Impedance Matching. RF Electronics Spring, 2018 Robert R. Krchnavek Rowan University
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1 Impedance Matching RF Electronics Spring, 8 Robert R. Krchnavek Rowan University
2 Objectives Be able to design an L-section matching network. Understand the importance of T and Pi matching networks. Understand distributed parameter matching networks. Be able to design biasing networks.
3 Matching Networks Matching networks are often used to achieve maximum power transfer. Matching networks are also used for minimizing noise influence. maximizing power handling capabilities. linearizing the frequency response. In general, matching networks simply provide impedance transformation.
4 L-Section Matching Networks Two-Component Networks C C C 2 C Z S L Z L Z S L Z L Z S C Z L Z S C 2 Z L L L L 2 L Z S L Z L Z S L 2 Z L Z C S Z Z C L S Z L Analytical solution Smith Chart solution
5 L-Section Matching Networks Z in Z T = R T + ȷX T Z in = R T ȷX T Z in =(Z A + ȷX L ) ȷX C Z A = R A + ȷX A Z M = R A ȷX A Z M = Z T ȷX C + ȷX L
6 L-Section Matching Networks Analytical method precise but slow. best used with the aid of a computer. Graphical method (Smith Chart) quick. not precise. yields a visual indication of the design space.
7 L-Section Matching Networks Analytical Solution Z T = R T + ȷX T =+ȷ25 Ω Z A = R A + ȷX A =25 ȷ Ω For maximum transfer of power, Z M = Z A
8 L-Section Matching Networks Analytical Solution Z M = Z T k!c +!L = Z A Z M =(R T + X T ) k!c +!L = R A X A = Z A Separate into real and imaginary parts and solve for L and C.
9 L-Section Matching Networks Smith Chart Solution Z T = R T + ȷX T =+ȷ25 Ω z T = Z T + ȷ25 = =+ȷ Z 0 Z A = R A + ȷX A =25 ȷ Ω z A = Z A 25 ȷ = = ȷ Z 0
10 L-Section Matching Networks Smith Chart Solution
11 L-Section Matching Networks Smith Chart Solution General Approach Find the normalized source and load impedance. Plot constant R and G circles that pass through zs. Use dashed lines or a unique color. Plot constant R and G circles that pass through zl*. Use solid lines or a different color. Find the intersection points between the dashed and solid lines. These are unique solutions to the matching problem. Find the normalized values of reactances and susceptances by tracing a path from zs to intersection point, to zl*. Determine actual values of L and C.
12 L-Section Matching Networks Smith Chart Solution Specific Example Find the normalized source and load impedance. z T = Z T Z 0 = + ȷ25 =+ȷ z A = Z A Z 0 = 25 ȷ = ȷ
13 L-Section Matching Networks Smith Chart Solution Specific Example Plot constant R and G circles that pass through z S. Use dashed lines or a unique color. More specifically, if the first component is a shunt component, plot a constant G circle. If it is a series component, plot a constant R circle. For this example, z S is z T.
14 NORMALIZED IMPEDANCE AND ADMITTANCE COORDINATES ± > WAVELENGTHS TOWARD GENERATOR > < WAVELENGTHS TOWARD LOAD < INDUCTIVE REACTANCE COMPONENT (+jx/zo),orcapacitivesusceptance(+jb/yo) RESISTANCE COMPONENT (R/Zo), OR CONDUCTANCE COMPONENT (G/Yo) EACTANCE COMPONENT (-jx/zo), ORINDUCTIVE SUSCEPTANCE(-jB Yo) VE R CAPA C IT I ANGLE OF TRANSMISS ON COEFFICIENT IN DEGREES ANGLE OF REFLECTION COEFF CIENT IN DEGREES SWR dbs RTN. LOSS [db] RFL. COEFF, P RFL. COEFF, E or I RADIALLY SCALED PARAMETERS TOWARD LOAD > < TOWARD GENERATOR CENTER ATTEN. [db] S.W. LOSS COEFF RFL. LOSS [db] S.W. PEAK (CONST. P) TRANSM. COEFF, P TRANSM. COEFF, E or I ORIGIN
15 NORMALIZED IMPEDANCE AND ADMITTANCE COORDINATES ± > WAVELENGTHS TOWARD GENERATOR > < WAVELENGTHS TOWARD LOAD < INDUCTIVE REACTANCE COMPONENT (+jx/zo),orcapacitivesusceptance(+jb/yo) RESISTANCE COMPONENT (R/Zo), OR CONDUCTANCE COMPONENT (G/Yo) EACTANCE COMPONENT (-jx/zo), ORINDUCTIVE SUSCEPTANCE(-jB Yo) VE R CAPA C IT I ANGLE OF TRANSMISS ON COEFFICIENT IN DEGREES ANGLE OF REFLECTION COEFF CIENT IN DEGREES SWR dbs RTN. LOSS [db] RFL. COEFF, P RFL. COEFF, E or I RADIALLY SCALED PARAMETERS TOWARD LOAD > < TOWARD GENERATOR CENTER ATTEN. [db] S.W. LOSS COEFF RFL. LOSS [db] S.W. PEAK (CONST. P) TRANSM. COEFF, P TRANSM. COEFF, E or I ORIGIN
16 NORMALIZED IMPEDANCE AND ADMITTANCE COORDINATES ± > WAVELENGTHS TOWARD GENERATOR > < WAVELENGTHS TOWARD LOAD < INDUCTIVE REACTANCE COMPONENT (+jx/zo),orcapacitivesusceptance(+jb/yo) RESISTANCE COMPONENT (R/Zo), OR CONDUCTANCE COMPONENT (G/Yo) EACTANCE COMPONENT (-jx/zo), ORINDUCTIVE SUSCEPTANCE(-jB Yo) VE R CAPA C IT I ANGLE OF TRANSMISS ON COEFFICIENT IN DEGREES ANGLE OF REFLECTION COEFF CIENT IN DEGREES SWR dbs RTN. LOSS [db] RFL. COEFF, P RFL. COEFF, E or I RADIALLY SCALED PARAMETERS TOWARD LOAD > < TOWARD GENERATOR CENTER ATTEN. [db] S.W. LOSS COEFF RFL. LOSS [db] S.W. PEAK (CONST. P) TRANSM. COEFF, P TRANSM. COEFF, E or I ORIGIN
17 L-Section Matching Networks Smith Chart Solution Specific Example Plot constant R and G circles that pass through z L *. Use solid lines or a different color. More specifically, if the component near the load is a series element, plot a constant R circle. In this example, z L * is z A *.
18 NORMALIZED IMPEDANCE AND ADMITTANCE COORDINATES ± > WAVELENGTHS TOWARD GENERATOR > < WAVELENGTHS TOWARD LOAD < INDUCTIVE REACTANCE COMPONENT (+jx/zo),orcapacitivesusceptance(+jb/yo) RESISTANCE COMPONENT (R/Zo), OR CONDUCTANCE COMPONENT (G/Yo) EACTANCE COMPONENT (-jx/zo), ORINDUCTIVE SUSCEPTANCE(-jB Yo) VE R CAPA C IT I ANGLE OF TRANSMISS ON COEFFICIENT IN DEGREES ANGLE OF REFLECTION COEFF CIENT IN DEGREES SWR dbs RTN. LOSS [db] RFL. COEFF, P RFL. COEFF, E or I RADIALLY SCALED PARAMETERS TOWARD LOAD > < TOWARD GENERATOR CENTER ATTEN. [db] S.W. LOSS COEFF RFL. LOSS [db] S.W. PEAK (CONST. P) TRANSM. COEFF, P TRANSM. COEFF, E or I ORIGIN
19 L-Section Matching Networks Smith Chart Solution Specific Example Find the intersection points between the dashed and solid lines. These are unique solutions to the matching problem.
20 NORMALIZED IMPEDANCE AND ADMITTANCE COORDINATES ± > WAVELENGTHS TOWARD GENERATOR > < WAVELENGTHS TOWARD LOAD < INDUCTIVE REACTANCE COMPONENT (+jx/zo),orcapacitivesusceptance(+jb/yo) RESISTANCE COMPONENT (R/Zo), OR CONDUCTANCE COMPONENT (G/Yo) EACTANCE COMPONENT (-jx/zo), ORINDUCTIVE SUSCEPTANCE(-jB Yo) VE R CAPA C IT I ANGLE OF TRANSMISS ON COEFFICIENT IN DEGREES ANGLE OF REFLECTION COEFF CIENT IN DEGREES SWR dbs RTN. LOSS [db] RFL. COEFF, P RFL. COEFF, E or I RADIALLY SCALED PARAMETERS TOWARD LOAD > < TOWARD GENERATOR CENTER ATTEN. [db] S.W. LOSS COEFF RFL. LOSS [db] S.W. PEAK (CONST. P) TRANSM. COEFF, P TRANSM. COEFF, E or I ORIGIN
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22 Forbidden Regions, Frequency Response, and Q Not every matching condition will allow all 8 L- type matching networks. Although the L-type matching network is matched at one frequency, the frequency response of the different networks varies. The loaded Q for each matching network will also, in general, vary.
23 Forbidden Regions ZS = Z0 = Ω
24 T and Pi Matching Networks T and Pi matching networks have an additional element compared to an L matching network. The additional element allows more control over the Q of the network. Can be used to control the bandwidth of the matching network.
25 Microstrip Matching Networks At higher frequencies, distributed element networks are used to achieve matching. Single-stub and double-stub matching networks. Mid-GHz range one often uses transmission lines + discrete capacitors.
26 Mixed Design Matching Network Convert a load impedance of Z L =30+j Ω to an input impedance of Z in =60+j80 Ω Assume a characteristic impedance for the transmission lines of Ω. Smith Chart solution -> normalize everything to Ω. Traversing the length of the series transmission line elements results in a rotation on the Smith Chart on a constant radius circle.
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28 Mixed Design Matching Network Convert a load impedance of Z L =30+j Ω to an input impedance of Z in =60+j80 Ω Completed design: In general, these networks are very sensitive to precise placement of the discrete capacitor.
29 Fully Distributed-Element Matching Networks Single-stub tuning. See undergraduate notes for Engineering Electromagnetics. Also see textbook. Easily done on a Smith Chart. When a tunable matching network is required, double-stub tuning has an advantage over singlestub tuning because only the length of the stub and not its position needs to be varied.
30 Summary Impedance matching is necessary to maximize transfer of power from one stage to the next in an RF system. Two-component L-section matching has up to 8 different configurations. However, not all 8 are available in any given matching problem. The different L-type have different frequency response. T or Pi matching networks have an additional degree of freedom to control bandwidth of the matching network. At higher frequencies, matching may include C and X- lines. At still higher frequencies, X-lines with stubs.
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