” to easily simulate the circuits in this chapter, using the QUCS online workbook as a guide.
7.
The word “transfer” means that the response variable does not appear at the same port as the source serving as input. There are four types of TCs possible: vo-vs-vin, vo-vs-iin, io-vs-vin, and io-vs-iin.
8.
These correspond to Eqs. (2.84), (2.85), and (2.87).
9.
Recall that an opamp always has an external reference terminal, hence an ideal opamp can also be considered as a four-terminal resistor.
10.
The linear oscillator, modeled by an LC network, requires zero resistance for sustained oscillations. Since zero resistance is near impossible to obtain physically (save for superconductors), all practical oscillators are nonlinear.
11.
We want to clarify mutator terminology. In Chua’s seminal book “Introduction to Nonlinear Circuit Theory” [3], Dr. Chua refers to an L − R mutator as an R − L mutator. However, in Dr. Chua’s publication defining the mutator [2] and all subsequent works, the terminology is consistent with the one used in this book.
12.
For details on realizing other types of mutators such as C − R, R − L, etc., please refer to [2].
13.
Some CFOAs do not have an externally accessible compensation pin z, to maintain pin-compatibility with voltage feedback amplifiers. However, such devices are actually a special class of CFOAs and in this book we will use only the very general CFOAs such as the AD844 that have an externally accessible compensation pin. We will henceforth refer to such CFOAs as an ideal CFOA.
14.
A literature search revealed that there is no standard symbol for a CFOA. We are defining this symbol because it closely mimics the symbol of an ideal opamp with the If clarifying that we have current feedback.
References
Biolek, D. et al.: Mutators for transforming nonlinear resistor into memristor. In: 20th European Conference on Circuit Theory and Design (ECCTD), pp. 488–491 (2011)
Ranganathan, S., Tsividis, Y.: Discrete-time parametric amplification based on three-terminal MOS varactor: analysis and experimental results. IEEE J. Solid-State Circuits 38(12), 2087–2093 (2003)
