Electronic Circuits with MATLAB, PSpice, and Smith Chart

7Smith Chart and Impedance Matching

CHAPTER OUTLINE

1. 7.1 Transmission Line
2. 7.2 Smith Chart
3. 7.3 Impedance Matching Using Smith Chart
   1. 7.3.1 Reactance Effect of a Lossless Line
   2. 7.3.2 Single‐Stub Impedance Matching
   3. 7.3.3 Double‐Stub Impedance Matching
   4. 7.3.4 Quarter‐Wave Transformer
   5. 7.3.5 Filter Implementation Using Stubs
   6. 7.3.6 Impedance Matching with Lumped Elements
4. Problems

This chapter introduces the concept of the transmission line (TL) theory, impedance matching, and how the Smith Chart can be used for impedance matching.

7.1 Transmission Line

The sinusoidal steady‐state voltage and current of a TL (as depicted in Figure 7.1) at point of distance d from the load end can be written in cosine‐based phasor form as^[P-1]

(7.1.1)

(7.1.2)

where and are called the forward(incident)/reflected voltages and currents (each propagating from the source/load to the load/source), respectively. The characteristic impedance Z₀ and the propagation constant γ = α + jβ (α: attenuation constant, β: phase constant) are defined as

Figure 7.1 A transmission line (TL) terminated in a load impedance ...