Chapter 3 Transmission lines3.1 Distribution circuit analysis of transmission lines transmission line equation and solution, characteristic impedance, input impedance 3.2 Sending end impedance load impedance, reflection coefficient, return loss, insertion loss, lossless line, low loss line, distortionless line 3.3 Standing wave and standing wave ratio VSWR, load impedance measurement 3.4 Smith chart general properties, examples

3-1

3.1 Distribution circuit analysis of transmission linesBasics 1. Transmission line equations

distributed elements

3-2

2. Traveling wave solution

3-3

Discussion 1. Characteristic impedance (wave impedance) of a transmission line is the ratio of the incident voltage to the incident current wave, or the ratio of voltage to current as the line is non-reflective

input impedance

2. phase constant phase velocity

=vp =

2

w

=

w vp

wavelength

=

2

1

group velocity

d vg = d

3-4

3. Attenuation constant

4. Ex.3.1. A line operated at 1.6GHz has parameters of L=0.002uH/m, C=0.012pF/m, R=0.015/m and G=0.1mS/m, Find Z, Y and Z0

3-5

5. Ex.3.2 Signal source is at 100MHz and v p = 2.5 108 m / s , find v(z,t), i(z,t)

6. Ex.3.3 A line has parameters R=2/m, G=0.5mS/m, L=8nH/m, and C=0.23pF/m. Operation frequency is 1GHz. Find Z0 and

3-6

7. Ex.3.4 Antenna A and B are exited through a 50 line to give current IA and IB. Find Z0, matching element reactance

3-7

3.2 Sending end impedanceBasics 1. Standing wave solution

2. Input impedance at z=0

3. Input impedance at z=l

3-8

4. Input impedance

5. Reflection coefficient

3-9

Discussion 1. Lossless line =0 (R=G=0)

3-10

2. Low loss line R