Chapter 5: Impedance Matching and Tuning ELCT564 Spring 2012 Chapter 5: Impedance Matching and Tuning 4/20/2017 ELCT564

Impedance Matching 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 4/20/2017 ELCT564

Matching with Lumped Elements (L Network) 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 capacitor Positive B implies an capacitor and negative B implies a inductor 4/20/2017 ELCT564

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Matching with Lumped Elements (L Network) Smith Chart Solutions 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. 4/20/2017 ELCT564

ZL=2-j1 yL=0.4+j0.5 B=0.29 X=1.22 B=-0.69 X=-1.22 4/20/2017 ELCT564

Matching with Lumped Elements (L Network) Smith Chart Solutions B=0.29 X=1.22 B=-0.69 X=-1.22 4/20/2017 ELCT564

Matching with Lumped Elements (L Network) Smith Chart Solutions 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 4/20/2017 ELCT564

Single Stub Tunning Shunt Stub G=Y0=1/Z0 Series Stub 4/20/2017 ELCT564

Single Shunt Stub Tuner Design Procedure 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. 4/20/2017 ELCT564

Single Stub Tunning 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=0.095λ l1=0.405λ 4/20/2017 ELCT564

Single Stub Tunning 4/20/2017 ELCT564

Single Stub Tunning 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=0.09λ l1=0.41λ 4/20/2017 ELCT564

Single Series Stub Tuner Design Procedure 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. 4/20/2017 ELCT564

Single Stub Tunning 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=0.397λ l1=0.103λ 4/20/2017 ELCT564

Single Stub Tunning 4/20/2017 ELCT564

Single Stub Tunning 4/20/2017 ELCT564

Double Stub Tunning 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. 4/20/2017 ELCT564

Double Stub Tunning 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 4/20/2017 ELCT564

Double Stub Tunning 4/20/2017 ELCT564

Theory of Small Refelections 4/20/2017 ELCT564

Multisection Transformer Partial reflection coefficients for a multisection matching transformer 4/20/2017 ELCT564

Binomial Multisection Matching Transformers 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. 4/20/2017 ELCT564

Binomial Transformer Design 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. 4/20/2017 ELCT564

Binomial Transformer Design 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.         4/20/2017 ELCT564

Chebyshev Multisection Matching Transformers Chebyshev transformer optimizes bandwidth Chebyshev Polynomials 4/20/2017 ELCT564

Design of Chebyshev Transformers 4/20/2017 ELCT564

Design Example of Chebyshev Transformers Design a three-section Chebyshev transformer to match a 100Ω load to a 50Ω line, with Гm=0.05, using the above theory.     4/20/2017 ELCT564

Design Example of Chebyshev Transformers Design a three-section Chebyshev transformer to match a 100Ω load to a 50Ω line, with Гm=0.05, using the above theory. 4/20/2017 ELCT564

Tapered Lines 4/20/2017 ELCT564

Tapered Lines Triangular Taper Klopfenstein Taper 4/20/2017 ELCT564

Tapered Lines 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. 4/20/2017 ELCT564