[...]... 296 10 Airbridges and Dielectric Crossovers 299 10 .1 Airbridge and Crossover 299 10 .2 Analysis Techniques 10 .2 .1 Quasistatic Method 10 .2.2 Full-Wave Analysis 3 01 3 01 306 10 .3 Models 10 .3 .1 Analytical Model 10 .3.2 Measurement-Based Model References 308 308 310 315 11 Transformers and Baluns 317 11 .1 11. 1 .1 11. 1.2 11 .1. 3 11 .1. 4 11 .1. 5 11 .1. 6 11 .1. 7 Basic Theory Parameters Definition Analysis of Transformers... Ferrite Transformers 336 11 .5 Parallel Conductor Winding Transformers on Si Substrate 339 11 .6 Spiral Transformers on GaAs Substrate 11 .6 .1 Triformer Balun 11 .6.2 Planar-Transformer Balun References 3 41 344 345 349 12 Lumped- Element Circuits 353 12 .1 12 .1. 1 12 .1. 2 12 .1. 3 12 .1. 4 12 .1. 5 Passive Circuits Filters Hybrids and Couplers Power Dividers/Combiners Matching Networks Lumped- Element Biasing Circuit... Transformers Equivalent Circuit Representation Equivalent Circuit of a Practical Transformer Wideband Impedance Matching Transformers Types of Transformers 318 318 319 322 323 325 326 329 11 .2 Wire-Wrapped Transformers 11 .2 .1 Tapped Coil Transformers 11 .2.2 Bond Wire Transformer 329 329 332 11 .3 332 Transmission-Line Transformers xiv Lumped Elements for RF and Microwave Circuits 11 .4 Ferrite Transformers... Current Handling of Wires 14 6 14 7 15 0 15 1 4.2.5 4.2.6 4.2.7 4.3 4.3 .1 4.3.2 4.3.3 4.4 15 3 15 4 15 5 15 5 Wire Models Numerical Methods for Bond Wires Measurement-Based Model for Air Core Inductors Measurement-Based Model for Bond Wires 15 6 15 6 15 6 15 8 Magnetic Materials References 16 0 16 1 x Lumped Elements for RF and Microwave Circuits 5 Capacitors 16 3 5 .1 Introduction 16 3 5.2 5.2 .1 5.2.2 5.2.3 5.2.4 5.2.5... incentives to use 1 2 Lumped Elements for RF and Microwave Circuits LEs to develop compact and lower cost active and passive RF and microwave circuits [29] Figure 1. 1 shows the basic lumped elements used in MMICs Also shown are via holes and dielectric crossovers, which are integral parts of these elements 1. 2 Why Use Lumped Elements for RF and Microwave Circuits? Although lumped- element circuits typically... 370 372 377 12 .2 12 .2 .1 12.2.2 12 .2.3 Control Circuits Switches Phase Shifters Digital Attenuator References 380 3 81 387 390 392 13 Fabrication Technologies 395 13 .1 13 .1. 1 13 .1. 2 13 .1. 3 Introduction Materials Mask Layouts Mask Fabrication 395 396 4 01 4 01 13.2 Printed Circuit Boards 13 .2 .1 PCB Fabrication 13 .2.2 PCB Inductors 402 404 405 13 .3 Microwave Printed Circuits 13 .3 .1 MPC Fabrication 13 .3.2 MPC... 44, 19 74, pp 414 –420 [10 ] Gupta, K C., ‘ Lumped Elements for MICs,’’ Microwave Integrated Circuits, K C Gupta and A Singh, (Eds.), New Delhi, India: Wiley Eastern, 19 74, Chap 6 [11 ] Gupta, K C., Microwaves, New Delhi: Wiley Eastern, 19 79, Chap 11 [12 ] Gupta, K C., R Garg, and R Chadha, Computer-Aided Design of Microwave Circuits, Dedham, MA: Artech House, 19 81, Chap 7 14 Lumped Elements for RF and Microwave. .. 408 13 .4 Hybrid Integrated Circuits 13 .4 .1 Thin-Film MICs 410 410 Contents xv 13 .4.2 Thick-Film Technology 13 .4.3 Cofired Ceramic and Glass-Ceramic Technology 412 414 13 .5 GaAs MICs 13 .5 .1 MMIC Fabrication 13 .5.2 MMIC Example 416 418 4 21 13.6 CMOS Fabrication 4 21 13.7 Micromachining Fabrication References 424 425 14 Microstrip Overview 429 14 .1 Design Equations 429 14 .1. 1 Characteristic Impedance and. .. wavelength Lumped elements for use at RF and microwave frequencies are designed on the basis of this consideration RF and microwave circuits use three basic lumped- element building blocks; capacitors, inductors and resistors Lumped inductor transformers and baluns are also commonly used in many circuits 1. 1 History of Lumped Elements Lumped elements (LEs) came into existence for possible use in microwave. .. IEEE Trans Microwave Theory Tech., Vol MTT -18 , December 19 70, pp 10 28 10 33 [5] Caulton, M., et al., ‘‘Status of Lumped Elements in Microwave Integrated Circuits Present and Future,’’ IEEE Trans Microwave Theory Tech., Vol MTT -19 , July 19 71, pp 588–599 [6] Coulton, M., ‘‘Film Technology in Microwave Integrated Circuits, ’’ Proc IEEE, Vol 59, Oct 19 71, pp 14 81 14 89 [7] Aitchison, C S., et al., ‘ Lumped Circuit . 310 References 315 11 Transformers and Baluns 317 11 .1 Basic Theory 318 11 .1. 1 Parameters Definition 318 11 .1. 2 Analysis of Transformers 319 11 .1. 3 Ideal Transformers 322 11 .1. 4 Equivalent Circuit. xix 1 Introduction 1 1 .1 History of Lumped Elements 1 1.2 Why Use Lumped Elements for RF and Microwave Circuits? 2 1. 3 L, C, R Circuit Elements 4 1. 4 Basic Design of Lumped Elements 6 1. 4 .1 Capacitor. 7 1. 4.2 Inductor 8 1. 4.3 Resistor 8 1. 5 Lumped- Element Modeling 9 1. 6 Fabrication 11 1. 7 Applications 12 References 13 2 Inductors 17 2 .1 Introduction 17 vii viii Lumped Elements for RF and Microwave