RF Devices and RF Circuit Design for Digital Communication Agenda Fundamentals of RF Circuits Transmission ine Reflection Coefficient & Smith Chart Impedance Matching S-matrix Representation Amplifiers & Unilateral Gain RF Devices Digital RF Fundamentals of RF Circuits umped-element circuits: λ, is a typical length of device. e.g. λ 3 cm for f 1GHz Distributed-element circuits: λ ~ ead ine becomes a coil and/or capacitance. Historically i Rayleigh analyzed an undersea cable based on distributed circuit concept. Image Impedance and Propagation Constant Basic distributed element: Transmission ine F-matrix of Transmission ine cosθ j sinθ F j sinθ cosθ : Characteristic impedanceof Transmission ine θ : Phase delay( βl ω εμl ωl v) l : length v : velocity 1
Transmission ine Inductance, Capacitance, Filter, Impedance Transformer Short-end Open-end Impedance Inverter : in Shunt to Series Connection 2
Equivalent Circuit of Transmission ine by Foster Expansion 2 ( π ) 2 1 1 2 2 1 ( 2ππ ) 2 2 Short (Open) - circuited load: Reactance element X in tanθ: short-circuited load <θ < π 2 : Inductance θ π 2 : Parallel resonance circuit π 2 < θ < π : Capacitance Stub Quater-wavelength Transformer Matching coating lense A Series Connection of Parallel Resonance Circuits Reflection coefficient (Г) and oad Impedance ( ) Γ + : Bilinear mapping : reference characteristic impedance Circle to Circle Mapping (Moebius Transform) Short-terminated ine 3
Smith Chart Re Re Re ( ) > : Γ < 1(Passive) ( ) : Γ 1(ossless) ( ) Reflection type phase modulator < : Γ > 1(Active) Rfl Reflection typeamplifier Voltage Standing Wave Ratio (VSWR) 1 V VSWR V Vr Γ V V i i max min Vi + V V V VSWR 1 VSWR+ 1 : incident wave V : reflected wave V r Special Terminations / Circuits Matched load: ( ) Г, No reflection i r r Smith-chart and its usage Smith-chart (Bell ab. 195's) Γ in in ~ Γ exp j2θ + + j j tanθ tanθ ~ ~ 1 + 1 Γ ~ 1+Γ 1 Γ in in in in 4
Impedance Transforming Smith Chart How to use Smith-chart Matching Circuit Design Microstrip ine Effective permittivity and guided wavelength Characteristic Impedance Several notes : Finite conductor thickness Single-stub Matching 5
Coaxial ine 138 log b a ε r Microstrip ine (Effective Permittivity) Pair-cable ine Coplanar Waveguide 12cosh 1 b a 6
Slot ine Meta Material Right-Hand Transmission ine eft-hand Transmission ine Composite RH/H Transmission ine Compact Directional Coupler Super-ense 7
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S-parameter and RF Circuit Design S-parameter (195 s Nuclear Physics) voltage, current incident wave, reflected wave impedance reflection coefficient impedance matrix scattering matrix, [ S ] For lossless circuit, S-matrix Unitary Matrix For lossy circuit, it S S I Para-unitary For Reciprocal circuit, S-matrix Symmetric matrix SVD (Singular Value Decomposition) SU DV (Youla) U,V : Unitary matrix (ossless Circuit) D: Diagonal Matrix ( Isolated n-port circuit) D Diag[λ 1,, λ n ] Generalization of Darlington realization ossless 1 + λ1 2n port 1 λ 1 λ i < 1 λ i >1 resistance negative resistance V U 1 + λ 1 λ n n 9
Basics of RF Circuit Design Impedance Matching Circuits g : Generator Impedance g : oad Impedance Conjugate Matching Unilateral Transducer Gain G TU (For the case, S 12 Reverse transfer coefficient from output to input) S11 S12 FET S - parameter S S G 2 2 ( 1 Γs ) 2 ( 1 Γ ) S TU 2 21 2 1 S11Γs 1 S22Γ Gs G G G TU,max 1 1 S 2 11 S 2 21 21 1 1 S 2 22 22 Input and Output Matching Circuit 1
Unilateral Gain U : Mason s Invariant Circuit Invariant Unilateral Gain (U) Maximum Available Gain (MAG) Noise Measure (M) 2-state diode (m Q) Circulator Invariant (α) Directional Coupler Invariant (K) Unilateralization of a two-port network 2-state device On-state impedance 1, Off-state impedance 2 M 1-2 / 1+2* Invariant w.r.t. ossless 2port connection M Γ1-Γ2 / 1-Γ1Γ2* Optimum BPSK Direct Modulation Design RF Devices Passive Components / Circuits Reactance Elements Distributed-element: Open-stub, Short-stub, ine Gap Wide ine, Narrow ine umped-element: Spiral Inductor, Gap Capacitor, Thin Film Capacitor 11
Attenuators: Thin Film Resistor Impedance Transformers: Quarter-wavelength Impedance Transformer in 2 Resonator: umped Element Type Microstrip ine Type Dielectric Resonator Type (Good Ceramic) Distributing Components / Circuits Directional Coupler: Power Monitor, Balanced Type Modulator / Amplifier / Mixer ossless reciprocal matched two-fold symmetry 4-port Perfect Directional Coupler with 9deg. Phase Difference Coupled ine Type Inter-digital Type Branch ine Type Rat-race Type Branch-line Coupler 12
Power Divider / Combiner: Perfect Matching + Perfect Isolation Absorbing Resistance Filter ow Pass Filter (PF):, C adder Filter Band Pass Filter (BPF): Half-wavelength transmission line resonator Band Stop Filter (BSF): Transmission Scheme and RF Circuits Objectives: ow Power Consumption, Higher Frequency, Small Size, ow Weight Block diagram of Transceiver Basic configuration of RF Circuits: Super-Heterodyne Mixer: Up-conversion Down-conversion Amplifier: Power Amp. (TX) ow Noise Amp. (RX) Oscillator: ocal Oscillator Filter: PF, BPF 13
TX evel Diagram RX evel Diagram Digital RF Circuits RF-CMOS Technology Analog Signal Processing & Digital Signal Processing Continuous Time & Discrete Time Direct Conversion & Sampling Built-in RF Self Test & Calibration 14
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