RF Devices and RF Circuit Design for Digital Communication
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1 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 GHz 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
2 Transmission ine Inductance, Capacitance, Filter, Impedance Transformer Short-end Open-end Impedance Inverter : in Shunt to Series Connection
3 Impedance Matrix of Transmission ine Equivalent Circuit of Transmission ine by Foster Expansion cos θ o j sinθ cosθ j o θ n θ ( ) ( nπ ) ( ) + n n θ ( π ) ( ππ ) A Series Connection of Parallel Resonance Circuits Short (Open) - circuited load: Reactance element X in tanθ: short-circuited load <θ < π : Inductance θ π : Parallel resonance circuit π < θ < π : Capacitance Stub Quater-wavelength Transformer Matching coating lense Short-terminated ine 3
4 Reflection coefficient (Г) and oad Impedance ( ) Smith Chart Γ + : Bilinear mapping : reference characteristic impedance Circle to Circle Mapping (Moebius Transform) Re Re Re ( ) > : Γ < (Passive) ( ) : Γ (ossless) ( ) Reflection type phase modulator < : Γ > (Active) Rfl Reflection typeamplifier Voltage Standing Wave Ratio (VSWR) V VSWR V Vr Γ V V i i max min Vi + V V V VSWR VSWR+ : incident wave V : reflected wave V r Special Terminations / Circuits Matched load: ( ) Г, No reflection i r r 4
5 Smith-chart and its usage Smith-chart (Bell ab. 95's) Γ in in ~ Γ exp j + + j j tanθ tanθ ~ ~ + Γ θ ~ +Γ Γ in in in in Impedance Transforming How to use Smith-chart Matching Circuit Design Smith Chart Single-stub Matching 5
6 Microstrip ine Effective permittivity and guided wavelength Characteristic Impedance Several notes : Finite conductor thickness Microstrip ine (Effective Permittivity) Coaxial ine 38 log b a ε r Pair-cable ine cosh b a 6
7 Coplanar Waveguide Slot ine Meta Material Right-Hand Transmission ine eft-hand Transmission ine Composite RH/H Transmission ine Compact Directional Coupler Super-ense RHT HT 7
8 8
9 S-parameter and RF Circuit Design S-parameter (95 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 9
10 SVD (Singular Value Decomposition) SU DV (Youla) U,V : Unitary matrix (ossless Circuit) D: Diagonal Matrix ( Isolated n-port circuit) D Diag[λ,, λ n ] Generalization of Darlington realization ossless + λ n port λ λ i < λ i > resistance negative resistance V U + λ λ n n Basics of RF Circuit Design Impedance Matching Circuits g : Generator Impedance g : oad Impedance Conjugate Matching
11 Unilateral Transducer Gain G TU (For the case, S Reverse transfer coefficient from output to input) S S FET S - parameter S S G ( Γs ) ( Γ ) TU S SΓs SΓ Gs G G G TU,max S S S Input and Output Matching Circuit Unilateral Gain U : Mason s Invariant Circuit Invariant Unilateral Gain (U) Maximum Available Gain (MAG) Noise Measure (M) -state diode (m Q) Circulator Invariant (α) Directional Coupler Invariant (K) Unilateralization of a two-port network
12 Available Power -state device e g P av g e oss ess e e ( ) P av 4 R 4R o g o g e g On-state impedance, Off-state impedance M - / +* Invariant w.r.t. ossless port connection M Γ-Γ / -ΓΓ* 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 Attenuators: Thin Film Resistor Impedance Transformers: Quarter-wavelength Impedance Transformer in
13 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 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): Branch-line Coupler 3
14 Transmission Scheme and RF Circuits Block diagram of Transceiver Objectives: ow Power Consumption, Higher Frequency, Small Size, ow Weight Basic configuration of RF Circuits: Super-Heterodyne TX evel Diagram Mixer: Up-conversion Down-conversion Amplifier: Power Amp. (TX) ow Noise Amp. (RX) Oscillator: ocal Oscillator Filter: PF, BPF 4
15 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 5
16 6
17 7
18 8
19 9
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