Linear Circuit Transfer Functions

Christophe Basso, Engineering Director, ON Semiconductor, Toulouse, FranceChristophe Basso holds a BSEE equivalent from Montpellier University (France) and an MSEE from the Institut National Polytechnique of Toulouse. He has over 20 years of power supply industry experience. His recent research interests focus on developing new offline PWM controller specifications. On top of his 3 published books on Switch mode power supplies, Basso also has 30 patents on power conversion and has authored numerous conference papers and trade magazines.

• About the Author ix Preface xiAcknowledgement xiii1 Electrical Analysis – Terminology and Theorems 11.1 Transfer Functions, an Informal Approach 11.1.1 Input and Output Ports 31.1.2 Different Types of Transfer Function 61.2 The Few Tools and Theorems You Did Not Forget . . . 111.2.1 The Voltage Divider 111.2.2 The Current Divider 121.2.3 Thévenin’s Theorem at Work 141.2.4 Norton’s Theorem at Work 191.3 What Should I Retain from this Chapter? 251.4 Appendix 1A – Finding Output Impedance/Resistance 261.5 Appendix 1B – Problems 37Answers 392 Transfer Functions 412.1 Linear Systems 412.1.1 A Linear Time-invariant System 432.1.2 The Need for Linearization 432.2 Time Constants 442.2.1 Time Constant Involving an Inductor 472.3 Transfer Functions 492.3.1 Low-entropy Expressions 542.3.2 Higher Order Expressions 592.3.3 Second-order Polynomial Forms 602.3.4 Low-Q Approximation for a 2nd-order Polynomial 622.3.5 Approximation for a 3rd-order Polynomial 682.3.6 How to Determine the Order of the System? 692.3.7 Zeros in the Network 762.4 First Step Towards a Generalized 1st-order Transfer Function 782.4.1 Solving 1st-order Circuits with Ease, Three Examples 822.4.2 Obtaining the Zero with the Null Double Injection 892.4.3 Checking Zeros Obtained in Null Double Injection with SPICE 942.4.4 Network Excitation 952.5 What Should I Retain from this Chapter? 100References 1012.6 Appendix 2A – Problems 102Answers 1053 Superposition and the Extra Element Theorem 1163.1 The Superposition Theorem 1163.1.1 A Two-input/Two-output System 1203.2 The Extra Element Theorem 1263.2.1 The EET at Work on Simple Circuits 1303.2.2 The EET at Work – Example 2 1323.2.3 The EET at Work – Example 3 1373.2.4 The EET at Work – Example 4 1383.2.5 The EET at Work – Example 5 1403.2.6 The EET at Work – Example 6 1463.2.7 Inverted Pole and Zero Notation 1503.3 A Generalized Transfer Function for 1st-order Systems 1533.3.1 Generalized Transfer Function – Example 1 1563.3.2 Generalized Transfer Function – Example 2 1593.3.3 Generalized Transfer Function – Example 3 1633.3.4 Generalized Transfer Function – Example 4 1703.3.5 Generalized Transfer Function – Example 5 1743.4 Further Reading 1803.5 What Should I Retain from this Chapter? 180References 1823.6 Appendix 3A – Problems 183Answers 185References 2184 Second-order Transfer Functions 2194.1 Applying the Extra Element Theorem Twice 2194.1.1 Low-entropy 2nd-order Expressions 2274.1.2 Determining the Zero Positions 2314.1.3 Rearranging and Plotting Expressions 2334.1.4 Example 1 – A Low-Pass Filter 2354.1.5 Example 2 – A Two-capacitor Filter 2414.1.6 Example 3 – A Two-capacitor Band-stop Filter 2454.1.7 Example 4 – An LC Notch Filter 2484.2 A Generalized Transfer Function for 2nd-Order Systems 2554.2.1 Inferring the Presence of Zeros in the Circuit 2564.2.2 Generalized 2nd–order Transfer Function – Example 1 2574.2.3 Generalized 2nd–order Transfer Function – Example 2 2624.2.4 Generalized 2nd–order Transfer Function – Example 3 2664.2.5 Generalized 2nd–order Transfer Function – Example 4 2734.3 What Should I Retain from this Chapter ? 277References 2794.4 Appendix 4A – Problems 279Answers 282References 3115 Nth-order Transfer Functions 3125.1 From the 2EET to the NEET 3125.1.1 3rd-order Transfer Function Example 3175.1.2 Transfer Functions with Zeros 3205.1.3 A Generalized Nth-order Transfer Function 3275.2 Five High-order Transfer Functions Examples 3355.2.1 Example 2: A 3rd-order Active Notch Circuit 3415.2.2 Example 3: A 4th-order LC Passive Filter 3495.2.3 Example 4: A 4th-order Band-pass Active Filter 3555.2.4 Example 5: A 3rd-order Low-pass Active GIC Filter 3685.3 What Should I Retain from this Chapter ? 383References 3855.5 Appendix 5A – Problems 385Answers 388References 431Conclusion 433Glossary of Terms 435Index 439