ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 1 Lecture 19

Time-Domain Analysis of Resonantand Soft-Switching Converters

Principles of state-plane analysis and averagingIn a large number of cases, the circuit waveforms are not approximately

sinusoidal The mechanisms of soft-switching PWM converters cannot be understood

using the sinusoidal approximationThe mechanisms of switching loss in hard-switched PWM converters

cannot be understood using the sinusoidal approximation“Exact” time-domain analysis of these converters initially appears to be

very complex, but is considerably simplified when certain analysis principles are employed (there are 4-5 logical leaps to be learned)

Goals of this part of the course:• learn the basic analysis principles• learn to analyze the basic soft-switching circuits and resonant

converters• learn the physical properties of the most well-known soft-switching

converters

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 2 Lecture 19

Key Concepts

Averaging current (charge) and voltage (flux-linkages) over one switching period

Relating average current to change in tank capacitor charge, and relating average voltage to change in tank inductor flux linkages

Kirchhoff’s Laws in integral formSteady-state tank capacitor charge balance and inductor volt-second (flux

linkage) balance for resonant circuit waveformsNormalization of voltage, current, time, and other quantitiesThe state plane trajectory of resonant tank waveformsExamples: series and parallel resonant dc-dc convertersExamples: quasi-resonant, zero-voltage transition, and active-clamp

convertersExamples: modeling switching loss in hard-switched converters having

ringing waveforms

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 3 Lecture 19

Averaging: Charge Arguments

Averaging a terminal current of a (resonant) converter to find the dc or low-frequency component:

where

We will relate this charge to the change in charge on a tank capacitor within the converter

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 4 Lecture 19

Averaging: Volt-Second,or Flux-Linkage, Arguments

Averaging a terminal voltage of a (resonant) converter to find the dc or low-frequency component:

where

We will relate these volt-seconds to the change in flux-linkages in a tank inductor within the converter

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 5 Lecture 19

Tank Capacitor Charge Variation

where

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 6 Lecture 19

Relating the tank capacitor ac voltageto the dc load current

q = C (VCP – (–VCP)) = 2CVCP

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 7 Lecture 19

Tank inductor flux linkage variation

where

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 8 Lecture 19

Relating the tank inductor ac currentto the dc load voltage

= L (ILP – (–ILP)) = 2LILP

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 9 Lecture 19

Kirchhoff’s Laws in Integral Form: KCL

KCL: sum of currents into a node = 0

Integrate over a time interval: net charge entering the node = 0

where

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 10 Lecture 19

Integral KCL: Example

By KCL, we know that i1 = iC + i2. Hence,

where

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 11 Lecture 19

Kirchhoff’s Laws in Integral Form: KVL

KVL: sum of voltages around a loop = 0

Integrate over a time interval: net volt-seconds around the loop = 0

where

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 12 Lecture 19

Integral KVL: Example

By KVL, we know that v2 = v1 – vL. Hence,

where

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 13 Lecture 19

Normalization and Notation

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 14 Lecture 19

Normalization and Notation

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 15 Lecture 19

Normalization and Notation: Time and Frequency

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 16 Lecture 19

State plane trajectory of a series tank circuit

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 17 Lecture 19

State plane trajectory of a series tank circuit

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 18 Lecture 19

State plane trajectory of a parallel-loaded tank circuit

ECEN 5817 Resonant and Soft-Switching Techniques in Power Electronics 19 Lecture 19

State plane trajectory of a parallel-loaded tank circuit