Lecture 5: RMS and Average Value of Triangular Periodic Signal скачать в хорошем качестве

Lecture 5: RMS and Average Value of Triangular Periodic Signal

In this lecture, Dr. S.M. Gudhe provides a comprehensive derivation of the Average and RMS (Root Mean Square) values for a Triangular Periodic Signal. Beyond just the math, this video explains a fascinating concept: Why do Triangular Waves and Sawtooth Waves share the exact same RMS and Average values? We explore the physics of waveform symmetry and signal orthogonality to address this question. Key Topics Covered: 1. Signal Decomposition & Equations: How to split a symmetrical triangular wave into two parts (y1 and y2) to simplify analysis. Deriving the signal equations using y = mx + c and direct observation. 2. The Derivations (Formulas): Average Value: Calculated via the Area Method (Area of Triangle / Time). Result: Vm / 2 (or 0.5 * Peak). RMS Value: Calculated via Integration (Square → Mean → Root). Result: Vm / √3 (or 0.577 * Peak). 3. Advanced Concepts (Why Triangular = Sawtooth?): Linear vs. Non-Linear Operations: Understanding why Average values add up linearly, but RMS values do not. Orthogonality: How the product of split signals becomes zero, allowing us to calculate RMS as the square root of the sum of squares. Timestamps: 0:00 - Introduction to Triangular Waves 0:09 - Splitting the Signal (Symmetry Analysis) 0:43 - Finding Equations for y1(t) and y2(t) 2:46 - Direct Method for Signal Equations 4:12 - Average Value Derivation (Peak/2) 4:55 - RMS Value Derivation (Step-by-Step Integration) 8:25 - Result: RMS = Peak/√3 8:27 - Conceptual Deep Dive: Linear vs. Non-Linear Properties 11:10 - Orthogonal Signals Explanation 13:35 - Summary & Importance in Electrical Engineering Helpful for Signals & Systems and Basic Electrical Engineering students! Don't forget to Like, Share, and Subscribe. #TriangularWave #RMSValue #AverageValue #OrthogonalSignals #SignalsAndSystems #CircuitTheory #DrSMGudhe #ElectricalEngineering #WaveformAnalysis #EngineeringMath #RootMeanSquare