This document provides information about RF and microwave engineering: 1. It defines radio frequency as any electromagnetic wave frequency between 3KHz to 300GHz, which includes frequencies used for communications and radar signals. Microwaves are defined as electromagnetic waves between 300MHz to 300GHz. 2. Microwave engineering deals with the design of communication, navigation, and other systems that operate in the microwave frequency range. Key applications discussed include microwave ovens, radar, satellite communication, and TV. 3. Analysis of microwave circuits differs from low frequency circuits as the physical length of components is larger than signal wavelengths. S-parameters are used to relate the amplitude of scattered waves to incident waves in microwave circuit analysis.

1. RF and Microwave
Engineering
Mrs. V.SrirengaNachiyar
Ramco Institute of Technology
Rajapalayam

2. Radio Frequency
• It is any of the electromagnetic wave frequency that lie in the
range extending from around 3KHz to 300GHz, which include
those frequencies used for communications (or) radar signals
• RF components are
• Antenna,
• Oven
• Circuit elements,
• radio applications
• It is used in digital circuits

3. Introduction
 What is Microwave?
Microwaves are electromagnetic waves of wavelengths
ranging from about 30cm down to about 0.3mm corresponding
frequency range of 109 Hz to 1012 Hz.
 Microwave Engineering deals with Systems operating at these
frequencies.
3

4. Microwave engineering
• Used to design of Communication/navigation systems in the
microwave frequency range
Applications
– Microwave oven
– Radar (RADAR is an electromagnetic system for the detection and
location of target objects such as aircraft, ships, spacecraft, vehicles,
people, and the natural environment which can reflect a signal back).
– Satellite communication
– TV etc.,
• Microwave is a region in the electromagnetic wave spectrum in the
frequency range from 300MHz to 300GHz.
• This corresponds to a range of wavelength from 100cm to 1mm in
frequency space

5. At Microwave frequencies, the conventional electronic
circuits radiate more and more power from the circuit.
New Circuit techniques for handling signals in this
frequency are needed.
Increasing frequency to microwave range is the fact that the
propagation time for signals from one point in a circuit to
another becomes comparable with time period of the signal.
5

6. Thus conventional Low frequency circuit analysis
techniques based on KVL and KCL concepts are
inapplicable to microwave circuits.
It becomes necessary to carryout analysis of microwave
circuit in terms of electric and magnetic fields.
6

7. Microwave Frequency Bands in
Radio Spectrum
 The entire Electromagnetic spectrum is broadly classified into two
regions namely
Radio Spectrum – 0 to 300 GHz
Radio frequency Spectrum: 300KHz to 300MHz
Microwave frequency spectrum: 300 MHz to 300 GHz
Optical Spectrum – 300GHz to infinity
 The term Microwave is commonly used to designate frequencies
ranging from 300 MHz to 300GHz and wavelengths in air ranging from
100 cm – 1 mm.
 The word Microwave means very short wave, which is the shortest
wavelength region of the radio spectrum and a part of the
electromagnetic spectrum.
7

8. Electromagnetic Spectrum
8

9. • Relationship between frequency ( ) and wavelength ( )
where c is the speed of light
• Energy of a photon
where h is Planck’s constant



c

hE 
Wavelength

10. IEEE Frequency Band Designations
Band Designator Frequency (GHz)
Wavelength in Free
Space (centimeters)
Radio
wave
Region HF 0.003 to 0.030 10000 to 1000
VHF 0.030 to 0.300 1000 to 100
UHF 0.300 to 1 100 to 30.0
MicrowaveRegion
L band 1 to 2 30.0 to 15.0
S band 2 to 4 15 to 7.5
C band 4 to 8 7.5 to 3.8
X band 8 to 12 3.8 to 2.5
Ku band 12 to 18 2.5 to 1.7
K band 18 to 27 1.7 to 1.1
Ka band 27 to 40 1.1 to 0.75
illimeterwave
Region
V band 40 to 75 0.75 to 0.40
W band 75 to 110 0.40 to 0.27
mm 110 to 300 0.27 to 0.10
Submillimeter
300 to 3000
10

11. Characteristics of Microwave
• Wavelengths are very small
• Pulses are very short – used for distance or time measurement
• Very large BW is available-because it has HF
• Radiation penetrates fog and clouds, travels in straight lines and
give reflection – used for RADAR systems
• It is necessary for communications through satellite – because it
can pass through ionosphere which reflects lower frequency
radio waves
• Microwave Power is absorbed by water (or) any other material
containing water so that microwaves can be used for heating and
drying

12. Advantages of Microwaves
• It does not require a dedication path between stations
• It can carry large quantities of information
• Requires relatively small antennas
• Easily propagates through ionised layers-most suited for satellite
communication
• Transmission distance is large – less no. of repeaters are required
for amplification
• Propagation delay is negligible (or) minimum
• Signal cross talk is eliminated
• Highly reliable systems
• Less maintenance is required

13. Advantages of Microwaves
 High Bandwidth Capability – More information
Capacity
 High antenna Gain – ShortestWavelength
 LOS Propagation – Not affected by ionosphere
 Fading effect and reliability – Due to LOS, less Fading
effects occurs at high frequencies
 Transparency property of microwaves
 Low power requirements
2
4

 eA
G 
13

14. Disadvantages of Microwave
At microwave frequencies, circuit design is complex
Measurement at microwave frequencies are difficult
LOS propagation limits the use of microwave

15. Applications of Microwaves
 Long Distance Communication
 Terrestrial Communication
 Radars
 Defence Applications
 AirTraffic Controlling and Navigation
 Microwave heating
 Microwave oven
 Remote Sensing
 Wireless data Networks
 Astronomy
 Medical Applications
 Heating & detection of foreign bodies in food
15

16. Review of Low Frequency
Parameters
 A Microwave Network is formed when several microwave
devices and components such as Sources, attenuators,
resonators, filters, amplifiers etc are coupled by transmission
lines or waveguides for the desired transmission of a
microwave signal.
 The point of interconnection of two or more devices is called a
Junction.
 In Low Frequency Network, a port is a pair of terminal.
 In a Microwave Network, a port is a reference plan transverse
to the length of the microwave transmission line or waveguide.
16

17. At Low Frequencies, Physical Length of the network is much
smaller than the wavelength of the signal transmitted.
The measureable input and output variables are voltage and
current which can be related interms of the
 Impedance Z-Parameters
 AdmittanceY-Parameters
 Hybrid Parameters
 ABCD Parameters
 These Parameters can be measured under short or open
circuit condition for use in the analysis of the circuit.
17

18. In Microwave frequency, Physical Length of the component
or line is much Larger than the wavelength of the signal
transmitted.
Voltages and currents cannot be uniquely defined at a given
point in a single conductor/waveguide.
18

19. Low Frequency Microwave
Electronic circuits operating at
low frequency, port is a pair of
terminals
Port is a reference plane transverse
to the length of the microwave
transmission line (or) waveguide
Physical length of the network
is smaller than wavelength of
signal transmitted
Physical length of the network is
larger than wavelength of signal
transmitted
Input and Output variables are
measured by voltage and current
Voltage and Current cannot be
uniquely defined at a given point in
a single waveguide
Circuits are analyzed using
Z,Y,H and ABCD parameters
Circuits are analyzed using S
parameters
These parameters may be
measured under Short (or) Open
circuit condition for the analysis
of the circuit
S-parameters linearly relate to the
amplitude of scattered waves with
those of incident waves

20. The measurement of Z-Parameter, Y-Parameter, H-parameter
and ABCD Parameters is difficult at microwave frequencies
due to the following reasons:
 Absence of unique definition of voltage and current
 Short and open circuit are not easily achieved for a wide
range of frequency
 Presence of active devices makes the circuit unstable for
open and short circuit analysis.
20

21. Analysis of Microwave Circuits
• Microwave Circuits are analyzed using Scattering (S-
parameters) which relates the amplitude of scattered waves
(Reflected and transmitted) with those of incident waves.
• For Microwave circuits analysis, S- parameters can be
related to the Z/Y/ABCD Parameters.
21

22. Two Port Networks
Generalities: The standard configuration of a two port:
The NetworkInput
Port
Output
Port
+
_ _
+
V1 V2
I1 I2
The network ?
The voltage and current convention ?
22

23. Two Port Networks
Network Equations:
V1 = z11I1 + z12I2
V2 = z21I1 + z22I2
I1 = y11V1 + y12V2
I2 = y21V1 + y22V2
V1 =AV2 - BI2
I1 = CV2 - DI2
V2 = b11V1 - b12I1
I2 = b21V1 – b22I1
V1 = h11I1 + h12V2
I2 = h21I1 + h22V2
I1 = g11V1 + g12I2
V2 = g21V1 + g22I2
Impedance
Z parameters
Admittance
Y parameters
Transmission
A, B, C, D
parameters
Hybrid
H parameters
23

24. Two Port Networks
Z parameters:
1
1
11 I
V
z 
0
2
I
2
1
12 I
V
z 
0
1
I
1
2
21 I
V
z 
0
2
I
2
2
22 I
V
z 
0
1
I
z11 is the impedance seen looking into port 1
when port 2 is open.
z12 is a transfer impedance. It is the ratio of the
voltage at port 1 to the current at port 2 when
port 1 is open.
z21 is a transfer impedance. It is the ratio of the
voltage at port 2 to the current at port 1 when
port 2 is open.
z22 is the impedance seen looking into port 2
when port 1 is open.
24

25. Two Port Networks
Y parameters:
1
1
11 V
I
y 
0
2
V
2
1
12 V
I
y 
0
1
V
1
2
21 V
I
y 
0
2
V
2
2
22 V
I
y 
0
1
V
y11 is the admittance seen looking into port 1
when port 2 is shorted.
y12 is a transfer admittance. It is the ratio of the
current at port 1 to the voltage at port 2 when
port 1 is shorted.
y21 is a transfer impedance. It is the ratio of the
current at port 2 to the voltage at port 1 when
port 2 is shorted.
y22 is the admittance seen looking into port 2
when port 1 is shorted.
* notes 25

26. Two Port Networks
Z parameters: Example 1
Given the following circuit. Determine the Z parameters.
8
20 20 


10
+
_
+
_
V1 V2
I1 I2
Find the Z parameters for the above network.
26

27. Two Port Networks
Z parameters: Example 1 (cont 1)
For z11:
Z11 = 8 + 20||30 = 20 
For z22:
For z12:
Z22 = 20||30 = 12 
2
1
12 I
V
z 
0
1
I
8
20 20 


10
+
_
+
_
V1 V2
I1 I2
2
2
1 8
3020
2020
xI
xxI
V 


Therefore:
8
8
2
2
12 
I
xI
z  = 21z
27

28. Two Port Networks
Z parameters: Example 1 (cont 2)
The Z parameter equations can be expressed in
matrix form as follows.


















2
1
2
1
128
820
I
I
V
V


















2
1
2221
1211
2
1
I
I
zz
zz
V
V
28

29. Two Port Networks
Hybrid Parameters: The equations for the hybrid parameters are:


















2
1
2221
1211
2
1
V
I
hh
hh
I
V
1
1
11
I
V
h 
V2 = 0
2
1
12
V
V
h 
I1 = 0
1
2
21
I
I
h 
V2 = 0
2
2
22
V
I
h 
I1 = 0
29

30. Interconnection of Two Port Networks
Three ways that two ports are interconnected:
* Parallel
* Series
* Cascade
     ba
yyy 
     ba
zzz 
     ba
TTT 
ya
yb
za
zb
Ta Tb
parametersY
parametersZ
parametersABCD
30

31. Interconnecting Networks: Series Connection
  



















2
1
22
11
2
1
"'
"'
i
i
vv
vv
v
v
Z
      








"''
"'"'
2222"2121
12121111
ZZZZ
ZZZZ
Z"Z'Z
Note that individual networks may not be connected indiscriminately.
31

32. Interconnecting Networks: Parallel Connection
  



















2
1
22
11
2
1
"'
"'
v
v
ii
ii
i
i
Y
      








"'"'
"'"'
22222121
12121111
YYYY
YYYY
Y"Y'Y
Note that individual networks may not be connected indiscriminately.
32

33. III – ABCD Parameters
)(
)(
221
221
iDCvi
iBAvv

 +
+
























2
2
1
1
"
"
""
""
''
''
'
'
i
v
DC
BA
DC
BA
i
v
33

34. Deriving one parameter from other
parameter
34

35. High Frequency Parameters
• The S-parameter is called high frequency parameter
• To characterize any network at microwave frequencies S-
parameters are used
• The S-parameters provide complete description of network
• S-parameters can be converted into other matrix parameters if
needed

36. Formulation of S-parameters
Scattering Matrix:
• It is a square matrix which gives all the combinations of power
relationship between the various input and output port of a
microwave junction
• S-parameters are complex numbers
• S-matrix is a useful analytical technique for studying multiport
microwave networks
• The elements of the scattering matrix are called scattering
coefficients or scattering parameters
• The importance of S-parameter is derived from the fact that
practical system characterizations can no longer be accomplished
through simple open/short circuit measurements

37. • Because, when we attempt to create a short circuit with wire:
the wire itself possess an inductance of substantial magnitude at
high frequency. Also the open circuit leads to capacitive loading
at the terminal
• In either case, the open/short circuit conditions needed to
determine z, h, y and ABCD parameters can no longer be
guaranteed
• S-parameters denote the fraction of incident power reflected at a
port and transmitted to other ports
• The addition of phase information allows the complete
description of any linear circuit

38. S-matrix Representation of Two-port Network:
• The incident and reflected wave amplitudes of microwaves at any
port are used to characterize a microwave circuit
• The amplitudes are normalized in such a way that the square of
any of these variables gives the average power
• Input power at nth port, Pin = ½ l an l2
• Reflected power at nth port, Prn = ½ l bn l2
Where an represent normalized incident wave peak amplitude
bn represent normalized reflected wave peak amplitude at nth
port

39. • The concept of S-parameter may come from the fact that RF and
microwave circuit may contain some discontinuity in the signal
path.
• At discontinuity, the wave scattered in different directions
containing “infinite number of higher order modes”
• These modes attenuated very fast after a short distance from the
point of discontinuity within about a quarter wavelength
• Then, only the executed modes comes out from the different ports.
• All these emerging waves are considered as reflected waves at the
corresponding ports.
• The waves entering the ports are considered the input (or) incident
wave

40. Losses of S-parameters
Insertion loss:
• It is the loss of signal power resulting from the insertion of a
device in a transmission line which is usually described in
decibels(dB).
Attenuation loss (or) Transmission loss:
• It is the measure of the power loss due to signal absorption in the
device
Reflection loss:
• It is the measure of the power loss during transmission due to
the reflection of the signal as a result of impedance mismatch
Return loss:
• It is the measure of the power reflected by a line (or) network
through a line

41. Properties of S-Matrix
• S-matrix [S] is always a square matrix of order (n x n) and its
elements are complex quantities (real and imaginary part)
• [S] is a symmetric matrix (i.e) Sij=Sji
• [S] is a unitary matrix (i.e) [S][S]* = [I]
Where [S]* - Complex Conjugate of [S]
[I] - Unit Matrix (or) Identity matrix of same order as
that of [S]
• Under perfect matched conditions; the diagonal elements of [S]
are zero
• The sum of product of each term of any row (or) column
multiplied by the complex conjugate of the corresponding terms
of any other row ((or) column) is zero
jkforSS ij
n
i
ik 
0*
1

42. References
• Reinhold Ludwig and Gene Bogdanov, “RF Circuit
Design: Theory and Applications”, Pearson Education
Inc., 2011
• Robert E Colin, “Foundations for Microwave
Engineering”, John Wiley & Sons Inc, 2005
• Annapurna Das and Sisir K Das,’ Microwave
Engineering”, Tata Mc Graw Hill Publishing
Company Ltd, New Delhi, 2005