Microwave Network Analysis

1
Chapter 4

• Microwave Network Analysis

2
Equivalent Voltage and Current

• For non-TEM lines, the quantities of voltage,
  current, and impedance are not unique, and are
  difficult to measured. Following considerations
  can provide useful result
• 1) Voltage and current are defined only for a
  particular mode, and are defined so that the
  voltage is proportional to the transverse
  electric field, and the current is proportional
  to transverse magnetic field.
• 2) The product of equivalent voltage and current
  equals to the power flow of the mode.
• 3) The ratio of the voltage to the current for a
  single traveling wave should be equal to the
  characteristic impedance of the line. This
  impedance is usually selected as equal to the
  wave impedance of the line.

3
The Concept of Impedance

• Various types of impedance
• 1) ?(?/?)1/2 intrinsic impedance of medium.
  This impedance is dependent only on the material
  parameters of medium, and is equal to the wave
  impedance of plane wave.
• 2) ZwEt /Ht1/Yw wave impedance, e.g. ZTEM,
  ZTM, ZTE. It may depend on the type of line or
  guide, the material, and the operating frequency.
• 3) Z0 (L /C)1/2 1/Y0 characteristic
  impedance. It is the ratio of voltage to current.
  The characteristic impedance is unique definition
  for TEM mode but not for TM or TE modes.
• The real and imaginary parts of impedance and
  reflection coefficient are even and odd in ?0
  respectively.

4
Impedance and Admittance Matrices

• The terminal plane (e.g. tN) is important in
  providing a phase reference for the voltage and
  current phasors.
• At the nth terminal (reference) plane, the
  relations are given as

• Reciprocal Networks

• If the arbitrary network is reciprocal ( no
  active devices, ferrites, or plasmas), Y and
  Z are symmetric matrices .

5

• Lossless Networks

• If the arbitrary network is lossless, then the
  net real power delivered to the network must be
  zero. Thus

Example4.1 Find the Z parameters of the two-port
network?
Solution
6
The Scattering Matrices

• The scattering parameter Sij is the transmission
  coefficient from j port to port i when all other
  ports are terminated in matched loads.

• Z or Y ? S

• S ? Z

7
Example4.2 Find the S parameters of the 3 dB
attenuator circuit?
Solution
A matched 3B attenuator with a 50 O
Characteristic impedance
8

• Reciprocal Networks

• Lossless Networks

• No real power delivers to network.Besides

• S is symmetric matrix

Example4.3 Determine if the network is
reciprocal, and lossless? If port 2 terminated
with a matched load, what is the return loss at
port 1? If port 2terminated with a short circuit,
what is the return loss seen at port 1?
Solution

• Since S is not symmetric, the network is not
  reciprocal.

• So the network is not lossless.

9
When port 2 terminated with a matched load,
?S110.15.
When port 2 terminated with a short circuit,
10
Summary

• Reciprocal Networks (symmetric)
• No active elements, no anisotropic material

• Lossless Networks
• No resistive material, no radiation