RT ( 150) R A ( 75) choose "" argument () of & 2011-12Ĭomplex ZT to complex ZA conjugate matching ZT 150 j 75 Z A 75 j15 f 2 GHzĬomplex ZA to complex ZT conjugate matching (Conjugate Matching for maximum power transfer ) jX jBĪdmittance complex ZL to real Z0 matching (2) Complex to complex conjugate matching (Ludwig, RF Circuit Design P401) Smith Chart Representation of the Matching Process 38.8nH Since RL = 200 > Z0 = 100 (zL is inside the (1 + jx) circle) We choose (a) The solutions are RL Z L Z L / Z o r jx L ( Z L Z o ) /( Z L Z o ) | L | ĥ-5 EX (Pozar MW EX 5.1) (Pozar RF EX 2.5) BZ ( X X L ) Z 0 R L 0 ( X X L ) BZ 0 R L (2) if RL Z 0 ( z 1) => choose (b) why? 1 1 for impedance matching (to Z 0 ) => jB R L j ( X X L ) Z0 X (1 B ) ( X L Z 0 RL ) ( Z 0 B RL ) (1) if RL Z 0 ( z 1) => choose (a) why? 1 for impedance matching (to Z 0 ) => jX Z0 jB 1 ( R L jX L ) X RL Z 0 RL2 X L2 Z 0 RL B( XR L X L Z 0 ) R L Z 0 B L => RL2 X L2 X BX BZ R X ( ) 1 L 0 L L Let zL = ZL / Zo = (RL + jXL) / Zo = r + jx L-section Network (1) complex ZL to real Z0 matching jX This may be important, for example, for powerH.-R. Harmonic filtering can be done with a lowpass matching network (series L, parallel C ). In such a case, sometimes a highpass network (series capacitor, parallel inductor) at the input may be more stable.ĥ.
Since transistor gain is higher at lower frequencies, there may be a lowfrequency stability problem. Sometimes when all paths look equal, you just have to shoot from the hip and pick one. Some circuits may result in more reasonable component values. Sometimes matching components can be used as dc blocks (capacitors) or to provide bias currents (inductors). How does one choose? There are a number of popular reasons for choosing one over another. The figure shows what matching networks will work in which regions. In any particular region on the Smith chart, several matching circuits will work and others will not. Matching Network Types: L-/T-/-section Networks L-section Networks (Two-component ): Lumped elements: L/C C * At high freq., capacitance is like Short-cirucited 2 X sc / Z 0
.png "smith chart forbidden region")
* Factors in the selection of matching networks - complexity -bandwidth requirement (such as broadband design) - adjustability - implementation (transmission line, chip R/L/C elements. Minimum power loss in the feed line & maximum power delivery linearizing the frequency response of the circuit improving the S/N ratio of the system for sensitive receiver components (lownoise amplifier, etc.) reducing amplitude & phase errors in a power distribution network (such as antenna array-feed network) Z in Reflection coefficien t (or Return Loss) : in (or S11 ) ( Z in Z 0 ) /( Z in Z 0 ) Impedance matching (or tuning) is important for the following reasons : incident (or input) Microstrp Single-Stub and Double-Stub Tuning Quarter-Wave Transformer * The Bode-Fano Criteria Matching with Lumped Elements - L Network - T & Networks - Lumped Elements for MIC : Chip R, L, C. CHAPTER 5 Impedance Matching and Smith Chart * Pozar MW (Ch 5), “Impedance Matching and Tuning” * Pozar RF (Ch 2), “Itransmission Lines & Microwave Networks” *Ludwig, (Ch 3, Ch 8), “Matching and Biasing Networks” *Rogers, (Ch 4), “Radio Frequency Integrated Circuit Design”
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