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

Optimum noise performance of transistor input circuits

The single common-emiter transistor amplifier fed from a resistive source exhibits a minimum noise figure, when the source resistance has an optimum value. A generalized amplifier is next shown that is fed from a complex source impedance and containing a single common-emitter transistor in the first stage. It is assumed that noise in succeeding stages is negligible. Various feedback paths to either the base or emitter of the first transistor are shown, and an effective shunt input resistor with thermal noise and an effective emitter degeneration resistor with thernlal noise are given. If the signal source is purely resistive, analysis of the circuit shows that a minimum noise figure is obtainable with an optimum source resistance. If the source is a complex impedance, the quantity of interest is the signal-to-noise ratio (SNR) at the output of the amplifier. This quantity will in general be dependent on the signal frequency chosen, and on the gain characteristics of the entire amplifier. An expression for SNR in the circuit is given. Again, the result is independent of any feedback, except insofar as the feedback affects the gain characteristic. It is to be emphasized that the criteria for best noise performance are in no way connected with the criteria for maximum power transfer from the source

Design of Transistor Regulated Power Supplies

A new form of transistor series regulated power supply is presented which permits unusually good performance characteristics to be realized with simple and economical circuitry. Expressions are given for the open-circuit output voltage and the output resistance in terms of the supply voltages and the circuit parameters. Application of the new circuit to two practical laboratory regulated power supplies is described, the specifications of which are: 0.5 ampere at 18 to 22 volts, and 1 a at 5 to 25 v. The output resistance is of the order of 0.01 ohm for both supplies; for sudden change of load current between minimum and maximum the transient in output voltage is 80 mv or less, and decays in 40 µsec or less. At full load, ripple in the output voltage is less than 5 mv and line voltage variations of ± 10 per cent produce output variations of less than 5 mv. Each supply uses only one line transformer

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

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

Methods of Design-Oriented Analysis: The Quadratic Equation Revisited

The conventional formula for quadratic roots suffers from two defects: it is High Entropy, and it is computationally inaccurate when two real roots are widely separated. An improved formula is suggested that overcomes both defects. Both roots are expressed in terms of a single parameter F that contains the radical sign and is a unique function of the single parameter Q that determines the nature of the roots. Both roots are computed in terms of F with the same computational accuracy, and the Low Entropy format exposes the useful design-oriented result that, for well-separated real roots, F approaches unity so that the radical disappears and both roots reduce to simple ratios of the original quadratic coefficients

A Simple Derivation of Field-Effect Transistor Characteristics

In the conventional treatment of the field effect transistor, the first step is the specification of an impurity profile that describes the nature of the gate-channel contact. Solutions for the static and small-signal characteristics are then valid only for the particular impurity profile chosen, and must be repeated from the beginning for different structures. The purpose of this communication is to present a simple, though approximate, development of the characteristics of an FET without specifying the detailed nature of the structure. The charge-control approach is used, and it is shown that in the pinch-off region the relation between the drain current and the gate-source voltage is approximately square law. The results are applicable to all gate-channel structures, including the insulated gate types

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