Design a three-section binomial transformer to match a 100Ω load to

Download Report

Transcript Design a three-section binomial transformer to match a 100Ω load to

ELCT564
Spring 2012
Chapter 5: Impedance Matching
and Tuning
4/9/2015
ELCT564
1
Impedance Matching
Maximum power is delivered when the load is matched the line and the power loss
in the feed line is minimized
Impedance matching sensitive receiver components improves the signal to noise
ratio of the system
Impedance matching in a power distribution network will reduce amplitude and
phase errors
Complexity
Bandwidth
Implementation
Adjustability
4/9/2015
ELCT564
2
Matching with Lumped Elements (L Network)
Network for zL inside the 1+jx circle
Network for zL outside the 1+jx circle
Positive X implies an inductor and negative X implies a capacitor
Positive B implies an capacitor and negative B implies a inductor
4/9/2015
ELCT564
3
4/9/2015
ELCT564
4
Matching with Lumped Elements (L Network)
Smith Chart Solutions
Design an L-section matching network to match a series RF load with an impedance
zL=200-j100Ω, to a 100 Ω line, at a frequency of 500 MHz.
4/9/2015
ELCT564
5
ZL=2-j1
yL=0.4+j0.5
B=0.29
X=1.22
B=-0.69
X=-1.22
4/9/2015
ELCT564
6
Matching with Lumped Elements (L Network)
Smith Chart Solutions
4/9/2015
ELCT564
7
Single Stub Tunning
Shunt Stub
G=Y0=1/Z0
Series Stub
4/9/2015
ELCT564
8
Single Stub Tunning
For a load impedance ZL=60-j80Ω, design two single-stub (short circuit) shunt
tunning networks to matching this load to a 50 Ω line. Assuming that the load is
matched at 2GHz and that load consists of a resistor and capacitor in series.
yL=0.3+j0.4
d1=0.176-0.065=0.110λ
d2=0.325-0.065=0.260λ
y1=1+j1.47
y2=1-j1.47
l1=0.095λ
l1=0.405λ
4/9/2015
ELCT564
9
Single Stub Tunning
4/9/2015
ELCT564
10
Single Stub Tunning
For a load impedance ZL=25-j50Ω, design two single-stub (short circuit) shunt
tunning networks to matching this load to a 50 Ω line.
yL=0.4+j0.8
d1=0.178-0.115=0.063λ
d2=0.325-0.065=0.260λ
y1=1+j1.67
y2=1-j1.6
l1=0.09λ
l1=0.41λ
4/9/2015
ELCT564
11
Single Stub Tunning
For a load impedance ZL=100+j80Ω, design single series open-circuit stub
tunning networks to matching this load to a 50 Ω line. Assuming that the load is
matched at 2GHz and that load consists of a resistor and inductor in series.
zL=2+j1.6
d1=0.328-0.208=0.120λ
d2=0.5-0.208+0.172=0.463λ
z1=1-j1.33
z2=1+j1.33
l1=0.397λ
l1=0.103λ
4/9/2015
ELCT564
12
Single Stub Tunning
4/9/2015
ELCT564
13
Single Stub Tunning
4/9/2015
ELCT564
14
Double Stub Tunning
The susceptance of the first stub, b1, moves the load
admittance to y1, which lies on the rotated 1+jb circle; the
amount of rotation is de wavelengths toward the load. Then
transforming y1 toward the generator through a length d of
line to get point y2, which is on the 1+jb circle. The second
stub then adds a susceptance b2.
4/9/2015
ELCT564
15
Double Stub Tunning
Design a double-stub shunt tuner to match a load impedance ZL=60-j80 Ω to a 50 Ω
line. The stubs are to be open-circuited stubs and are spaced λ/8 apart. Assuming
that this load consists of a series resistor and capacitor and that the match frequency
is 2GHz, plot the reflection coefficient magnitude versus frequency from 1 to 3GHz.
yL=0.3+j0.4
b1=1.314
b1 =-0.114
’
y2=1-j3.38
l1=0.146λ
l2=0.204λ
l1’=0.482λ
l2’=0.350λ
y2’ =1+j1.38
4/9/2015
ELCT564
16
Double Stub Tunning
4/9/2015
ELCT564
17
Theory of Small Refelections
4/9/2015
ELCT564
18
Multisection Transformer
Partial reflection coefficients for a multisection matching transformer
4/9/2015
ELCT564
19
Binomial Multisection Matching Transformers
The passband response of a binomial matching transformer is optimum in the sense,
and the response is as flat as possible near the design frequency.
Maximally Flat: By setting the first N-1 derivatives of |Г(θ)| to zero at the frequency.
4/9/2015
ELCT564
20
Binomial Transformer Design
Design a three-section binomial transformer to match a 50Ω load to a 100Ω line, and
calculate the bandwidth for Гm=0.05. Plot the reflection coefficient magnitude versus
normalized frequency for the exact designs using 1,2,3,4, and 5 sections.
4/9/2015
ELCT564
21
Binomial Transformer Design
Design a three-section binomial transformer to match a 100Ω load to a 50Ω line, and
calculate the bandwidth for Гm=0.05. Plot the reflection coefficient magnitude versus
normalized frequency for the exact designs using 1,2,3,4, and 5 sections.
4/9/2015
ELCT564
22
Chebyshev Multisection Matching Transformers
Chebyshev transformer optimizes bandwidth
Chebyshev Polynomials
4/9/2015
ELCT564
23
Design of Chebyshev Transformers
4/9/2015
ELCT564
24
Design Example of Chebyshev Transformers
Design a three-section Chebyshev transformer to match a 100Ω load to a 50Ω line,
with Гm=0.05, using the above theory.
4/9/2015
ELCT564
25
Design Example of Chebyshev Transformers
Design a three-section Chebyshev transformer to match a 100Ω load to a 50Ω line,
with Гm=0.05, using the above theory.
4/9/2015
ELCT564
26
Tapered Lines
4/9/2015
ELCT564
27
Tapered Lines
Triangular Taper
Klopfenstein Taper
4/9/2015
ELCT564
28
Tapered Lines
Design a triangular taper, an exponential taper, and a Klopfenstein taper (with
Гm=0.05) to match a 50Ω load to a 100Ω line. Plot the impedance variations and
resulting reflection coefficient magnitudes versus βL.
4/9/2015
ELCT564
29