1. Determining Input Impedance of given lumped circuit elements with TL segments.
A lossless TL, with a characteristic load impedance of ZL=100+j75Ω is shown below. Calculate the input impedance if the L-C circuit shown is inserted at a point 0.12λ away from the load end. Use Smith Chart and show the impedances or admittances at Load, A, B, C points with clear explanations for each, leading to a calculation of the input impedance Zin.

6. From the beginning

7. Determining Input Impedance of given lumped
circuit elements connected arbitrarily.
On a Smith Chart, obtain and show all the impedance values at points
a, b, c, d and Zin of the circuit below at the frequency operation of f=2GHz. d c b a

8. a b za=31.25/50=0.625 ya=1/0.625=1.6 BcL=ωcL=24 mS bcL=50BcL =1.2
yb=1.6+j1.2
za=0.625
ya=1.6
zb=0.4-j0.3
BcL=ωcL=24 mS
bcL=50BcL =1.2
yb=1.6+j1.2
Zb=0.4-j0.3
Normalized by 50

9. d c b a xL1=ωL1/50=1.1 zc=0.4+j0.8 yc=0.5-j1.0 bc=50ωc=1.5
yd=0.5+j0.5
bc=50ωc=1.5
yd=0.5+j0.5
zd=1-j1
yin=zin=1.0
zd=1.0-j1.0
xL2=ωL2/50=1
zin=yin=1
yc=0.5-j1.0
Normalized by 50

10. Find the input impedance in terms of magnitude and phase of the following network at an operating frequency of 950 MHz.
Z0=50

11. 0.1 λ
zR=75/50=1.5
yR=1/1.5=0.667
z= j1.6292
xL=ωL/50=23.88/50
xL =0.4775
bL=-2.094
yL=0.667-j2.094
zL= j0.4336
zL= j0.4336
z= j0.1580
zR=1.5
yR=0.667
Move from toward
generator 0.1λ
y= j0.5720
z= j1.6292
y= j0.5720
yL=0.667-j2.094
zR=30/50=0.6
yR=1/0.6=1.66
y= j0.5720
z= j0.1580
y= j0.5720

12. Continued from Go 0.25λ toward generator to find: z=1.8146-j0.57191
0.25 λ
Go 0.25λ toward generator to find:
z= j
y= j0.1580
Note: a 0.25λ TL is the same as
changing from impedance
to admittance or vice versa
A 0.1 λ shorted TL
has an input impedance of:
z= j
y= -j1.3764
y= j1.2184
z= j0.7019
y= j0.1580
z= j0.1580
z= j
As in case:
z= j1.2184
zin = j2.8937
y= j1.2184
z= j1.2184
xc=-1/50ωc=
zin= j2.8937
50Zin= j144.69

13. Single Stub matching network design with fixed characteristic impedances
For a load impedance of ZL=(60-j45)Ω, design two single-stub matching networks that transform the load to a Zin=(75+j90)Ω input impedance. Assume that both stub and transmission line shown below have a chracteristic impedance of Z0=75Ω.

14. Try to move the load admittance to SWR circle of input impdance
by adding the admittance
of the stub.
The two possibilities
for the susceptance
value of the stub are:

15. The two other possibilities are made by using short circuit stubs
With open circuit
Reactances are:
The two lengths are:
lSA,o=
=0.067λ
lSB,o=
=0.337λ
The two other possibilities are made by using short circuit stubs

16. Design of a double-stub matching network
It is assumed that in the double-stub matching network seen below, the lengths of the TLs are l1=λ/8 and l3=l2=3λ/8. Find the lengths of the short circuited stubs that match the load impedance ZL=(50+j50)Ω to a 50Ω input impedance. The chracteristic line impedance for all components is Z0=50Ω

18. MAKE SURE THAT YD IS NOT INSIDE THE FORBIDDEN REGION
The difference between YD
and YC is:
Forbidden
Region
Therefore the length of
first stub is lS1 = 0.074λ.
The difference between YB
and YA is:
Therefore the length of
second stub is lS2 = 0.051λ.