ELCT564 Spring 2012 Chapter 5: Impedance Matching and Tuning 4/9/2015 ELCT564 1 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 4/9/2015 ELCT564 2 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 4/9/2015 ELCT564 3 4/9/2015 ELCT564 4 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. 4/9/2015 ELCT564 5 ZL=2-j1 yL=0.4+j0.5 B=0.29 X=1.22 B=-0.69 X=-1.22 4/9/2015 ELCT564 6 Matching with Lumped Elements (L Network) Smith Chart Solutions 4/9/2015 ELCT564 7 Single Stub Tunning Shunt Stub G=Y0=1/Z0 Series Stub 4/9/2015 ELCT564 8 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 4/9/2015 ELCT564 9 Single Stub Tunning 4/9/2015 ELCT564 10 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 4/9/2015 ELCT564 11 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 4/9/2015 ELCT564 12 Single Stub Tunning 4/9/2015 ELCT564 13 Single Stub Tunning 4/9/2015 ELCT564 14 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. 4/9/2015 ELCT564 15 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=0.146λ l2=0.204λ l1’=0.482λ l2’=0.350λ y2’ =1+j1.38 4/9/2015 ELCT564 16 Double Stub Tunning 4/9/2015 ELCT564 17 Theory of Small Refelections 4/9/2015 ELCT564 18 Multisection Transformer Partial reflection coefficients for a multisection matching transformer 4/9/2015 ELCT564 19 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. 4/9/2015 ELCT564 20 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. 4/9/2015 ELCT564 21 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. 4/9/2015 ELCT564 22 Chebyshev Multisection Matching Transformers Chebyshev transformer optimizes bandwidth Chebyshev Polynomials 4/9/2015 ELCT564 23 Design of Chebyshev Transformers 4/9/2015 ELCT564 24 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. 4/9/2015 ELCT564 25 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. 4/9/2015 ELCT564 26 Tapered Lines 4/9/2015 ELCT564 27 Tapered Lines Triangular Taper Klopfenstein Taper 4/9/2015 ELCT564 28 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. 4/9/2015 ELCT564 29