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A parallel - plate capacitive transducer having air as dielectric between the plates, plate area is 50 mm × 50 mm and plate spacing is 0.5 mm. The displacement causes the capacitance to change by 10 pF. The sensitivity of the capacitive displacement transducer is:

  A parallel - plate capacitive transducer having air as dielectric between the plates, plate area is 50 mm × 50 mm and plate spacing is 0.5 mm. The displacement causes the capacitance to change by 10 pF. The sensitivity of the capacitive displacement transducer is: A. 50.23 pF/mm B. 66.67 pF/mm C. 61.25 pF/mm D. 59.12 pF/mm Answer: Option B Solution: C =    ε * A/d or, C =8.854 *10^-12* 50*50/0.5*10^-3 = 44.27 pF sensitivity =  Δc/ Δd or, sensitivity = - ε * A/(d^2) or, sensitivity = -  8.854 *10^-12* 50*50/(0.5*10^-3)^2 = 88 pF (approx)

Interactive OFDM Simulator: The "CP" Effect

Interactive OFDM: The "CP" Effect Compare how Cyclic Prefix converts linear convolution into circular convolution for perfect channel estimation. Cyclic Prefix (CP) Enabled (Standard) Disabled (No CP) Multipath Taps (Delay) Subcarriers (N) Noise Level (σ) Run Simulation Estimation Error (MSE): 0.000 Condition: --- Observation: Click Simulate to see the results. The Mathematical Secret: Why the Simulator Works The simulator demonstrates a fundamental conflict in digital communications: FFT properties vs. Physical reality. Here is the step-by-step math behind the visualization. 1. The Linear Convolution Problem In a real-world wireles...

Interactive Simulator for Q-function

Q-Function Interactive Simulator Move the slider to see how the "Tail Probability" (the area in red) changes. This red area represents the Probability of Error (BER) . Threshold Distance ( x ) — (Simulates Increasing SNR) x = 1.0 Q(x) = 0.1587 At x = 1.0 , the probability of noise crossing the boundary is 15.87% . In digital comms, this would be a very high bit error rate. The Math Behind the Q-function To understand why the BER formula for BPSK is Q(√(2E b /N 0 )) , we must look at the geometry of the signal and the physics of the noise. 1. What is the "Threshold Distance"? In a BPSK system, we transmit two possible signal levels. In a simplified model, these are represented as amplitudes: Bit 1: +√E b Bit 0: -√E b The Decision Boundary: The...

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