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BME 153 lab 7 _Nigel

# BME 153 lab 7 _Nigel - BME 153 Lab 7 Lab 7 Transient...

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BME 153 Lab 7 Lab 7 – Transient response Nigel Chou Shijie Lab Partner: Tim Liu Section 1 November 28, 2007 I have adhered to the Duke Community Standard in completing this assignment. Objectives The objective of this lab is to learn to measure the time constant for first-order circuits, both for RC integrating circuits and RC differentiating circuits. We will also measure the resonant and natural frequencies of a second order RLC circuit, and observe the behaviour of an LC resonant circuit. Finally, we will learn to use Multisim to perform transient analysis on a simulated circuit. Apparatus LCR Meter Fluke 45 Dual Display Digital Multimeter (DMM) Tektronic TDS 1012 Digital Storage Oscilloscope TGS 50 Signal generator Resistors, capacitors and inductors Potentiometer Solderless breadboard Procedure The procedure listed in the lab manual was followed with no deviation. The procedure used to measure the time constant is as follows: we first recorded the peak-to-peak voltage of the input square wave, then used the horizontal cursors to find the approximate position of 63.2% of the peak-to-peak voltage. We then time-shifted the waveform such that the point where the output waveform crosses the vertical cursor is at the center of the screen. Finally, we used the vertical cursors to find the time difference between the point where the input square wave changes from positive to negative voltage to the center of the screen. To measure the resonant frequency , we switched to sinusoidal input and adjusted the frequency until the amplitude of the output voltage reached a maximum. To find the damped natural frequency , we measured the period of the oscillations observed in the output response and took the inverse of the period. Data and Calculations 3.1 and 3.2 RL differentiating and integrating circuits The theoretical time constants for the figure 1 circuit is calculated by RC = τ e.g. s RC μ τ 5 . 215 10 214 1007 9 = × × = = - s RC μ τ 1472 10 450 3270 9 = × × = = - The theoretical time constant for the figure 2 circuit is calculated by R L / = τ E,g. s R L μ τ 920 . 4 9878 10 6 . 48 3 = × = = - The % difference of measured time constant with respect to the theoretical time constant: % 100 constant time l theoretica constant time l theoretica - costant time measured diff % × = 1

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BME 153 Lab 7 The approximate frequency range over which the figure 1 circuit integrates the input is calculated by: RC RC ) 85 tan( ) arctan( 85 ° - ° - ϖ ϖ e.g. 0nF) 70 4 C and k 3 . 3 (R Hz 236 1 s krad 767 . 7 ) 10 450 ( 3270 ) 85 tan( 220nF) C and 1k (R kHz 8.28 s krad 04 . 52 ) 10 214 ( 1007 ) 85 tan( 1 - 9 1 - 9 = = = = × ° = = = = × ° - - ϖ ϖ The approximate frequency range over which the figure 2 circuit integrates the input is calculated by: L R R L ) 5 tan( ) / arctan( 90 85 ° < - ° < ° ϖ ϖ e.g. Hz 2830 s krad 78 . 17 0486 . 0 ) 5 tan( 9878 1 - = = ° < ϖ 3.3 Series RLC Circuit The theoretical resonant frequency for the figure 3 circuit is calculated by LC n 1 = ϖ E.g.
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