In this chapter, first the parametric principle is illustrated by two simple examples, one mechanical and one electrical. Then the realization of time­ varying reactances is explained, followed by a short history of "parametric electronics". This survey demonstrates the importance of parametric circuits in the field of low-noise microwave electronics as well as explains the organization of this book. 1.1 The Parametric Principle An oscillating system comprising a single or several time-varying energy­ storing elements is called a parametric system; usually the variations are harmonic functions of time. Everybody knows one example of a mechanical parametric system from his childhood, namely, a swing. Therefore, we will start with this example though as it turns out, a swing is a rather compli­ cated parametric system. Fortunately, the electrical parametric systems, which form the object of this book, are simpler. Figure 1.1 shows such a swing. If it is removed from its equilibrium position and the child stands on it in a fixed attitude, the swing oscillates with a certain amplitude, the magnitude of which decreases with time due to the mechanical friction of the system. To increase the amplitude of oscil­ lation, the child changes positions during swinging: it crouches and straightens in a certain way twice during one cycle of the swing.

1. Introduction.- 1.1 The Parametric Principle.- 1.2 Problems.- 2. Lumped Nonlinear Reactances.- 2.1 Capacitances.- 2.1.1 pn Diodes.- a) Physical Fundamentals of Semiconductors.- b) The variable Capacitance of a pn Diode.- c) The Varactor Diode.- d) The Charge-Storage (Step-Recovery) Diode.- e) Specific Examples.- 2.1.2 The Schottky Diode.- 2.1.3 The MIS Diode.- 2.1.4 Capacitors with Nonlinear Dielectrics.- 2.1.5 Varactor Diode Measurement Techniques.- a) Reflection Test Method for Varactor Quality.- b) Transmission Test Method.- c) Determination of More Detailed Equivalent Circuits.- 2.2 Inductances.- 2.2.1 Nonlinear Magnetics.- 2.2.2 Josephson Junctions.- 2.3 Problems.- 3. Distributed Nonlinear Reactances.- 3.1 Ferroelectrics.- 3.2 Nonlinear Magnetics.- 3.3 Electron Beams.- 3.4 Superconductors.- 3.5 Piezoelectrics.- 3.6 Problems.- 4. Basic Relations for Parametric Circuits.- 4.1 The Manley-Rowe Power Relations.- 4.1.1 General Case.- 4.1.2 Special Three-Frequency Cases.- 4.1.3 Special Four-Frequency Cases.- 4.2 The Basic Three-Frequency Circuit.- 4.2.1 Current and Voltage Pumping.- 4.2.2 The Different Modes of Operation of the Basic Circuit.- 4.3 The Small-Signal Conversion Equations.- 4.3.1 Conversion Equations of the Ideal Varactor Diode for Four- and Three-Frequency Operation.- 4.3.2 The Conversion Equations of the Basic Circuit for the Four- and Three-Frequency Cases.- 4.4 Large-Signal Conversion Equations.- 4.4.1 Four-Frequency Conversion Equations for the Ideal Varactor Diode.- 4.4.2 The Conversion Equations for the Four- and Three-Frequency Basic Circuits.- 4.5 Problems.- 5. Signal Performance of Single-Varactor Diode Parametric Circuits.- 5.1 Three-Frequency Converters.- 5.1.1 Classification.- 5.1.2 The Equivalent Circuit.- 5.1.3 Transducer Gain.- 5.1.4 Available Gain.- 5.1.5 Bandwidth.- 5.1.6 Sensitivity.- 5.2 Four-Frequency Converters for Small-Signal Operation.- 5.2.1 Classification.- 5.2.2 The Noninverting Down-Converter with Resistive Image Termination.- 5.3 Large-Signal Converters.- 5.3.1 Power Up-Converters.- 5.3.2 Harmonic Multipliers.- 5.4 Small-Signal Behavior of the Three-Frequency Amplifier.- 5.4.1 The Equivalent Circuit.- 5.4.2 Transducer Gain.- 5.4.3 Bandwidth.- 5.4.4 Sens itivity.- 5.4.5 The Degenerate Case.- 5.4.6 The Amplifier with Circulator.- 5.5 Large-Signal Effect with Amplifiers.- 5.6 Problems.- 6. Fundamentals of Electronic Noise.- 6.1 Noise - What Is It?.- 6.2 Noise Sources in Communication Transmission Systems.- 6.2.1 Background.- 6.2.2 Thermal (or Johnson) Noise. Noise Temperature of a Two-Pole.- 6.2.3 Shot Noise.- 6.2.4 Antenna Noise. Noise Temperature of an Antenna.- 6.3 Noisy Four-Poles.- 6.3.1 Equivalent Circuits.- 6.3.2 Noise Figure, Noise Temperature, Noise Bandwidth.- a) Spectral Noise Figure and Temperature.- b) The Integral (or Band) Noise Figure. Equivalent Noise Bandwidth.- 6.3.3 Cascading Noisy Four-Poles. Noise Measure of a Four-Pole.- 6.3.4 Examples of Passive Four-Poles.- a) The Lossy Transmission Line.- b) Attenuator.- 6.4 Noise Measurement Techniques.- 6.4.1 Measuring Instruments.- 6.4.2 Measurement of Noise Bandwidth.- 6.4.3 Noise Figure Measurement.- 6.5 Problems.- 7. Noise Performance of Single-Varactor Diode Parametric Circuits.- 7.1 Noise Sources in Parametric Circuits.- 1.2 Converters.- 7.2.1 The Three-Frequency Converter.- 7.2.2 The Four-Frequency Converter with Resistive Image Termination.- 7.3 The Amplifier.- 7.3.1 The Amplifier Without Circulator.- 7.3.2 The Amplifier with Circulator.- 7.4 Problems.- 8. Multiple Controlled-Reactance Parametric Circuits.- 8.1 Lumped Elements.- 8.1.1 Two Cascaded Converters with High Pump Frequency.- 8.1.2 Two Cascaded Converters with Low Pump Frequency.- 8.1.3 Traveling-Wave Structures.- 8.2 Distributed Elements.- 8.2.1 Ferroelectrics.- 8.2.2 Nonlinear Magnetics.- 8.2.3 Electron Beams.- a) Longitudinal Amplifiers.- b) Transverse Amplifiers.- 8.3 Problems.- 9. Applications of Parametric Circuits.- 9.1 Parametric Amplifiers.- 9.1.1 Paramp Cooling.- 9.1.2 Stabilizing the Amplifier.- 9.1.3 Pump Generators.- 9.1.4 Low-Noise Design of Noncryogenic Paramps.- 9.1.5 Means of Broadbanding a Paramp.- 9.1.6 Development and Manufacture of Paramps.- 9.2 Parametric Converters.- 9.2.1 Up-Converters.- 9.2.2 Down-Converters.- 9.3 Problems.- Appendix : Calculation of pn-Diode Barrier Capacitance.- References.- List of Symbols.