elct564 spring 2012 8/19/20151elct564 chapter 5: impedance matching and tuning
TRANSCRIPT
![Page 1: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/1.jpg)
ELCT564 Spring 2012
04/19/23 1ELCT564
Chapter 5: Impedance Matching and Tuning
![Page 2: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/2.jpg)
Impedance Matching
04/19/23 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
![Page 3: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/3.jpg)
Matching with Lumped Elements (L Network)
04/19/23 3ELCT564
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
![Page 4: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/4.jpg)
04/19/23 4ELCT564
![Page 5: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/5.jpg)
Matching with Lumped Elements (L Network)Smith Chart Solutions
04/19/23 5ELCT564
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.
![Page 6: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/6.jpg)
04/19/23 6ELCT564
ZL=2-j1
yL=0.4+j0.5
B=0.29 X=1.22
B=-0.69 X=-1.22
![Page 7: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/7.jpg)
Matching with Lumped Elements (L Network)Smith Chart Solutions
04/19/23 7ELCT564
B=0.29 X=1.22
B=-0.69 X=-1.22
![Page 8: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/8.jpg)
Matching with Lumped Elements (L Network)Smith Chart Solutions
04/19/23 8ELCT564
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
![Page 9: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/9.jpg)
Single Stub Tunning
04/19/23 9ELCT564
Shunt Stub
Series Stub
G=Y0=1/Z0
![Page 10: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/10.jpg)
Single Shunt Stub Tuner Design Procedure
04/19/23 10ELCT564
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.
![Page 11: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/11.jpg)
Single Stub Tunning
04/19/23 11ELCT564
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
![Page 12: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/12.jpg)
Single Stub Tunning
04/19/23 12ELCT564
![Page 13: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/13.jpg)
Single Stub Tunning
04/19/23 13ELCT564
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
![Page 14: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/14.jpg)
Single Series Stub Tuner Design Procedure
04/19/23 14ELCT564
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.
![Page 15: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/15.jpg)
Single Stub Tunning
04/19/23 15ELCT564
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
![Page 16: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/16.jpg)
Single Stub Tunning
04/19/23 16ELCT564
![Page 17: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/17.jpg)
Single Stub Tunning
04/19/23 17ELCT564
![Page 18: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/18.jpg)
Double Stub Tunning
04/19/23 18ELCT564
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.
![Page 19: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/19.jpg)
Double Stub Tunning
04/19/23 19ELCT564
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
![Page 20: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/20.jpg)
Double Stub Tunning
04/19/23 20ELCT564
![Page 21: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/21.jpg)
Theory of Small Refelections
04/19/23 21ELCT564
![Page 22: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/22.jpg)
Multisection Transformer
04/19/23 22ELCT564
Partial reflection coefficients for a multisection matching transformer
![Page 23: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/23.jpg)
Binomial Multisection Matching Transformers
04/19/23 23ELCT564
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.
![Page 24: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/24.jpg)
Binomial Transformer Design
04/19/23 24ELCT564
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.
![Page 25: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/25.jpg)
Binomial Transformer Design
04/19/23 25ELCT564
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.
![Page 26: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/26.jpg)
Chebyshev Multisection Matching Transformers
04/19/23 26ELCT564
Chebyshev transformer optimizes bandwidth
Chebyshev Polynomials
![Page 27: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/27.jpg)
Design of Chebyshev Transformers
04/19/23 27ELCT564
![Page 28: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/28.jpg)
Design Example of Chebyshev Transformers
04/19/23 28ELCT564
Design a three-section Chebyshev transformer to match a 100Ω load to a 50Ω line, with Гm=0.05, using the above theory.
![Page 29: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/29.jpg)
Design Example of Chebyshev Transformers
04/19/23 29ELCT564
Design a three-section Chebyshev transformer to match a 100Ω load to a 50Ω line, with Гm=0.05, using the above theory.
![Page 30: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/30.jpg)
Tapered Lines
04/19/23 30ELCT564
![Page 31: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/31.jpg)
Tapered Lines
04/19/23 31ELCT564
Triangular Taper
Klopfenstein Taper
![Page 32: ELCT564 Spring 2012 8/19/20151ELCT564 Chapter 5: Impedance Matching and Tuning](https://reader036.vdocument.in/reader036/viewer/2022081503/56649dc85503460f94abe588/html5/thumbnails/32.jpg)
Tapered Lines
04/19/23 32ELCT564
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.