A Modern Approach to Semiconductor and Vacuum Device Theory

An integrated approach to the understanding of charge-controlled electronic devices is presented. Although only vacuum triodes and diffusion-type transistors are discussed in detail, the methods suggested are also applicable to gas-filled and multi-electrode vacuum structures, to surface-barrier and to drift-type transistors, and to space-charge-limited solid-state devices. The treatment is tutorial in nature, and begins with the development of general equations of current flow applicable in any medium. The principles of charge-controlled devices are then summarized, and a general functional relationship between the total charge in transit and the transit time is developed. These results are then applied in turn to vacuum and semiconductor diodes and triodes to derive in a remarkably simple and consistent manner the salient features of their operation. 'Ideal' vacuum triode and transistor structures are first discussed, and the voltage and current amplification factors are then introduced as arbitrary parameters to account for practical departures from ideality. Specific results obtained are the d.c. characteristics and incremental equivalent circuits for each device. The model established for the transistor is identical with the hybrid-77 circuit due to Giacoletto, and both low- and high-level injection conditions are included. Finally, it is suggested that the transistor collector saturation current with open base is a more fundamental quantity than that with open emitter, and the temperature dependence of the base-emitter voltage is shown to be linear at any injection level. Throughout, emphasis is on the principles involved and on the method of approach, and a particular effort is made to present the development of the vacuum and the semiconductor devices in a completely analogous manner

Describing function properties of a magnetic pulse-width modulator

An analysis is presented for the transfer functions of a particular pulse-width modulator and power switch subsystem that has been widely used in practical switching-mode d-c regulator systems. The switch and filter are in a "buck" configuration, and the switch is driven by a constant-frequency variable duty-ratio push-pull magnetic modulator employing square-loop cores. The two transfer functions considered are that with modulator control signal as input and that with line voltage as input. For a-c signals, the corresponding describing functions (DF) are derived. It is shown that current-source drive to the modulator extends the control DF frequency response over that with voltage drive, and that complete cancellation of the effects of line variations can be obtained at d-c but not for a-c. Experimental confirmation of the analytical results for the control DF are presented

Modelling a current-programmed buck regulator

A general small-signal model for current-programmed switching power stages is used for design-oriented analysis of a 150W buck regulator. The model, into which the current-programming minor feedback loop is absorbed, exposes the desired tendency towards "constant" output current. The regulator voltage loop remains the only explicit feedback loop, allowing the regulator closed-loop properties to be easily obtained from those of the open-loop current-programmed power stage. The design-oriented analytic results allow easy inference of the effects of element changes on the regulator performance functions. Results are obtained for the regulator line-to-output transfer function (audio susceptibility) and output impedance

Null Double Injection and the Extra Element Theorem

The extra element theorem (EET) states that any transfer function of a linear system can be expressed in terms of its value when a given “extra” element is absent, and a correction factor involving the extra element and two driving point impedances seen by the element. One class of applications is when a system has already been analyzed and later an extra element is to be added to the model: the EET avoids the analysis having to be restarted from scratch. Another class of applications is when a system is to be analyzed for the first time: if one element is designated as “extra,” the analysis can be performed on the simpler model in the absence of the designated element, and the result modified by the EET correction factor upon restoration of the “extra” element. Although the EET itself is not new, its interpretation and application appear to be little known. In this paper, the EET is derived and applied to several examples in a manner that has been developed and refined in the classroom over a number of years. The concept of “null double injection” is introduced first, because it is the key to making easy the calculation of the two driving point impedances needed for the EET correction factor

Low-Entropy Expressions: The Key to Design-Oriented Analysis

The perception of many electronics design engineers is that they are able to apply few of the formal analysis methods they have been taught, and are largely unprepared for the realization that Design is the Reverse of Analysis. Suggested here is a different perspective for teaching, based on the premise that only analysis that is design-oriented is worth doing, and that results should be presented in Low-Entropy Expressions. High- and Low-Entropy Expressions are described. A simple analog circuit example illustrates one Method of Design-Oriented Analysis: Doing the Algebra on the Circuit Diagram

Topics in multiple-loop regulators and current-mode programming

Some general considerations about multiple-loop feedback are discussed, and it is concluded that incorporation of a current-programmed power stage into a "new" power stage model is both justified and useful. A new circuit-oriented model of the current feedback path is derived which augments the well-known power stage canonical circuit model. The current loop gain, though wide-band, is always stable if the conventional stabilizing ramp is employed but has a relatively small low-frequency value. Consequently, the "new" power stage is more usefully modeled by a y-parameter model in which the current loop is not explicit. Expressions for the y parameters are given that are extensions of those previously derived. Another form of the model resembles the original canonical form for duty ratio programming, and shows that current programming effectively introduces lossless series damping that separates widely the two poles of the power stage LC filter. Therefore, although current programming tends to make the power stage output behave as a current source, the control-to-output voltage transfer function exhibits, in addition to the familiar dominant pole, a second pole at the current loop gain crossover frequency, which may lie anywhere from one-sixth to two-thirds of the switching frequency

Topics in multiple-loop regulators and current-mode programming

Some general considerations about multiple-loop feedback are discussed, and it is concluded that incorporation of a current-programmed power stage into a "new" power stage model is both justified and useful. A new circuit-oriented model of the current feedback path is derived which augments the well-known power stage canonical circuit model. The current loop gain, though wideband, is always stable if the conventional stabilizing ramp is employed, but has a relatively small low-frequency value. Consequently, the "new" power stage is more usefully modelled by a y parameter model in which the current loop is not explicit. Expressions for the y parameters are given that are extensions of those previously derived. Although current-programming tends to make the power stage output behave as a current source, the control to output voltage transfer function exhibits, in addition to the familiar dominant pole, a second pole at the current loop gain crossover frequency, which may lie from one-sixth to two-thirds of the switching frequency

Transformerless DC-to-DC converters with large conversion ratios

A new switching dc-to-dc converter is introduced in which large voltage step-down ratios can be achieved without a very small duty ratio and without a transformer. The circuit is an extension of the Ćuk converter to incorporate a multistage capacitor divider. A particularly suitable application would he a 50-V to 5-V converter in which dc isolation is not required. The absence of a transformer and a larger duty ratio permits operation at a high switching frequency and makes the circuit amenable to partial integration and hybrid construction techniques. An experimental 50-W three-stage voltage divider Ćuk converter converts 50 V to 5 V at 500 kHz, with efficiency higher than for a basic Ćuk converter operated at the same conditions. A corresponding voltage-multiplier Ćuk converter is described, and also dual buck-boost-derived step-down and step-up converters

Modeling Current-Programmed Buck and Boost Regulators

A general small-signal model for current-programmed switching power stages is used for design-oriented analysis of a 150-W buck regulator and of a 280-W boost regulator. The model, into which the current-programming minor feedback loop is absorbed, exposes the desired tendency towards “constant” output current. The regulator voltage loop remains the only explicit feedback loop, allowing the regulator closed-loop properties to be easily obtained from those of the open-loop current-programmed power stage. The design-oriented analytic results allow easy inference of the effects of element changes on the regulator performance functions. Results are obtained for the regulator line-to-output transfer function (audio susceptibility) and output impedance