Transcript Design a three-section binomial transformer to match a 100Ω load to
ELCT564 Spring 2012
Chapter 5: Impedance Matching and Tuning
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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 5/2/2020 ELCT564 2
Matching with Lumped Elements (L Network) Network for
z L
inside the 1+jx circle Network for
z L
outside the 1+jx circle 5/2/2020 Positive X implies an inductor and negative X implies a capacitor Positive B implies an capacitor and negative B implies a inductor ELCT564 3
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Matching with Lumped Elements (L Network) Smith Chart Solutions
Design an L-section matching network to match a series RF load with an impedance z L =200-j100 Ω, to a 100 Ω line, at a frequency of 500 MHz.
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Z L
=2-j1
y L
=0.4+j0.5
B=0.29 X=1.22
B=-0.69 X=-1.22
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Matching with Lumped Elements (L Network) Smith Chart Solutions 5/2/2020 ELCT564 7
5/2/2020 Single Stub Tunning
Shunt Stub G=Y 0 =1/Z 0 Series Stub
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Single Stub Tunning
For a load impedance ZL=60-j80 Ω, 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. y L
=0.3+j0.4
d1=0.176-0.065=0.110
λ d2=0.325-0.065=0.260
λ y1=1+j1.47
y2=1-j1.47
l1=0.095
λ l1=0.405
λ
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Single Stub Tunning 5/2/2020 ELCT564 10
Single Stub Tunning
For a load impedance ZL=25-j50 Ω, design two single-stub (short circuit) shunt tunning networks to matching this load to a 50 Ω line. y L
=0.4+j0.8
d1=0.178-0.115=0.063
λ d2=0.325-0.065=0.260
λ y1=1+j1.67
y2=1-j1.6
l1=0.09
λ l1=0.41
λ
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Single Stub Tunning
For a load impedance ZL=100+j80 Ω, 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. z L
=2+j1.6
d1=0.328-0.208=0.120
λ d2=0.5-0.208+0.172=0.463
λ z1=1-j1.33
z2=1+j1.33
l1=0.397
λ l1=0.103
λ
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Single Stub Tunning 5/2/2020 ELCT564 13
Single Stub Tunning 5/2/2020 ELCT564 14
Double Stub Tunning 5/2/2020
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.
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Double Stub Tunning
Design a double-stub shunt tuner to match a load impedance Z L =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.
y L
=0.3+j0.4
b 1
=1.314
b 1 ’
=-0.114
y 2
=1-j3.38
l1=0.146
λ l2=0.204
λ l1’=0.482λ l2’=0.350λ y 2’
=1+j1.38
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Double Stub Tunning 5/2/2020 ELCT564 17
Theory of Small Refelections 5/2/2020 ELCT564 18
5/2/2020 Multisection Transformer
Partial reflection coefficients for a multisection matching transformer
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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.
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Binomial Transformer Design
Design a three-section binomial transformer to match a 50 Ω load to a 100Ω line, and calculate the bandwidth for Г m =0.05. Plot the reflection coefficient magnitude versus normalized frequency for the exact designs using 1,2,3,4, and 5 sections.
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Binomial Transformer Design
Design a three-section binomial transformer to match a 100 Ω load to a 50Ω line, and calculate the bandwidth for Г m =0.05. Plot the reflection coefficient magnitude versus normalized frequency for the exact designs using 1,2,3,4, and 5 sections.
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Chebyshev Multisection Matching Transformers
Chebyshev transformer optimizes bandwidth Chebyshev Polynomials
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Design of Chebyshev Transformers 5/2/2020 ELCT564 24
Design Example of Chebyshev Transformers
Design a three-section Chebyshev transformer to match a 100 Ω load to a 50Ω line, with Г m =0.05, using the above theory.
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Design Example of Chebyshev Transformers
Design a three-section Chebyshev transformer to match a 100 Ω load to a 50Ω line, with Г m =0.05, using the above theory.
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Tapered Lines 5/2/2020 ELCT564 27
Triangular Taper
Tapered Lines
Klopfenstein Taper
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Tapered Lines
Design a triangular taper, an exponential taper, and a Klopfenstein taper (with Г m =0.05) to match a 50 Ω load to a 100Ω line. Plot the impedance variations and resulting reflection coefficient magnitudes versus βL.
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