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IMPEDANCE TRANSFORMERS In the preceding chapter, several techniques were considered to match a given load impedance at a ®xed frequency. These techniques included transmission line stubs as well as lumped elements. Note that lumped-element circuits may not be practical at higher frequencies. Further, it may be necessary in certain cases to keep the re¯ection coef®cient below a speci®ed value over a given frequency band. This chapter presents transmission line impedance transformers that can meet such requirements | Radio-Frequency and Microwave Communication Circuits Analysis and Design Devendra K. Misra Copyright 2001 John Wiley Sons Inc. ISBNs 0-471-41253-8 Hardback 0-471-22435-9 Electronic 6 IMPEDANCE TRANSFORMERS In the preceding chapter several techniques were considered to match a given load impedance at a fixed frequency. These techniques included transmission line stubs as well as lumped elements. Note that lumped-element circuits may not be practical at higher frequencies. Further it may be necessary in certain cases to keep the reflection coefficient below a specified value over a given frequency band. This chapter presents transmission line impedance transformers that can meet such requirements. The chapter begins with the single-section impedance transformer that provides perfect matching at a single frequency. Matching bandwidth can be increased at the cost of a higher reflection coefficient. This concept is used to design multisection transformers. The characteristic impedance of each section is controlled to obtain the desired pass-band response. Multisection binomial transformers exhibit almost flat reflection coefficient about the center frequency and increase gradually on either side. A wider bandwidth is achieved with an increased number of quarter-wave sections. Chebyshev transformers can provide even wider bandwidth with the same number of sections but the reflection coefficient exhibits ripples in its pass-band. This chapter includes a procedure to design these multisection transformers as well as transmission line tapers. The chapter concludes with a brief discussion on the Bode-Fano constraints which provide an insight into the trade-off between the bandwidth and allowed reflection coefficient. 189 190 IMPEDANCE TRANSFORMERS 6.1 SINGLE SECTION QUARTER-WAVE TRANSFORMER We considered a single-section quarter-wavelength transformer design problem earlier in Example 3.5. This section presents a detailed analysis of such circuits. Consider the load .
