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Unformatted text preview: BME 153 Lab 5 Lab 5 –Inductors and Capacitors Nigel Chou Shijie Lab Partner: Tim Liu Section 1 October 31, 2007 I have adhered to the Duke Community Standard in completing this assignment. Objectives Apparatus • LCR Meter • Fluke 45 Dual Display Digital Multimeter (DMM) • Tektronic TDS 1012 Digital Storage Oscilloscope • TGS 50 Signal generator • Resistors, capacitor and inductor Procedure The procedure listed in the lab manual was followed with no deviation. Data and Calculations Inductors and capacitors The RMS voltage was obtained by taking V pk-pk and dividing by 2 2 : 2 2 2 of Amplitude pk pk RMS V V V- = = The phase shifts of the voltages are calculated by: f t × × ∆ = π 2 shift) (time shift Phase The % difference of the DMM measurements and Oscilloscope measurements is calculated by: % 100 V pe Oscillosco V pe Oscillosco- V DMM diff % RMS RMS RMS × = The Vpk-pk and phase angle across the capacitor is calculated by: out source element circuit V V V- = Where element circuit V , source V and out V are phasor quantities The % difference of the capacitance and inductance of each circuit element is calculated by: % 100 Value Nominal Value Nominal- value Measured diff % × = Calculating complex impedances To calculate the complex impedance of the circuit elements, we observe that 1 R element(s) circuit 1 R in out Z Z Z V V + = , where all quantities are phasor quantities and Z R1 is given by a phasor with amplitude = R1 and phase = 0. 1 BME 153 Lab 5 Hence, we can calculate the complex impedance using Z R1, V in and V out . - = ∴ 1 out in 1 R element(s) circuit V V Z Z The complex impedance is then calculated using capacitance/inductance values measured by the LCR meter: eq C j Z ) 2000 )( 2 ( 1 s) capacitor( π = and eq L j Z ) 2000 )( 2 ( ) inductor(s π = where C eq and L eq are the equivalent capacitances and inductances of the single, series or parallel combinations of circuit elements. Equivalent capacitances are calculated by: In series: 2 1 2 1 C C C C C eq + = In parallel: 2 1 C C C eq + = Equivalent inductances are calculated by: In series: 2 1 L L L eq + = In parallel: 2 1 2 1 L L L L L eq + = Input and Output impedances Since the output voltage and the output current of the function generator are in phase, we can find the output impedance by: (RMS) output (RMS) output output I V Z = (both are real numbers) Phase shifts are calculated as in the previous section The currents across R4 and R5 are calculated as follows: 5 R 5 R R5 V I = and 4 R 4 R R4 V I = where R4 & R5 are measured with the LCR meter The input and output impedances are calculated as follows: R4 OC out I V Z = and R5 in in I V Z = (note that all of the above values are phasor quantities) Input and Output impedances The transfer function of Figure 7 is given by: - ∠ + = + = + + + = 501000 ) 0149 . ( 2 arctan )) 0149 . ( 2 ( 501000 500000 )...
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This lab report was uploaded on 04/09/2008 for the course BME 153 taught by Professor Malkin during the Fall '07 term at Duke.
- Fall '07