阻抗匹配和阻抗转换
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Series Multi-Loop Spiral Inductor
Deposited carbon film, or semiconductor
Metal-Insulator-Metal (MIM) Capacitor Shunt Multi-Loop Spiral Inductor
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2003 Fabian Kung Wai Lee
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Types of Transformation Network
Single lumped element (either L or C) Dual lumped elements (L impedance matching network) Triple lumped elements (Pi or T impedance matching network) More lumped elements (ladder type) Distributed elements (consists of section of Tlines) Hybrid - Consists of both Tline and lumped elements
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Impedance Transformation Using Lumped Elements
Lumped components such as surface mounted device (SMD) inductor and capacitor can be easily purchased nowadays. SMD capacitors have a range from 0.47pF to greater than 10000pF. With tolerance less than ± 5% and operating temperature between 55oC to 125oC. SMD inductors have a range from 1.0nH to greater than 4000nH. With tolerance from ± 5% to± 10%, operating temperature from -40oC to 125oC and Q factor from a minimum of 15 to greater than 45. The inductors come in a variety of form, from coil-type, thin-film, to spiral inductors mounted in SMD package. Self-resonance frequency ranges from 200MHz (coil type) for L=2200nH to greater than 5GHz for L<100nH (thin-film).
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Dual Lumped Elements Transformation Network
jX
1 1 Ys = = jB + Zs RL + j ( X L + X )
jB
If Zs = Rs + jXs is given, we could solve for X and B by equating the real and imaginary parts:
R 2 X = X s ± Rs (RL Rs ) + s X L RL B=
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Rs RL RL X s + Rs X L RL X
2003 Fabian Kung Wai Lee
(1.2)
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Example 1
Transform ZL=100 + j80 to 50 + j40 at 410MHz.
Low resistance Resistors
High resistance
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Single Lumped Element Transformation Network
jX Zs = ZL + jX ZL = RL+jXL ZL
3A - Impedance Transformation and Impedance Matching
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2003 Fabian Kung Wai Lee
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References
[1] R. Ludwig, P. Bretchko, “RF circuit design - Theory and applications”, 2000 Prentice-Hall. [2] D.M. Pozar, “Microwave engineering”, 2nd edition, 1998 John-Wiley & Sons. [3] R.E. Collin, “Foundation for microwave engineering”, 2nd edition, 1992, McGraw-Hill.
RL + jXL
R 2 X = X L ± RL (Rs RL ) + L X s Rs B=
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This configuration is only applicable for Rs > RL
Rs RL Rs X L + RL X s + Rs X
2003 Fabian Kung Wai Lee
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Impedance Transformation and Matching
RS
~
Zo
Det
50
50
50
50
50
50
50
50
50
50
~
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Why Impedance Tuning is Needed?
(
X
) = 44.83nH ) = 5.468 pF
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Since B is +ve, a capacitor can be used to realize it:
C= 2π 410 × 106
(
B
July 2004
2003 Fabian Kung Wai Lee
Example 1 Cont...
(1.1)
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Dual Elements Transformation Network Cont...
jX
Z s = jX + 1 jB + 1 RL + jX L
jB RL + jXL
This configuration is only applicable for RL> Rs
If Zs = Rs + jXs is given, again we could solve for X and B by equating the real and imaginary parts:
(0805) (0603), (1210), NPO dielectric Y5V dielectric
80mils
0805
50mils
Thick film resistor
(1210)
Another size from IPC (international package consortium ) - 0402, even smaller than 0603. - 1210, bigger than Thin film inductor Coil inductor 0805. (0805) (0603)
44.83nH 100+j80
50+j40
5.47pF
At 410MHz Only!
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Exercise 1
Transform ZL= 50 + j100 to 300 - j10 at 900MHz using 2 lumped element matching networks.
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Ultra High Frequencies Passive Components (>250MHz)
Multilayer electrolytic Multilayer ceramic capacitor capacitor (1812) (0603), NPO dielectric Aluminium oxide
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Medium Frequency Passive Components (up to 250MHz)
Coil inductor with Ferrite core
Multilayer ceramic capacitor
Coil inductor with air core Carbon/metal film resistor
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Impedance Transformation
An impedance transformation network is a two-port network that when connected in series with an impedance ZL at one port, will result in Zs being seen on another port. ZL is usually not equal to Zs (otherwise there will be no need for transformation). Zs is known as the image impedance of ZL. We immediately notice that the transformation network is a 2-port network. Zs Transformation Network ZL