Transformers — Lesson 4

This lesson covers the intricate details transformers and the formula for the input reflection coefficient. It delves into the design process of an impedance transformer, explaining how to reverse-engineer the characteristic impedances of individual transmission lines. The lesson also introduces the concept of binomial and chebyshev transformers, explaining their formulas and how they are used in circuit design. For instance, it uses a three-section binomial transformer as an illustrative example to demonstrate the design process.

Video Highlights

00:15 - Introduction
01:30 - Binomial transformer and its formula .
12:47 - Result comparison and design example.
14:23 - Introduction to the chebyshev transformer.
24:15 - Expansion for chebyshev polynomial transformer.
28:45 - Summary

Key Takeaways

- The design of an impedance transformer involves reversing the analysis formula to derive the design formula.
- Binomial and chebyshev transformers have different prototype functions and properties, affecting their design procedures.
- The bandwidth and fractional bandwidth can be calculated and equated to derive the values of gamma.
- Binomial transformers offer a flat response but have a constrained bandwidth, while chebyshev transformers allow for a wider bandwidth at the cost of some ripples in the passband.