ELCT564 Spring 2012

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Chapter 5: Impedance Matching and Tuning

Impedance Matching

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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

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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.

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ZL=2-j1

yL=0.4+j0.5

B=0.29 X=1.22

B=-0.69 X=-1.22

Matching with Lumped Elements (L Network)Smith Chart Solutions

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B=0.29 X=1.22

B=-0.69 X=-1.22

Matching with Lumped Elements (L Network)Smith Chart Solutions

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a) An L section LC network is employed for matching a series RC circuit (R=100 Ω, C=6.366 pF) to a 50 Ω transmission line at 500 MHz. Find the values of L and C. Show the matching process on the Smith chart and plot the reflection coefficient from 0 to 1 GHz.

C=1.84 pF and L= 19.49 nH

Single Stub Tunning

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Shunt Stub

Series Stub

G=Y0=1/Z0

Single Shunt Stub Tuner Design Procedure

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1. Locate normalized load impedance and draw VSWR circle (normalized load admittance point is 180o from the normalized impedance point).

2. From the normalized load admittance point, rotate CW (toward generator) on the VSWR circle until it intersects the r = 1 circle. This rotation distance is the length d of the terminated section of t-tline. The nomalized admittance at this point is 1 + jb.

3. Beginning at the stub end (rightmost Smith chart point is the admittance of a short-circuit, leftmost Smith chart point is the admittance of an open-circuit), rotate CW (toward generator) until the point at 0 - jb is reached. This rotation distance is the stub length l.

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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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 Series Stub Tuner Design Procedure

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1. Locate normalized load impedance and draw VSWR circle

2. From the normalized load impedance point, rotate CW (toward generator) on the VSWR circle until it intersects the r = 1 circle. This rotation distance is the length d of the terminated section of t-tline. The nomalized impedance at this point is 1 + jx.

3. Beginning at the stub end (leftmost Smith chart point is the impedance of a short-circuit, rightmost Smith chart point is the impedance of an open-circuit), rotate CW (toward generator) until the point at 0 ! jx is reached. This rotation distance is the stub length l.

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

Single Stub Tunning

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Single Stub Tunning

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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=0.46λ

l2=0.204λ

Double Stub Tunning

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Theory of Small Refelections

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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 of Chebyshev Transformers

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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.

Tapered Lines

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Tapered Lines

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Triangular Taper

Klopfenstein Taper

Tapered Lines

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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.