RF Microwave & Transmission Line Theory - RAHRF200

Explore the shift from lumped to distributed analysis in RF design, showing how transmission lines require distributed modeling when line lengths approach a wavelength and voltages differ along the line.

Examine transmission lines as distributed parameter networks and use lumped sections to derive the general transmission-line equation from per-unit-length resistance, inductance, conductance, and capacitance.

Derive phasor equations for a short transmission-line segment using kvl and kcl, obtain voltage and current phasors, and introduce the complex propagation constant gamma = alpha + j beta.

Define and analyze the characteristic impedance of a transmission line by relating voltage and current through phasors, gamma, and beta, and explain how wavelength and phase velocity arise.

Explore lossless transmission lines, where R and G are zero, yielding alpha zero and gamma = j omega sqrt(LC); Z0 = sqrt(L/C) and v = 1/sqrt(LC).

Derive time domain equations from phasors to show how voltage and current on a transmission line propagate in time and space, including reflections and standing waves.

Demonstrates wave propagation and standing waves, contrasts lossless (alpha zero) cosine form with reflected components, shows flat wave with constant amplitude, and explains attenuation by loss E^-alpha z.

Explore a numerical example on a transmission line to compute the propagation constant gamma (alpha and beta) and voltage at a point over time using boundary conditions.

Explore terminating a transmission line with a load, understand reflections and matching, and learn how the reflection coefficient governs power delivery, maximum power conditions, and input impedance.

solve a terminated transmission line example to determine the reflection coefficient gamma and input impedance, then compute the load voltage for a 50-ohm line with a 50+50j load.

Learn how reflections create standing waves on a transmission line, derive Vmax and Vmin from the incident and reflected waves, and relate them to the standing wave ratio.

Explore special cases of lossless terminated lines: a shorted end yields gamma minus one and standing waves; an open end yields gamma plus one and capacitive open stubs for matching.

Solve the shorted, lossless transmission line example to compute Vmax and end-of-line current. For Z0 = 300 Ω, length 0.8 m, input 10 V, Vmax ≈ 11.56 V and I0 ≈ 39 mA.

Explore quarter-wave transmission lines of lambda over four and their use as input impedance transformers, with Z_in = Z0^2 / ZL for real loads.

solves a quarter-wave transmission-line matching problem, deriving vp and lambda, then computes Z_in and gamma for 50 ohm line to 300 ohm load at 180 and 90 MHz.

Explore the Smith chart as a graphical tool for impedance matching in microwave design. Normalize impedances to the characteristic impedance to analyze reflection coefficient and standing wave ratio.

Find impedances on the smith chart by normalizing 100 + 100 j to 50 ohms, then read real and imaginary parts; practice with a parallel capacitor-resistor network and reflection coefficient.

Demonstrate finding the reflection coefficient on a Smith chart by normalizing Z_L to Z0, locating the load point, and reading magnitude and angle.

Learn impedance to admittance conversion using a Smith chart, applying admittance equals one over impedance, normalizing by the characteristic impedance, and deriving the original admittance from a given impedance.

Using a Smith chart, analyze a 50 ohm transmission line 0.4 lambda long terminated by 60 + 50 j, computing the reflection coefficient, load admittance, SWR, and input impedance.

Demonstrate simulating transmission lines and Smith chart analysis in ADS to verify input impedance and reflection coefficient from S-parameters, using 60 plus 50 j and 0.4 lambda examples.

Understand impedance matching to maximize power transfer by transforming the load into the conjugate of the source impedance, so Z_in matches Z_s via lumped L and C or transmission lines.

Design an l-section impedance matching network with lumped reactive elements (inductor and capacitor) to transform a load to 50 ohms, using shunt and series elements and smith chart guidance.

Explore the Smith chart that displays impedance and admittance without conversion, simplifying matching, with an example using a 150 plus j75 load and 75 plus j15 source at two gigahertz.

Design impedance matcher with lumped components in ads simulation, guided by smith chart, to conjugate match 75 to 150 at 2 ghz using a shunt capacitor and a series inductor.

Master impedance matching with transmission lines through single-stub tuning, using shunt and series stubs (open or short), on microstrip PCB with vias, analyzed via Smith chart and Momentum ADS layouts.

Design a 50-ohm matching circuit for a 60 − j80 ohm load using single-stub tuning on the Smith chart to cancel imaginary admittance.

Learn single stub tuning in ads using Smith chart and smart components to achieve 50 ohm input and 60 minus j80 ohm conjugate matching.

Apply quarter wave transmission line matching to convert a complex load (100 + 100j) to a real 50 Ω, using two sections to achieve a 50 Ω input impedance.

Design a matching network in ads using Smith chart; convert a 30 + j10 load to a 60 + j80 source at 1.5 GHz with transmission lines and one capacitor.

Explore wideband matching using constant Q lines on the Smith chart to design multi-section LC networks that achieve bandwidth, with trajectories inside low Q regions and optionally using ADS tools.

Design a wideband matching circuit in ADS for 8–12 GHz, matching 50 ohms to 10 ohms. Use constant circles and chart matching to optimize network response.

Design wideband impedance matching with a tool to connect a 100 Ω load to a 50 Ω source from 3–5 GHz, using a bandpass lumped network and series RC.

learn how microstrip lines act as planar transmission lines for designing matching circuits, and practice defining substrate parameters, drawing layouts in ads, and performing em simulations.

Explore microstrip line calculations for matching circuits, deriving widths and lengths from the angle of reflection coefficient via Smith chart, and validating with practical substrate and frequency parameters.

Define substrate and conductor parameters in ADS to model microstrip structures. Set thickness, dielectric constant, and relative permeability, select copper, and specify conductor roughness.

Design a 50 ohm to 60 plus 100 ohms matching circuit using microstrip lines, converting transmission lines, calculating widths and lengths with ADS line calc, and validating at 5 ghz.

Define a two-layer pcb substrate, create a dielectric one with permittivity 3.66, configure copper conductor thickness, and apply surface roughness, then model a simple microstrip layout for simulation.

Learn to simulate a simple microstrip transmission line, build schematic and layout, and compare schematic and layout results using momentum RF simulations and Z in calculations.

Explore an alternative copper substrate definition with a two-metal layer, align conductors to ground reference conductor two, and compare simulations to the previous method for validation in ADS.

Learn to construct a short stub in a simulation by defining a substrate, creating vias, and tuning the layout to match the schematic.