ELCT564 Spring 2012 4/13/20151ELCT564 Chapter 5: Impedance Matching and Tuning.
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Transcript of ELCT564 Spring 2012 4/13/20151ELCT564 Chapter 5: Impedance Matching and Tuning.
Impedance Matching
04/18/23 2ELCT564
Maximum power is delivered when the load is matched the line and the power loss in the feed line is minimizedImpedance matching sensitive receiver components improves the signal to noise ratio of the systemImpedance matching in a power distribution network will reduce amplitude and phase errors
ComplexityBandwidthImplementation
Adjustability
Matching with Lumped Elements (L Network)
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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 capacitorPositive B implies an capacitor and negative B implies a inductor
Matching with Lumped Elements (L Network)Smith Chart Solutions
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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.
Single Stub Tunning
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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=0.095λl1=0.405λ
Single Stub Tunning
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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=0.09λl1=0.41λ
Single Stub Tunning
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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=0.397λl1=0.103λ
Double Stub Tunning
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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.
Double Stub Tunning
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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
Multisection Transformer
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Partial reflection coefficients for a multisection matching transformer
Binomial Multisection Matching Transformers
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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.
Binomial Transformer Design
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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.
Binomial Transformer Design
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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.
Chebyshev Multisection Matching Transformers
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Chebyshev transformer optimizes bandwidth
Chebyshev Polynomials
Design Example of Chebyshev Transformers
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Design a three-section Chebyshev transformer to match a 100Ω load to a 50Ω line, with Гm=0.05, using the above theory.
Design Example of Chebyshev Transformers
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Design a three-section Chebyshev transformer to match a 100Ω load to a 50Ω line, with Гm=0.05, using the above theory.