Applied RF Techniques I
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Switching from traditional circuit definitions based on voltages and currents, to power-flow concepts and scattering parameters, this course offers a smooth transition into the wireless domain. We review S-parameter measurements and applications for both single-ended (unbalanced) and balanced circuits and have a brief introduction to RF systems and their components.
Impedance matching is vitally important in RF systems and we use both graphical (Smith Chart ) and analytical techniques throughout the course. We also examine discrete and monolithic component models in their physical forms, discussing parasitic effects and losses, revealing reasons why circuit elements behave in surprising manners at RF.
Filters, resonant circuits and their applications are reviewed through filter tables and modern synthesis techniques, leading into matching networks and matching filter structures. Since wires and printed circuit conductors may behave as transmission line elements, we also cover microstrip and stripline realizations. 2D and 2,5D electromagnetic field simulators are used in the course to illustrate transmission line behavior and component coupling effects.
In the area of active circuits, we first examine fundamental limitations posed by noise and distortion. The next topic is small-signal linear amplifier design, based on scattering parameter techniques, considering input/output match and gain flatness RF stability is examined both with S-parameters and also with the Nyquist test using nonlinear device models. Since DC biasing affects RF performance, we review active and passive bias circuits and see how they can be combined with impedance matching circuits. Another important consideration is circuit layout, therefore we look at problems caused by coupling, grounding and parasitic resistance. Narrow- and broadband designs are compared, using lossless and lossy impedance matching as well as feedback circuits. Low-noise amplifier design is illustrated, discussing trade-offs among gain flatness, noise, RF stability, and impedance match. Harmonic and inter-modulation performance is also examined. Performance trade-offs of balanced amplifiers are viewed. The course concludes by examining large-signal and ultra wideband feedback amplifiers.
Students are encouraged to bring their laptop computers to class.
Upon completing the course, the participant will be able to:
- Describe RF circuit parameters and terminology.
- State the effects of parasitics on circuit performance at RF.
- Use graphical design techniques and the Smith Chart.
- Match impedances and perform transformations.
- Design filters with lumped and distributed components.
- Perform statistical analysis: design centering, yield optimization.
- Predict RF circuit stability and stabilize circuits.
- Design various RF amplifiers: small-signal, low-noise, and feedback.
The course is designed for practicing engineers who are involved with the production, test, and development of RF/Wireless components, circuits, sub-systems, and systems, in the 100-4000 MHz frequency range. It is equally useful to new engineers and to those who may have practical experience but have not had opportunity of getting a thorough foundation of modern, computer-oriented RF circuit techniques.
Engineering degree or at least three years applicable practical experience is recommended.
Day OneIntroduction to RF Circuits
Linear circuit analysis in RF systems Frequency range of coverage: 100-3000 MHz Log conversion, dB and dBm scales Complex numbers in rectangular and polar form Component Qs Importance of Impedance Matching Normalization RF component related issues
Computer Aided Design Methods Major Optimization Methods in Microwave CAD Network Synthesis Procedure Physical Limitation on Broadband Impedance Matching Electromagnetic (EM) Simulation Reliability and Yield Considerations Monte Carlo Simulation
Complex impedance and admittance systems Resonance effects One-port impedance and admittance Series and parallel circuit conversions Lumped vs. distributed element representation Characteristic impedance and electrical length Signal transmission/reflection and directional couplers Key parameters : Gamma, mismatch loss, return loss, SWR Impedance transformation and matching Illustrative exercise
The Smith Chart and Its Applications
Polar Gamma vs. Rectangular Z plots Impedance and Admittance Smith Charts Normalized Smith Charts Lumped series/parallel element manipulations Constant Q circles Expanded and compressed Smith Charts Impedance and admittance transformations Transmission line manipulations Illustrative examples
Review of one-port parameters Two-port Z-, Y-, and T-parameters Cascade connections and de-embedding S-parameters of commonly used two-ports Generalized S-parameters Illustrative examples Mixed-mode S-parameters
Day TwoImpedance Matching Techniques
Power-flow in two-port networks Transmission zeros, LC network order Maximum power transfer from Z1 to Z2 Single LC-section impedance matching Bandwidth and parasitic considerations Wideband match -- low circuit-Q Narrowband match -- high circuit-Q Illustrative examples
Lumped RF Component Models
Resistors Inductors Effective Inductance and Q Variations Capacitors Effective Capacitance and Q Variations Primary self-resonance variations Definitions of Magnetic Properties Magnetic Core Applications Ferrite Bead Impedance Exercise: Complex Impedance Matching
Day ThreeTransmission Lines and Ground Parasitics
Via-Hole and Wrap-Around Ground Inductance Parasitic Inductance and Capacitance Effects at RF Multilayer PC-Board Parasitics PCB/Interconnects Open Stub Effects in Differential Vias PC Board Materials Transmission Line Realizations Transmission Line Discontinuities Converting an Electrical Circuit to Physical Form
Filters and Resonant Circuits
Introduction Recipes for lumped-element filters Parasitic loss and Q factor Impedance inverters Band pass filters with resonant structures Piezoelectric filters
Day FourActive Circuit Fundamentals
Linear circuit definition Amplifier Performance Limitations Thermal Noise Definition Harmonic Distortion Definitions Gain Compression Intermodulation Distortion Spurious-Free Dynamic Range Error Vector Magnitude Various Power Gain Definitions Testing for RF Stability Causes of RF Oscillation Typical Stability Circles for an RF Transistor RF Stabilization Techniques Nyquist Stability Analysis
Small Signal Amplifier Design
Transducer Gain Expression Simultaneous Conjugate Match for Maximum Gain Class Exercise Two-stage Amplifier Design for Gmax Gain Definition - Block Diagram Operating Gain Definitions Operating Gain Circle Application Maximizing Output Power Available Gain Definitions Available Gain Circles
Day FiveLow Noise Amplifier Design
Sources of RF noise Noise Factor and Noise Figure definitions Noise of cascaded stages Two-port noise parameters Low-noise design procedure Illustrative example
Broadband Concepts Wideband Amplifier Design Overview Voltage Gain Phase Shift Gain Control and Impedance Matching in Feedback Amplifiers Series and Parallel Feedback Applications 10-4000 MHz Feedback Amplifier Design Equivalent Circuit for Microwave FET Lumped Transmission Line and Distributed Amplifier Mitigating Cdg: the Cascode
Subject Areas Covered
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