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Time-Domain Analysis of Resonant
and Soft-Switching Converters
Principles of state-plane analysis and averaging
In 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 approximation
The 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
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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 form
Steady-state tank capacitor charge balance and inductor volt-second (flux
linkage) balance for resonant circuit waveforms
Normalization of voltage, current, time, and other quantities
The state plane trajectory of resonant tank waveforms
Examples: series and parallel resonant dc-dc converters
Examples: quasi-resonant, zero-voltage transition, and active-clamp
converters
Examples: modeling switching loss in hard-switched converters having
ringing waveforms
ECEN 5817 Resonant and Soft-Switching
Techniques in Power Electronics
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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
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Techniques in Power Electronics
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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
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Techniques in Power Electronics
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Lecture 19
Tank Capacitor Charge Variation
where
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Techniques in Power Electronics
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Lecture 19
Relating the tank capacitor ac voltage
to the dc load current
q = C (VCP – (–VCP)) = 2CVCP
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Lecture 19
Tank inductor flux linkage variation
where
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Techniques in Power Electronics
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Lecture 19
Relating the tank inductor ac current
to the dc load voltage
 = L (ILP – (–ILP)) = 2LILP
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Techniques in Power Electronics
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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
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Techniques in Power Electronics
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Lecture 19
Integral KCL: Example
By KCL, we know that i1 = iC + i2. Hence,
where
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Techniques in Power Electronics
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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
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Techniques in Power Electronics
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Lecture 19
Integral KVL: Example
By KVL, we know that v2 = v1 – vL. Hence,
where
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Techniques in Power Electronics
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Normalization and Notation
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Techniques in Power Electronics
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Lecture 19
Normalization and Notation
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Techniques in Power Electronics
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Lecture 19
Normalization and Notation: Time and
Frequency
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Lecture 19
State plane trajectory of a series tank circuit
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State plane trajectory of a series tank circuit
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State plane trajectory of a parallel-loaded tank circuit
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Lecture 19
State plane trajectory of a parallel-loaded tank circuit
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Techniques in Power Electronics
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Lecture 19