# Foundations of

Radio Frequency Engineering

Dr Francesco Fornetti

Associate Professor of Radio Frequency Engineering

Why should I take this course?

**It's unlike any other courses on Radio Frequency Engineering!**

This course is designed to introduce you to the fundamental concepts of RF engineering, covering essential topics such as transmission lines, matching networks, and RF amplifier design.

What sets this course apart is the integration of a powerful simulation tool, Cadence AWR, which allows you to create your own virtual laboratory. You'll learn to design, simulate, and analyse RF circuits in a virtual environment through a problem-based approach, gaining hands-on experience without the need for expensive hardware.

If you have access to RF test and measurement equipment, the course includes practical laboratory exercises that complement the theoretical and simulation components. These exercises guide you through the process of turning virtual designs into physical circuits. You'll learn how to test and characterise these circuits, bridging the gap between theory and practice.

The course is based on 'Conquer Radio Frequency', Dr. Fornetti's multimedia textbook, which includes numerous video tutorials based on Cadence AWR. This course, however, greatly enhances this baseline material with additional presentations, video tutorials, animations, worked examples, problems, tests, design challenges, and practical laboratory experiments, significantly enriching the original content.

Whether you're a beginner or looking to enhance your RF engineering skills, this course offers a comprehensive, interactive learning experience to help you master the principles and applications of RF engineering.

Content Overview

### Module 1: Transmission Lines

- The transition from AC to RF
- Wavelength and its significance
- Transmission lines:
- Lossless Models and signal propagation mechanisms
- Infinite length lines and characteristic Impedance
- Finite length lines: ‘Long’ vs ‘Short’ transmission lines.
- Transmission lines and RF Circuits: conditions for maximum power transfer
- Quarter-wave lines
- Coaxial Lines
- Microstrip Lines
- Verification of the characteristic impedance of a transmission line
- Lossy models
- Definition of Load Reflection Coefficient

### Module 2: Passive Circuit Elements and their RF models

- Skin depth
- Self-inductance
- Parasitic capacitance
- RF models of passive circuit elements
- Distributed elements: short- and open-circuited transmission line stubs
- Quality Factor, Q
- Unloaded Q: Capacitors, Inductors
- Q and Series ↔ Parallel conversions of lumped R-C and R-L networks
- Loaded Q, L-C resonators

### Module 3: Impedance vs Reflection Coefficient, The Smith Chart

- Maximising power transfer: Introduction to impedance matching
- Algebraic matching
- Frequency response of matching networks
- Reflection Coefficient
- Deriving impedance values from the Reflection Coefficient
- The Smith Chart – an Introduction
- Scattering Parameters (S-parameters)
- VSWR and Slotted Lines

### Module 4: Impedance Matching Techniques

- S-parameters , Reflection coefficient and Impedance measurements in AWR
- Impedance and Admittance transformation using the
- Impedance Smith chart and series elements
- Admittance Smith chart and shunt elements
- Dual-coordinates (impedance and Admittance) Smith chart: design of two-element matching networks, comprising both shunt and series elements (L-section), for purely resistive terminations
- Understanding filter type and order using transmission zeros
- Frequency response of L-section matching networks and explanation of their fixed-Q limitations
- Three-elements matching: designing matching networks with a specific Q
- Case 1 - T-networks when R
_{L}< R_{S } - Case 2 - Pi-networks when R
_{L }> R_{S } - Matching any two-complex terminations using the Smith Chart
- Using series transmission line sections of specific lengths combined with a single capacitor or inductor to achieve a match
- Discrete vs Distributed Elements
- Distributed matching networks: using either a short-circuited or open-circuited transmission line stub, combined with transmission line sections of specific lengths to achieve a match

### Module 5: RF Amplifier Design

- The transistor at Radio Frequency
- Linear and non-linear Models for BJTs
- Input and Output Impedances
- Feedback Characteristics
- Gain
- Two-port S-Parameter characterisation of a transistor
- Amplifier Design Stages
- Biasing
- Stabilisation
- Impedance Matching
- Verification

Learning Objectives

### Module 1: Transmission Lines

- Explain the concept of wavelength and its significance in differentiating between RF circuits, which require specialised design and analysis techniques, and AC circuits, which can use lumped-element approximations.
- Understand lossless transmission line models and be able to employ them to explain signal propagation mechanisms along a transmission line.
- Explain the concept of characteristic impedance using infinite length transmission lines.
- Finite Length Transmission Lines
- Understand the transition from infinite to finite length transmission lines.
- Differentiate between 'long' and 'short' transmission lines.
- Maximum Power Transfer
- Understand the conditions necessary for maximum power transfer in RF circuits involving transmission lines.
- Compare these conditions to those in AC circuits.
- Understand the principles of operation, function and applications of quarter-wave transmission lines in RF circuits.
- Describe the structure of coaxial lines and calculate their characteristic impedance.
- Describe the structure of microstrip lines and calculate their characteristic impedance.
- Be able verify the characteristic impedance of coaxial and microstrip lines both through simulation and experimentally.
- Understand the circuital models of lossless and lossy transmission lines.
- Apply differential equations to such models to derive and analyse voltage and current relationships.
- Understand the definition of Load Reflection Coefficient.
- (Optional) Propagation of DC Step Voltage and Voltage Pulse
- Understand the propagation of a DC step voltage and a voltage pulse along open- and short-circuited transmission lines.
- Explain these propagation mechanisms using both lossless transmission line models and a physical approach based on charge distributions, voltages, and currents.

### Module 2: Passive Circuit Elements and their RF models

- Define skin depth and explain its significance in RF circuits.
- Calculate skin depth for a given frequency and material.
- Define self-inductance and its role in electrical circuits.
- Define parasitic capacitance and identify its physical sources.
- Describe the RF models of resistors, capacitors, and inductors.
- Explain how parasitics affect the performance of passive components.
- Understand the significance of self-resonance and analyse the impedances of components above and below their self-resonance frequencies.
- Use simulation models in AWR to accurately model the behaviour of passive components across a range of frequencies.
- Explain the concept of distributed elements in RF circuits.
- Describe the function and application of short-circuited and open-circuited transmission line stubs.
- Define the quality factor (Q) and its importance as a single figure of merit that accounts for component losses as well as the element’s nominal capacitance or inductance.
- Define unloaded Q for individual reactive components.
- Calculate the unloaded Q of capacitors and inductors.
- Perform series-to-parallel and parallel-to-series conversions with R-C and R-L networks.
- Understand the limited bandwidth over which such conversions are acceptable.
- Define loaded Q and explain how it differs from unloaded Q.
- Calculate the loaded Q for L-C resonators.

### Module 3: Impedance vs Reflection Coefficient, The Smith Chart

- Understand the importance of impedance matching in maximising power transfer in RF circuits.
- Explain the basic principles and concepts behind impedance matching.
- Understand algebraic techniques to solve impedance matching problems.
- Apply these techniques to design a two-element matching network to match two resistive impedances.
- Understand the differences in the frequency responses of different matching network topologies.
- Define the reflection coefficient and understand its significance.
- Calculate the reflection coefficient for a given impedance connected to a test port through transmission lines of various lengths.
- Derive impedance values from the reflection coefficient.
- Describe the structure, purpose, and basic use of the Smith chart in representing impedances and reflection coefficients, and easily converting between these two types of values.
- Define S-parameters and explain their significance in describing the behaviour of two-port networks.
- Understand the relationship between reflection coefficient Γ and S
_{11 } - Understand the concept of Voltage Standing Wave Ratio (VSWR) and how it is
- measured
- derived from a reflection coefficient measurement
- • (Optional) Describe the working principle of a slotted line, how it is used to measure standing waves and VSWR and how it may be implemented in AWR

### Module 4: Impedance Matching Techniques

- Measure and interpret S-parameters, specifically S
_{11}, to determine reflection coefficients and impedance in AWR. - Utilise the Smith Chart for impedance measurements and to convert between reflection coefficient, impedance and admittance.
- Understand and apply basic impedance and admittance transformations using the:
- Impedance Smith Chart with series elements.
- Admittance Smith Chart with shunt elements.
- Analyse and design two-element matching networks using the dual-coordinate (impedance and admittance) Smith Chart.
- Design and analyse L-section matching networks for purely resistive terminations when R
_{L}> R_{S}and R_{L}< R_{S}. - Analyse filter characteristics using transmission zeros to determine the filter's type and order.
- Evaluate the frequency response of L-section matching networks and understand their fixed-Q limitations.
- Design three-element matching networks with a specific quality factor (Q) to achieve precise impedance matching.
- Analyse and design T-networks when R
_{L}< R_{S } - Construct Pi-networks when R
_{L}> R_{S } - Apply the Smith Chart to match any two complex terminations.
- Utilise series transmission line sections of specific lengths combined with a capacitor or inductor to achieve impedance matching.
- Achieve an intuitive and mathematical understanding of distributed circuit elements and understand their use as replacements for discrete capacitors and inductors.
- Design distributed matching networks using short-circuited or open-circuited transmission line stubs combined with transmission line sections of specific lengths to achieve a match.

### Module 5: RF Amplifier Design

- Describe the differences between linear (S-parameter) and non-linear (Pspice) models for RF BJTs.
- Use PSpice models for RF BJTs to design bias networks that operate at a specified collector current and collector-emitter voltage.
- Identify the conditions that can lead to potential instability in RF transistors.
- Design stabilisation networks to ensure unconditional stability in RF circuits.
- Understand the differences and trade-offs among various stabilisation networks.
- Design input and output matching networks using the unilateral matching technique.
- Design input and output matching networks to maximise gain using simultaneous conjugate matching.
- Understand and be able to use operating and available gain circles to design amplifiers with a specified gain.

Course Structure

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