radio frequency engineering - guceee.guc.edu.eg › courses › communications › comm603...
TRANSCRIPT
GUC (Dr. Hany Hammad) 1/31/2016
COMM (603) Lecture #1 1
Radio Frequency Engineering
Associate Prof. Hany Hammad
Why Use Network Analysis?
• Objectives:
– Equivalent circuit that is open to all the tools of the circuit analysis.
• Reasons:
– Maxwell’s equations are much more difficult and provide more information than we need.
– We are only interested signal flow and the voltage and current at a set of terminals.
© Dr. Hany Hammad, German University in Cairo
GUC (Dr. Hany Hammad) 1/31/2016
COMM (603) Lecture #1 2
When to apply microwave network anlysis?
• Circuit dimensions << wavelength
– Lumped passive and active components.
– Negligible phase change throughout the circuit.
– Circuit theory (Kirchoff’s and Ohms laws)
• Circuit dimensions ~ wavelength
– Distributed passive and active components.
– Phase depends on position. Components are characterized by their dimensions, propagation constant and characteristics impedance.
© Dr. Hany Hammad, German University in Cairo
© Dr. Hany Hammad, German University in Cairo
Impedance parameters
2121111 IZIZV
2221212 IZIZV
2
1
2221
1211
2
1
I
I
ZZ
ZZ
V
V
01
111
2
II
VZ
IZV
01
221
2
II
VZ
02
112
1
II
VZ
02
222
1
II
VZ
Open Circuit
Linear
Network
1I
1V+
_ Port-1
2I
2V+
_ Port-2
Linear
Network
1I
1V Port-1
02 I
2V+
_ Port-2
+
Linear
Network
01 I
1V+
_ Port-1
2I
2VPort-2 +
GUC (Dr. Hany Hammad) 1/31/2016
COMM (603) Lecture #1 3
© Dr. Hany Hammad, German University in Cairo
Example 1
Find the impedance parameters for the two port network shown in Figure.
6
01
111
2
II
VZ
6
01
221
2
II
VZ
6
02
112
1
II
VZ
6
02
222
1
II
VZ
Ans.:
66
66
2221
1211
ZZ
ZZ
+
V1
+
V2
I1 I2
6
V1
+
V2
I1
6+
+
V1
V2
I2
6 +
© Dr. Hany Hammad, German University in Cairo
Example 2
Find the impedance parameters for the two port network shown in Figure.
Ans.:
12
01
111
2
II
VZ
0
01
221
2
II
VZ
0
02
112
1
II
VZ
3
02
222
1
II
VZ
30
012
2221
1211
ZZ
ZZ
21 3I1 I2
+
V1
+
V2
21 3I1
V1
+
V2
+
21 3
V2 V1 +
+
I2
GUC (Dr. Hany Hammad) 1/31/2016
COMM (603) Lecture #1 4
© Dr. Hany Hammad, German University in Cairo
Example 3
Find the impedance parameters for the two port network shown in Figure.
18
01
111
2
II
VZ
6
01
221
2
II
VZ
6
02
112
1
II
VZ
9
02
222
1
II
VZ
96
618
2221
1211
ZZ
ZZ
Ω12 3I1 I2
+
V1
+
V2
6
Ans.:
Ω12 3I1
+
V2
6V1 +
+
V1
Ω12 3
6 V2
+
© Dr. Hany Hammad, German University in Cairo
Example 3 (another technique)
2121111 IZIZV 2221212 IZIZV
2121111 IZIZV 2221212 IZIZV
211111111121211121211111 IZZIZZIZIZIZIZVV
222221212122212122212122 IZZIZZIZIZIZIZVV
2
1
22222112
12121111
22
11
I
I
ZZZZ
ZZZZ
VV
VV
Find the impedance parameters for the two port network shown in Figure.
Ans.:
96
618
2221
1211
ZZ
ZZ
Ω12 3I1 I2
+
V1
6
+
V2
Ω12 3I1 I2
+
V1
6
+
V2
+
+
+
1V
1V
2V
2V
GUC (Dr. Hany Hammad) 1/31/2016
COMM (603) Lecture #1 5
© Dr. Hany Hammad, German University in Cairo
Find the impedance parameters for the two port network shown in Figure.
Ans.:
ljZ
ljZ
Z
lZ
Zj
ZljZZ
ljZZZ
I
VZ o
L
o
L
o
o
Lo
oLoin
cot
tan
tan1
tan
tan
1
1
01
111
2
II
VZ LZ
or
zj
o
zj
o eVeVV
zj
o
zj
o
o
eVeVZ
I 1
z = 0
ljlj
o
lj
o
lj
o eeVeVeVV 1
ljlj
o
olj
o
lj
o
o
eeZ
VeVeV
ZI
11
oo VVLZ
oZ
l
+
V1
+
V2
I1 I2
+
1
o
o
V
V
= 0
= 0
Note: it is symmetrical
Open Circuit
(Open Circuit)
lz
lz
o
o
o
oo
I
V
I
VZ
Example 4
© Dr. Hany Hammad, German University in Cairo
Example 4
ljlj
o
lj
o
lj
o eeVeVeVV 1
ljlj
o
olj
o
lj
o
o
eeZ
VeVeV
ZI
11
11
1
1 cotsin2
cos2ZljZ
lj
lZ
ee
eeZ
I
Vooljlj
ljlj
o
01
221
2
II
VZ
ooo VVVV 22
lj
o
lj
o
o
eVeVZ
I 1
1
oo VV
l
jZ
lj
Z
eeV
ZVZ oo
ljlj
o
oo
sinsin2
2221
1221 ZZ 2211 ZZ
1
ljZl
jZl
jZljZ
oo
oo
cotsin
sincot
Since
GUC (Dr. Hany Hammad) 1/31/2016
COMM (603) Lecture #1 6
© Dr. Hany Hammad, German University in Cairo
Admittance Parameters
2121111 VYVYI
2221212 VYVYI
2
1
2221
1211
2
1
V
V
YY
YY
I
I
01
111
2
VV
IY
VYI
01
221
2
VV
IY
Linear
Network
1I
1V+
_ Port-1
2I
2V+
_ Port-2
Linear
Network
1I
1V Port-1
2I
02 V+
_ Port-2
+
02
112
1
VV
IY
02
222
1
VV
IY Linear
Network
1I
01 V Port-1
2I
2V+
_ Port-2
+
© Dr. Hany Hammad, German University in Cairo
Example 5
Find the admittance parameters for the two port network shown in Figure.
Ans.:
05.0
01
111
2
VV
IY
05.0
01
221
2
VV
IY
05.0
02
112
1
VV
IY
05.0
02
222
1
VV
IY
21 II
05.005.0
05.005.0
S05.0I1 I2
+
V1
+
V2
S05.0I1 I2
V1
V2=0 +
S05.0I1 I2
+
V1=0 V2
GUC (Dr. Hany Hammad) 1/31/2016
COMM (603) Lecture #1 7
© Dr. Hany Hammad, German University in Cairo
Example 6
Find the admittance parameters for the two port network shown in Figure.
Ans.:
0692.01.0025.02.0
1.0)025.02.0(
01
111
2
VV
IY
0615.0)889.0(0692.01
2
1
1
01
221
2
I
I
V
I
V
IY
V
112 889.0540
40III
S1.0 S2.0
S025.0
I1
+
V1
I2
+
V2
Current divider
S1.0 S2.0
S025.0
I1
V1
I2
+
V2=0
+
2.01025.01
© Dr. Hany Hammad, German University in Cairo
Example 6
121 8.01040
40III
0615.08.00769.02
1
2
2
02
112
1
I
I
V
I
V
IY
V
0769.02.0025.01.0
2.0)025.01.0(
02
222
1
VV
IY
0769.00615.0
0615.00692.0
2221
1211
YY
YY
S1.0 S2.0
S025.0
I1
V1=0
I2
+
V2
+
GUC (Dr. Hany Hammad) 1/31/2016
COMM (603) Lecture #1 8
© Dr. Hany Hammad, German University in Cairo
Example 7
Find the admittance parameters for the two port network shown in Figure.
ans.:
1269.01115.0
1115.01192.0
2221
1211
YY
YY
S1.0 S2.0
S025.0
I1
+
V1
I2
+
V2
S05.0
S1.0 S2.0
S025.0
I1
+
V1
I2
+
V2
S05.01I
1I
2I
2I
2
1
22222121
12121111
2
1
2221
1211
2
1
V
V
YYYY
YYYY
V
V
YY
YY
I
I
© Dr. Hany Hammad, German University in Cairo
Admittance Parameters
2121111 VYVYI
2221212 VYVYI
2121111 VYVYI
2221212 VYVYI
2121211111111 VYYVYYIII
2222212121222 VYYVYYIII
2
1
22222121
12121111
2
1
2221
1211
2
1
V
V
YYYY
YYYY
V
V
YY
YY
I
I
GUC (Dr. Hany Hammad) 1/31/2016
COMM (603) Lecture #1 9
© Dr. Hany Hammad, German University in Cairo
Hybrid Parameters
2121111 VhIhV
2221212 VhIhI
2
1
2221
1211
2
1
V
I
hh
hh
I
V
01
111
2
VI
Vh
01
221
2
VI
Ih
02
112
1
IV
Vh
02
222
1
IV
Ih
Linear
Network
1I
1V+
_ Port-1
2I
2V+
_ Port-2
Are especially important in transistor circuit analysis.
(dimensionless)
(dimensionless)
()
(Siemens)
(Input impedance) (forward current gain)
(reverse voltage gain)
(Output admittance)
© Dr. Hany Hammad, German University in Cairo
Example 8
Find the hybrid parameters for the two port network shown in Figure.
ans.:
14129
63
01
111
2VI
Vh
3
2
36
6
01
221
2
VI
Ih
3
2
36
6
02
112
1
IV
Vh
SV
Ih
I9
1
02
222
1
2
1
2
1
9
1
3
23
214
V
I
I
V
S
12 3
6
I1
+
V1
I2
+
V2
12 3
6
I1
V1
I2
+
V2
+
12 3
6
I1 I2
V2 +
GUC (Dr. Hany Hammad) 1/31/2016
COMM (603) Lecture #1 10
© Dr. Hany Hammad, German University in Cairo
Transmission Parameters
221 BIAVV
221 DICVI
221 BIAVV
221 DICVI
2
2
1
1
I
V
DC
BA
I
V
2
2
1
1
I
V
DC
BA
I
V
Linear
Network
1I
1V+
_ Port-1
2I
2V+
_ Port-2
Linear
Network
1I
1V+
_ Port-1
2I
2V+
_ Port-2
© Dr. Hany Hammad, German University in Cairo
Transmission Parameters
02
1
2
IV
VA
221 BIAVV
221 DICVI
02
1
2
VI
VB
02
1
2
IV
IC
02
1
2
VI
ID
Linear
Network
1I
1V+
_ Port-1
2I
2V+
_ Port-2
Linear
Network
1I
1V Port-1
02 I
2V+
_ Port-2
+
Open Circuit
Linear
Network
1I
1V Port-1
2I
2VPort-2 +
GUC (Dr. Hany Hammad) 1/31/2016
COMM (603) Lecture #1 11
© Dr. Hany Hammad, German University in Cairo
Example 9
Find the transmission parameters for the two port network shown in Figure.
Ans.:
1
02
1
2
IV
VA
1
02
1
2VI
VB
SV
IC
I
0
02
1
2
1
02
1
2
VI
ID
10
11
DC
BA
1I1 I2
+
V1
+
V2
1I1 I2
+
V2
1V +
1I1 I2
+
V2=0
1V +
© Dr. Hany Hammad, German University in Cairo
Example 10
Find the transmission parameters for the two port network shown in Figure.
Ans.:
1
02
1
2
IV
VA
0
02
1
2
VI
VB
SjV
IC
I
02
1
2
1
02
1
2
VI
ID
1
01
jDC
BA
+
V1
+
V2
Sj
I1 I2
V1
+
V2
Sj
I1 I2
+
V1
+
V2=0
Sj
I1 I2
+
GUC (Dr. Hany Hammad) 1/31/2016
COMM (603) Lecture #1 12
© Dr. Hany Hammad, German University in Cairo
Example 11
Find the transmission parameters for the two port network shown in Figure. Ans.:
2
2
1
1
10
11
I
V
I
V
2
2
1
1
1
01
I
V
jI
V
2
2
1
1
10
11
I
V
I
V
2
2
1
1
10
11
1
01
10
11
I
V
jI
V
2
2
1
1
1
21
I
V
jj
jj
I
V
1I1 I2”
+
V1
+
V2”
1
j
1I 2I
1 V
2 V
1I
j
2 I
2 V
1 V
1I 2I
1 V
2 V
2
2
1
11
10
11
I
V
jj
© Dr. Hany Hammad, German University in Cairo
Transmission Parameters
Microwave Engineering, 3rd Edition by David M. Pozar
Copyright © 2004 John Wiley & Sons
GUC (Dr. Hany Hammad) 1/31/2016
COMM (603) Lecture #1 13
© Dr. Hany Hammad, German University in Cairo
Z, Y & ABCD
Z
Z
Y
Y
DABC DABC
© Dr. Hany Hammad, German University in Cairo
Conversion between different parameters
2
1
2221
1211
2
1
V
V
YY
YY
I
I
1121
1222
21122211
1
2221
1211
2221
1211 1
ZZ
ZZ
ZZZZZZ
ZZ
YY
YY
YZ
One type of network parameter can be converted into another via the respective equations. Conversion between the impedance and admittance parameters.
2
1
1
2221
1211
V
V
ZZ
ZZ
GUC (Dr. Hany Hammad) 1/31/2016
COMM (603) Lecture #1 14
© Dr. Hany Hammad, German University in Cairo
Conversion between different parameters
YABCD
221 BIAVV
221 DICVI
212
1V
B
AV
BI
212221
1V
B
AV
BDCVDICVI
211 VB
BCADV
B
DI
B
A
B
B
BCAD
B
D
YY
YY
12221
1211
Conversion between the transmission and admittance parameters
© Dr. Hany Hammad, German University in Cairo
Reciprocity
• A network us reciprocal if a zero impedance source and a zero impedance ammeter can be placed at any locations in a network and their positions interchanged without changing the ammeter reading.
• Accordingly, as a consequence of reciprocity, for the Z matrix description of a reciprocal network.
2112 ZZ 2112 YY
2221
1211
YY
YY
2221
1211
ZZ
ZZ
GUC (Dr. Hany Hammad) 1/31/2016
COMM (603) Lecture #1 15
© Dr. Hany Hammad, German University in Cairo
Multiple Port Networks
NNNN
N
N V
V
V
YY
Y
YYY
I
I
I
2
1
1
21
11211
2
1
NNNN
N
N I
I
I
ZZ
Z
ZZZ
V
V
V
2
1
1
21
11211
2
1
jkforIj
iij
k
I
VZ
0
jkforVj
iij
k
V
IY
0Microwave Engineering, 3rd Edition
by David M. Pozar Copyright © 2004 John Wiley & Sons
© Dr. Hany Hammad, German University in Cairo
Scattering parameters (S-parameters)
• Z, Y, and ABCD parameters are very difficult to determine at radio and microwave frequencies.
• The scattering matrix (S-parameters) is to be employed at these frequencies.
ia is an incident wave at port i.
ib is a reflected wave at port i.
2121111 aSaSb
2221212 aSaSb
2
1
2221
1211
2
1
a
a
SS
SS
b
b aSb
Scattering Matrix
ijS is the scattering parameters
Two-port
Network Port-1
1aPort-2
1b
2a
2b
GUC (Dr. Hany Hammad) 1/31/2016
COMM (603) Lecture #1 16
© Dr. Hany Hammad, German University in Cairo
Scattering parameters (S-parameters)
01
111
2
aa
bS 0( 2 a Port 2 is matched)
01
221
2
aa
bS
0( 1 a Port 1 is matched) 02
112
1
aa
bS
02
222
1
aa
bS
iiS is the reflection coefficient i at the ith port when the
other port is matched terminated.
ijSis the forward coefficient i of the jth port if i is greater
than j, whereas it represents the reverse transmission coefficient if i is less than j with the other port terminated by a matched port.
© Dr. Hany Hammad, German University in Cairo
Scattering parameters (S-parameters)
• The steady state total voltage and current at the ith port is given by:
oioii VVV oioi
oi
oioii VVZ
III1
Incident
Reflected
iiioi IZVV 02
1 iiioi IZVV 0
2
1
2*
*
2
1Re
2
1Re
2
1
oi
oioi
oioioioii V
ZZ
VVIVP
2*
*
2
1Re
2
1Re
2
1
oi
oioi
oioioioii V
ZZ
VVIVP
Incident Reflected
oi
oi
oi
oioi
I
V
I
VZ
Note:
Objective: Try to find an expression for ai and bi in term of the incident and reflected voltage and currents
Solving the last two equations for reflected
and incident voltages
Incident power at port i
Reflected power at port i
GUC (Dr. Hany Hammad) 1/31/2016
COMM (603) Lecture #1 17
© Dr. Hany Hammad, German University in Cairo
Scattering parameters (S-parameters)
ioi
oi
i
oi
ioii
oi
oii IZ
Z
V
Z
IZV
Z
Va
22
1
22
1
2
ioi
oi
i
oi
ioii
oi
oii IZ
Z
V
Z
IZV
Z
Vb
22
1
22
1
2
ohmampereohm
voltwattba ii .&
2
11
aPP avsi
i
2
11
bPP refi
i
(Power available from the source)
(Power reflected from port1)
2
1
2
1 baPPP refavsdel (Power delivered to the port)
© Dr. Hany Hammad, German University in Cairo
Evaluating the values of S-parameters
01
111
2
aa
bS
01
221
2
aa
bS
1
1111
22
1
o
o
Z
IZVa
2
2222
22
1
o
o
Z
IZVb
022
1
2
2222
o
o
Z
IZVa 222 IZV o
2
222
2
222
222
2
2
1
o
o
o
o
Z
VZI
Z
IZb
1
11
22 o
S
Z
Va
11
01
1
11
111
2
Sa
b
ZZ
ZZ
ao
o
2
1
1
2
1
1
2
2
01
221
222
22
o
o
SS
o
oaZ
Z
V
V
V
Z
Z
V
a
bS
1SV
11 os ZZ
2oZ
1V
inputZZ 1
Two Port Network Device
2V
1I 2I
2oZ1oZ
?
From Previous Lecture
GUC (Dr. Hany Hammad) 1/31/2016
COMM (603) Lecture #1 18
© Dr. Hany Hammad, German University in Cairo
Evaluating the values of S-parameters
1
2
2
1
02
112
2
1o
o
SaZ
Z
V
V
a
bS
22
02
2
22
222
1
Sa
b
ZZ
ZZ
ao
o
2SV
22 os ZZ
1V
ouputZZ 2
Two Port Network Device
2V
1I 2I
2oZ1oZ1oZ
Same analysis as previous slide
© Dr. Hany Hammad, German University in Cairo
o
o
S ZZ
ZZ
V
V
21
1
o
o
ZZ
Z
V
V
1
2
Example
Find the S-parameters of a series impedance Z connected between the two ports.
Answer:
ooo
oo
ZZ
Z
ZZZ
ZZZS
211
Z
Zo Zo
Z
Zo Zo Zo V2 V1
Zo
VS
?11 S
?21 S1
2
1
221
2
o
o
S Z
Z
V
VS
01112
a
S
11
11
012
o
o
a ZZ
ZZ
1
1
1
2
1
2
SS V
V
V
V
V
V
12 oo ZZ 1
o
o
ZZ
ZS
2
221
GUC (Dr. Hany Hammad) 1/31/2016
COMM (603) Lecture #1 19
© Dr. Hany Hammad, German University in Cairo
Example
o
o
ZZ
ZS
2
212
11
11
2221
1211
1
1
SS
SS
ooo
oo
o
o
a
ZZ
Z
ZZZ
ZZZS
ZZ
ZZS
222
22
22
02221
Z
Zo Zo V2 V1
Zo
VS Zo
Same analysis as previous slide (Symmetry)
oZZ
ZS
222
1
2
2
1
02
112
2
1o
o
SaZ
Z
V
V
a
bS
211212
21 SS
ZZ
Z
o
o
Note:
© Dr. Hany Hammad, German University in Cairo
Reciprocal Networks and Lossless Networks
The impedance and admittance matrices are: • Symmetric for reciprocal networks. • Purely imaginary for lossless networks.
For Scattering parameters the S-parameters are symmetrical if: And Lossless if the matrix is unitary: In terms of Scattering matrix this can be written as:
jiij SS Symmetrical Matrix
1 AAT
The conjugate Transpose
The Inverse
otherwise
kjifSS
N
i
ikij
0
1
1
* Unitary Matrix “lossless”
1AAT
GUC (Dr. Hany Hammad) 1/31/2016
COMM (603) Lecture #1 20
© Dr. Hany Hammad, German University in Cairo
Verification
oZjX
jX
21
If in the previous example if show that the matrix is Unitary
22
2
21
2
112
12 oo ZjX
jX
ZjX
jXSS
022
2
2
2
2
*
2221
*
1211
oo
o
o
o
o ZjX
jX
ZjX
Z
ZjX
Z
ZjX
jXSSSS
12
2
222
2
22
2
o
o
o ZX
Z
ZX
X
02
2
222
2*
2122
*
1112
o
o
ooo
o
ZjX
Z
ZjX
jX
ZjX
jX
ZjX
ZSSSS
otherwise
kjifSS
N
i
ikij
0
1
1
*
11
11
2221
1211
1
1
SS
SS
12
22
2
12 SSalso
jXZ
Unitary Matrix “lossless”
© Dr. Hany Hammad, German University in Cairo
Verification
• It can be done in a simpler way:
– The dot product of any column of [S] with the conjugate of that column gives unity.
– The dot product of any column with the conjugate of a different column gives zero (orthogonal).
2221
1211
SS
SS
0*
2221
*
1211 SSSS
12
21
2
11 SS
GUC (Dr. Hany Hammad) 1/31/2016
COMM (603) Lecture #1 21
© Dr. Hany Hammad, German University in Cairo
Multiport Networks
NNNN
N
N a
a
a
SS
S
SSS
b
b
b
2
1
1
21
11211
2
1
jkforaj
iij
k
a
bS
0
Microwave Engineering, 3rd Edition by David M. Pozar
Copyright © 2004 John Wiley & Sons
© Dr. Hany Hammad, German University in Cairo
Conversion between different parameters
Microwave Engineering, 3rd Edition by David M. Pozar
Copyright © 2004 John Wiley & Sons
GUC (Dr. Hany Hammad) 1/31/2016
COMM (603) Lecture #1 22
© Dr. Hany Hammad, German University in Cairo
Network Analyzer
R&S® ZVB Vector Network Analyzer
(20 GHz & 4 ports)
http://www2.rohde-schwarz.com/en