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ELCT564 Spring 2012 4/13/20151ELCT564 Chapter 5: Impedance Matching and Tuning

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Impedance Matching 4/13/20152ELCT564 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

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Matching with Lumped Elements (L Network) 4/13/20153ELCT564 Network for z L inside the 1+jx circle Network for z L 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

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4/13/20154ELCT564

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Matching with Lumped Elements (L Network) Smith Chart Solutions 4/13/20155ELCT564 Design an L-section matching network to match a series RF load with an impedance z L =200-j100Ω, to a 100 Ω line, at a frequency of 500 MHz.

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4/13/20156ELCT564 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 4/13/20157ELCT564

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Single Stub Tunning 4/13/20158ELCT564 Shunt Stub Series Stub G=Y 0 =1/Z 0

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Single Stub Tunning 4/13/20159ELCT564 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. y L =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

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Single Stub Tunning 4/13/201510ELCT564

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Single Stub Tunning 4/13/201511ELCT564 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. y L =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

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Single Stub Tunning 4/13/201512ELCT564 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. z L =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

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Single Stub Tunning 4/13/201513ELCT564

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Single Stub Tunning 4/13/201514ELCT564

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Double Stub Tunning 4/13/2015 15 ELCT564 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 4/13/2015 16 ELCT564 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=0.146λ l2=0.204λ l1’=0.482λ l2’=0.350λ y 2’ =1+j1.38

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Double Stub Tunning 4/13/2015 17 ELCT564

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Theory of Small Refelections 4/13/2015 18 ELCT564

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Multisection Transformer 4/13/2015 19 ELCT564 Partial reflection coefficients for a multisection matching transformer

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Binomial Multisection Matching Transformers 4/13/2015 20 ELCT564 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 4/13/2015 21 ELCT564 Design a three-section binomial transformer to match a 50Ω 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 4/13/2015 22 ELCT564 Design a three-section binomial transformer to match a 100Ω 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 4/13/2015 23 ELCT564 Chebyshev transformer optimizes bandwidth Chebyshev Polynomials

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Design of Chebyshev Transformers 4/13/2015 24 ELCT564

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Design Example of Chebyshev Transformers 4/13/2015 25 ELCT564 Design a three-section Chebyshev transformer to match a 100Ω load to a 50Ω line, with Г m =0.05, using the above theory.

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Design Example of Chebyshev Transformers 4/13/2015 26 ELCT564 Design a three-section Chebyshev transformer to match a 100Ω load to a 50Ω line, with Г m =0.05, using the above theory.

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Tapered Lines 4/13/2015 27 ELCT564

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Tapered Lines 4/13/2015 28 ELCT564 Triangular Taper Klopfenstein Taper

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Tapered Lines 4/13/2015 29 ELCT564 Design a triangular taper, an exponential taper, and a Klopfenstein taper (with Г m =0.05) to match a 50Ω load to a 100Ω line. Plot the impedance variations and resulting reflection coefficient magnitudes versus βL.

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