1. ELEC 401 MICROWAVE ELECTRONICS Microwave Networks - Parameters
Instructor: M. İrşadi Aksun
Acknowledgements:
Art work on most of the illustrations, and most examples have been taken from the following book:
RF Circuit Design, by R. Ludwig and G. Bogdanow
Pearson Int. Ed., 2009

2. Outline
Chapter 1: Motivation & Introduction
Chapter 2: Review of EM Wave Theory
Chapter 3: Plane Electromagnetic Waves
Chapter 4: Transmission Lines (TL)
Chapter 5: Microwave Network Characterization
Chapter 6: Smith Chart & Impedance Matching
Chapter 7: Passive Microwave Components

3. Microwave Network Characterization
Linear network analysis methods are the fundamental topics in RF and Microwave circuit design
Microwave passive and active networks can be classified as multiport or N-port networks
Example: Voltage and current sources, antennas

4. Microwave Network Characterization
I - Impedence parameters:
- Z is called Impedence Matrix (parameters), or open-circuit parameters
- Currents are independent parameters; Voltages are dependent parameters

5. Microwave Network Characterization
II - Admittance parameters:
- Y is called Admittance Matrix (parameters), or short-circuit parameters
- Voltages are independent parameters; Currents are dependent parameters

6. Microwave Network Characterization
Some properties of Z- and Y-parameters:
In general, & may be complex, leading to 2 independent quantities for an arbitrary N-port network.
In practice, many networks are either reciprocal or lossless, or both:
Reciprocity
Lossless
& are purely imaginary

7. Microwave Network Characterization
Reciprocal Networks:

8. Microwave Network Characterization
Lossless Networks:
Total Complex Power =
Since are independents, one can set them to any values.
Let for all i except n
All diagonal entries are imaginary
Let for all i except m and n
All entries are imaginary

9. Microwave Network Characterization
Example: Find Z-parameters of the following network

10. Microwave Network Characterization
Interconnecting Networks: Series Connection
Note that individual networks may not be connected indiscriminately.

11. Microwave Network Characterization
Interconnecting Networks: Parallel Connection
Note that individual networks may not be connected indiscriminately.

12. Microwave Network Characterization
Example: Describe the common-emitter BJT transistor in terms of its hybrid network parameters for the low frequency, small signal transistor model shown below.

13. Microwave Network Characterization
III – ABCD Parameters + +

15. Microwave Network Characterization

16. Microwave Network Characterization
Example: Derive the relation between the elements of Z matrix and those of the ABCD matrix. C D A B

17. Microwave Network Characterization
Example: Determine the input impedance and voltage gain of a two-port network, whose Z-parameters are given by manufacturer, when terminated in a load impedance
For 2-port network:
For load:
Solving them together

18. Microwave Network Characterization
IV – S-Parameters or Scattering Parameters
It is difficult to define voltages and currents for non-TEM lines
A practical problem exists when trying to measure voltages and currents at microwave frequencies
Direct measurements at high frequencies usually involve the magnitude and phase of a wave traveling in a given direction
A representation more in accord with direct measurements, and with the ideas of incident, reflected and transmitted waves, is given by the Scattering matrix
Like the impedance or admittance matrices for an N-port network, the S matrix provides a complete description of the network as seen at its N ports.

19. Microwave Network Characterization
For an N-port network
How can we achieve ?
What does mean?
matched Port-k or what?

20. Microwave Network Characterization
Notes:
is the incident voltage wave at port-i
is the reflected voltage wave from port-i
is the reflection coefficient seen looking into port-i when all ports are terminated in a reference load
is the transmission coefficient from port-j to port-i, when all other ports are terminated in reference impedance

21. Microwave Network Characterization
There are two approaches to answer the question of how we can achieve :
Assume that one uses TLs at the ports, and the voltage waves are defined in the TLs, as shown in the following figure. If

22. Microwave Network Characterization
Assume that the ports are terminated in reference impedance, as shown below, to measure the s-parameters.

23. Microwave Network Characterization
Example: Find the S-parameters (as referenced to 50W) of the 3-dB attenuator circuit shown in the following figure:
For

24. Microwave Network Characterization
Example (Cont’ed):
Due to the symmetry of the circuit

25. Microwave Network Characterization
Example: Determine S-Matrix from Z-matrix
Let us first assume that the characteristic (reference) impedance of all the ports are identical , and unity.
Note that for a one-port network

26. Microwave Network Characterization
S-parameters for reciprocal networks
Note that [Z] and [Y] matrices are symmetric for reciprocal networks
[S] is a symmetric matrix

27. Microwave Network Characterization
S-parameters for lossless networks
Note that [Z] and [Y] matrices are purely imaginary for lossless network
[S] is a UNITARY matrix

28. Microwave Network Characterization
Example: A certain two-port network is measured and the following [S] matrix obtained
From this data,
determine whether the network is reciprocal or lossless;
what will be the resulting return loss at port-1 if a short circuit is placed on port-2 ?
[S] is symmetric Network is reciprocal
Network is not lossless
Return Loss

29. Microwave Network Characterization
Example: A shift in reference plane. Find [S’] in terms of [S].
Note that

30. Microwave Network Characterization
Example: Find the input impedance of a two-port network when terminated in a load impedance.

31. Microwave Network Characterization
Example: Define two-port power gains in terms of the given quantities.
1. Power Gain is the ratio of power dissipated in the load to the power delivered to the input of the 2-port network.