Power Electronics: Isolated Converters, Modeling, and Magnetics Reviewer

Vocabulary practice flashcards covering isolated DC-DC converters, AC small-signal modeling, frequency-domain Bode plots, stability dynamics, and magnetic design constraints.

Electrical Transformer

A static device that transfers electrical energy between two or more alternating current ($\text{AC}$) circuits through electromagnetic induction.

Transformer Isolation

The condition and electromagnetic phenomenon where electrical energy or signals transfer between separate circuits via magnetic flux without any direct conductive connection or physical electron flow.

Isolation Transformer

The physical hardware device built specifically to transfer $\text{AC}$ power from a power source to an electrical device without a direct electrical connection between them.

Faraday's Law of Induction

A fundamental physical principle stating that an electromotive force is induced only when magnetic flux changes over time, governed by $V = -N \frac{d\Phi}{dt}$.

Lenz's Law

A law stating that the direction of an induced electric current in a conductor produces a magnetic field that opposes the change in magnetic flux that generated it.

Dot Convention

A standard marking scheme used to show the relative polarity and phase relationship between transformer windings without requiring knowledge of the physical coil winding direction.

Forward Converter

An isolated DC-to-DC switched-mode power supply that transfers energy directly from input to output the moment the main switch turns ON (in phase), utilizing a transformer strictly forbidden from storing energy.

Flyback Converter

An isolated DC-to-DC power converter that stores energy in its magnetizing inductance ($L_m$) when the main switch turns ON and releases that energy to the output when the switch turns OFF.

Tertiary Winding

An additional winding incorporated into a forward converter transformer to demagnetize the magnetic core before the next switching cycle begins.

Boost Derived Isolated Converter

A converter based on the boost-conversion principle that incorporates an isolating transformer to produce a higher output voltage while electrically separating input and output circuits.

Push-Pull Isolated Buck Converter

A DC-DC converter combining a step-down (buck) regulation stage with a center-tapped push-pull transformer isolation stage using two switching transistors.

Full-Bridge Isolated Buck Converter

An isolated step-down DC-DC converter topology utilizing four switching devices in an H-bridge configuration to drive the transformer primary with $\pm V_g$, typically chosen for power levels of $750\,\text{W}$ and above.

Half-Bridge Isolated Buck Converter

An isolated step-down converter that replaces two switches of a full-bridge with two large capacitors ($C_a$ and $C_b$) to split the input voltage, resulting in a transformer primary drive of $\pm 0.5 V_g$ and an output voltage of $V = 0.5 n D V_g$.

Magnetizing Inductance ($L_m$)

The non-physical inductor behavior inherent to a real transformer caused by the magnetizing current ($i_M$) circulating through the core windings.

Shoot-Through

A hazardous condition occurring when two transistors on the same bridge leg conduct simultaneously, short-circuiting the input voltage source and risking catastrophic switch failure.

Coupled Inductor

A magnetic component containing two or more windings on a common core that functions by storing magnetic energy during one interval and releasing it during another.

SEPIC (Single-Ended Primary-Inductor Converter)

A converter circuit consisting of two inductors, two capacitors, and two switches that produces an output voltage that can be greater than, less than, or equal to the input voltage with the same polarity.

Isolated Ćuk Converter

A step-up or step-down DC-to-DC converter that provides electrical isolation between input and output through an integrated high-frequency transformer.

AC Modeling Approach

A mathematical technique that averages away high-frequency switching ripples to simplify choppy converter waveforms into a continuous, linear equivalent system for control loop design.

Perturbation and Linearization

The mathematical process of replacing converter state variables with a quiescent DC operating point plus a small AC variation ($x = X + \hat{x}$) and eliminating higher-order non-linear product terms.

Canonical Circuit Model

A unified small-signal circuit representation for any continuous conduction mode (CCM) PWM converter that models DC voltage/current conversion, low-pass filter dynamics, and duty-cycle control modulation.

Capacitor Impedance ($Z_C$)

The total AC opposition of an ideal capacitor, given by $Z_C = \frac{1}{sC}$, where $C$ is capacitance in farads and $s$ is the complex frequency variable.

Inductor Impedance ($Z_L$)

The total AC opposition of an ideal inductor, given by $Z_L = sL$, where $L$ is inductance in henrys and $s$ is the complex frequency variable.

Transfer Function ($G(s)$)

The mathematical relationship describing the ratio of a system's output to its input in the Laplace domain, assuming zero initial conditions: $G(s) = \frac{\text{Output}(s)}{\text{Input}(s)}$.

Buck Converter Control-to-Output Transfer Function ($G_{vd}(s)$)

The dynamic transfer function expressing the small-signal duty cycle-to-output voltage relationship: $G_{vd}(s) = \frac{v_o(s)}{d(s)} = \frac{V_{in}}{LCs^2 + \left(\frac{L}{R}\right)s + 1}$.

Pulse-Width Modulation (PWM)

A technique that controls analog power delivery by rapidly switching an electrical switch fully ON and fully OFF, varying the duty ratio in proportion to an analog control voltage.

Bode Plot

A graphical representation of frequency response consisting of a magnitude plot in decibels ($\text{dB}$) and a phase plot in degrees ($^\circ$) sharing a common logarithmic frequency axis.

Corner Frequency (Break Frequency)

The specific frequency on a Bode plot where a transfer function building block transitions its slope or behavior, such as moving from a flat asymptotic gain to a roll-off slope.

Right-Half-Plane (RHP) Zero

A non-minimum-phase transfer function characteristic where the magnitude increases like a standard zero while the phase drops like a pole, often manifesting as an initial wrong-way transient dip in the output.

Marginally Stable Converter

A system operating state in which output oscillations neither grow nor decay following a disturbance, continuing indefinitely with a constant amplitude without settling.

Settling Time

The elapsed duration required for an unsettled output response to stabilize and stay permanently within an acceptable specified tolerance band of its final reference value after a disturbance.

Steady-State Error

The persistent mathematical difference between the final settled output value and the target reference value after all dynamic transients have ceased.

Loop Gain ($T(s)$)

The total composite transmission gain around an entire closed feedback loop, calculated as the product of all component gains including the amplifier, modulator, power stage, and feedback network.

Core Losses

The energy dissipated as heat within a magnetic core during each switching cycle, consisting of hysteresis loss and eddy current loss.

Hysteresis Loss

Core power dissipation caused by the repeated physical alignment and friction of internal magnetic domains as the core traverses its $B\text{–}H$ loop.

Eddy Current Loss

Core power dissipation resulting from localized circulating electric currents induced inside conductive magnetic material by rapid changes in flux over time ($\frac{dB}{dt}$).

Copper Loss ($P_{cu}$)

Winding power dissipation caused by current flowing through the inherent electrical resistance of conductive wire turns, given by $P_{cu} = I_{rms}^2 R$.

Peak Flux Density Constraint

A filter inductor design constraint ensuring that the maximum internal magnetic flux density remains safely below the core material's saturation limit ($B_{sat}$) under peak operating current.

Winding Area (Window) Constraint

A magnetic physical design constraint requiring that the total cross-sectional area of wire turns, insulation, and bobbin layers fits completely within the core's available open window area.

Core Geometrical Constant ($K_g$)

A quantitative core sizing metric that merges saturation limits, target inductance, winding area, and copper resistance into a single algebraic calculation to eliminate trial-and-error core selection.

Multiple-Winding Magnetics Design

A transformer and inductor engineering method for units with three or more windings that manages complex field interactions, cross-regulation, leakage inductances, and AC proximity losses.

Optimum Flux Density ($B_{opt}$)

The specific operating magnetic flux density at which the sum of winding copper losses and magnetic core losses is minimized for a given operating frequency, material, and geometry.