Resonance 646
Resonance Trigonometry 652
The Arctangent 652
Sums of Sine and Cosine 655
Sine and Cosine with Angle Offset 656
Symmetric Phase Offsets of Sines 659
Resonance in Frequency and Time 660
Inverse Laplace Transform of Pole-Pair with Zero at Origin 660
Inverse Laplace Transform of Pole-Pair and Finite Zero 661
Inverse Laplace Transform of Pole-Pair and Pole at Origin 663
Inverse Laplace Transform of Pole-Pair, Pole at Origin, and Finite Zero 663
Trig and Inverse Laplace Transform Equations 664
Switched Linear Circuits 666
Parallel Resonant Circuit 667
Integral of Decaying Sinusoid 669
Derivative of Decaying Sinusoid 670
Switched Series Resonant Circuit 674
Resonant Circuit with Two Sources 676
RC Snubber 679
RC Snubber Three-Pole Solution 684
RC Snubber Time Response 686
RC Snubber Power Dissipation 689
Flyback Voltage Clamp 690
Flyback CD Clamp 696
RCD Clamp 701
RCD Clamp Power 719
RCD Flyback Clamp with CQ 712
Flyback Clamp State 1 713
Flyback Clamp State 2 714
Flyback Clamp State 3 716
Flyback Resonant Current Transfer 721
Push-Pull Circuit Resonance 726
Push-Pull Circuit States and Substates 728
Push-Pull State 1 730
State Sequencing 732
State 1 Circuit Analysis 734
Push-Pull State 2 738
Push-Pull Switched Currents 741
State 2 Duration 749
Push-Pull States 3 and 4 750
Push-Pull Resonance with RC Snubber 755
Push-Pull RC Snubber, State 4A 756
Push-Pull RC Snubber State 3 761
Push-Pull RC Snubber State 2 763
Boost Push-Pull Resonance 764
Secondary Diode RC Damping 768
Linearized Circuit Analysis 771
SPST Switch Impedances 772
PWM-Switch Model 776
PWM-Switch Incremental Circuit Model 778
PWM-Switch Impedance Transforms 779
PWM-Switch Inductance Transforms 783
Power-Transfer Output Circuit 785
CP (Buck) Incremental Model 786
CA (Boost) Incremental Model 789
CL Incremental Model 792
Cuk Incremental Model 799
SEPIC Incremental Model 802
Cuk and SEPIC Transfer Functions 805
Converter Model Development 807
Root Locations of Quadratic Equations 809
LC Output Circuits 812
Resonant Pole-Pair in Loop 813
Control Scheme Categories 817
Inductor-Current Waveform Control 820
CCM Triangle-Wave Convergence 822
Hysteresis CCM Current Control 825
Current-Driven Chopper 827
Hysteresis Voltage Control 829
Hysteresis CCM Voltage Control 830
Hysteresis DCM Voltage Control 832
Constant-Time Control 838
Constant Off-Time DCM Flyback Control 840
Constant On-Time CCM Buck Control 844
Burst Control 845
Burst PWM Voltage Control 846
Two-Parameter PWM 848
Constant-Power Load Resistance 850
Input Port Stability 851
Maximum Input-Power Charger 852
Laser Flashlamp Simmer Supply 855
Average-Current Incremental Models 862
Sampled Feedback Loops 865
Discrete-Time Integration 870
History of Model Progression 877
The Waveform Equations 879
The Slope Equations 884
Low-Frequency-Average and Unified Average iL 887
Closed-Loop Valley-Current Transfer Function 889
Valley and Average Currents Are Dynamically Different 894
Power-Transfer Function 896
Moving He(s) through the Summing Block 898
Simple Unified Model Derivation of Fm(s) 901
Refined Unified Model 902
Refined Model Fm 908
Slope Compensation 910
Current-Sampling Control Equation 913
Negative Slope Compensation Scheme 913
Equivalence of Localized iC 916
Negative-Slope Incremental iM 917
Positive-Slope Compensation Scheme 919
On-Time Compensation Scheme 919
Stable Response 920
Average Inductor Current with Slope Compensation 923
Incremental Average Current Transfer Function 926
Slope Variation from Input and Output Voltages 928
Fm0 Comparison Among Models 931
Simple Unified Model 931
Low-Frequency-Average and Unified Models 932
Sampled-Loop Model 933
Fairchild (and Early Middlebrook) Model 933
Refined Model 934
Fm with Localized Slope Compensation 934
Waveform- and Circuit-Based Model Convergence 936
Valley-Current Control 938
296 pages
