How to Use S-Parameters (S11, S12, S21 & S22) to Describe the Performance of RF / Microwave Filters. @technologiesdiscussion1676

Uploaded April 2025 | Updated September 2026, 1 week ago

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How to Use S-Parameters (S11, S12, S21 & S22) to Describe the Performance of RF / Microwave Filters.

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$Transmission Line #1. Circuit Theory, Short Breaks Down Here! Impedance, Wavelength & Why It Matters Transmission Line Theory playlist. https://www.youtube.com/watch?v=mrU84J3e26Y&list=PLFxhgwM1F4yz620k0WcHdRrO5JRAC0yFh For access to this presentation materials, membership is required: I need the Material PPT Sent me an email to Technologies.Discussion@gmail.com If you need the whole playlist material, send me email and we discuss. Give me some time to response. Thanks. Transmission Line #1. Difference Between Transmission Line Theory & Circuit Theory: Electrical Size! Transmission Line #1. Size λ: Circuit Theory (Short Circuit) Vs Transmission Line (Impedance Vary) Transmission Line #1. Circuit Theory (Short Circuit) / Tx Line (Impedance Vary): Electrical Size, λ. Transmission Line #1. SHORT Circuit (Circuit Theory) That Isnt Short (Tx Line Theory) Becos of λ. Transmission Line #1. Why a Short Circuit (Circuit Theory) Isnt Always Short (The λ Mystery) The key difference between transmission line theory and circuit theory is electrical size. Transmission lines may be a considerable fraction of a wavelength or even many wavelengths in size. Circuit theory (DC / low freq) assumes that the physical dimensions of the network (or cable) are much smaller than the electrical wavelength. In transmission lines, the inductance (L) & capacitance (C) per unit length introduce a delay in the propagation of electrical signals. Heres why: 1. Basic Concept of Wave Propagation in Transmission Lines A transmission line can be modeled as a distributed network of series inductance (L) and shunt capacitance (C). When a voltage signal is applied, the inductance resists sudden changes in current, while the capacitance resists sudden changes in voltage. This interaction causes the signal to propagate as a wave rather than instantaneously. 2. Propagation Delay Due to L & C The speed of propagation (v) in a transmission line is determined by: Higher L (inductance) → Slows down signal propagation because it opposes rapid current changes. Higher C (capacitance) → Slows down signal propagation because it takes time to charge/discharge the line. Thus, the more L and C per unit length, the slower the signal travels. 3. Intuitive Explanation Inductance (L): Acts like inertia against current changes, causing a lag. Capacitance (C): Acts like a storage that needs time to fill up (charge) before voltage builds up. Together, they create a low-pass filter effect, delaying high freq components. Transmission line is a distributed parameter network, where voltage and current can vary in magnitude and phase over its length, while circuit analysis deals with lumped elements, where voltage and current do not vary appreciably over the physical dimension of the elements. A transmission line is often schematically represented as a two-wire line since transmission lines always have at least two conductors. 1. Assumptions and Applicability: Circuit Theory (Lumped Element Model): Assumes that electrical components (resistors, capacitors, inductors) are lumped and that the physical dimensions of the circuit are much smaller than the wavelength of the signals. Works well for low freq applications (DC or AC where wavelength is large compared to circuit size). Ignores wave propagation effect (no time delay in signal transmission). Transmission Line Theory (Distributed Model): Considers the distributed nature of electrical parameters (resistance, inductance, capacitance, and conductance per unit length). When the circuit size is comparable to or larger than the signal wavelength (Eg. High freq, Rf or microwave or high-speed digital signals). Accounts for wave propagation, reflections and impedance matching. 2. Signal Behavior: Circuit Theory: Treats voltage and current as the same at all points in a node (no phase delay). Kirchhoff’s Voltage Law (KVL) and Kirchhoff’s Current Law (KCL) apply directly. Transmission Line Theory: Voltage and current vary along the length of the line due to wave propagation. Must account for time delay and phase shift due to finite propagation speed. Requires analysis using telegrapher’s equations, which describe wave behavior. 3. Key Parameters: Circuit Theory: Uses lumped elements: R, L, C. Impedance is simply the ratio of voltage to current (Ohm’s Law). Transmission Line Theory: Uses distributed parameters: Series resistance (R) and inductance (L) per unit length. Shunt conductance (G) and capacitance (C) per unit length. 4. Effects Considered: Circuit Theory: Neglects electromagnetic wave effects. No consideration for reflections or standing waves. Transmission Line Theory: Must account for: Reflections (due to impedance mismatches). Standing waves (when reflections interfere with incident waves). Signal integrity issues (Eg. ringing, crosstalk in high-speed circuits). 5. When to Use Which? Use Circuit Theory When: The circuit dimensions are ≪ λ (wavelength of the signal). Dealing with low freq power systems or analog circuits (Eg. audio frequencies). Use Transmission Line Theory When:$

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