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Unformatted text preview: Boise State University Department of Electrical and Computer Engineering ECE 212L – Circuit Analysis and Design Lab Experiment #3: Impedance Measurements 1 Objectives The objectives of this laboratory experiment are: • to use phase and amplitude measurements in the determination of unknown series and parallel impedance connections. 2 Theory In this experiment, we will explore several ways of measuring the impedance of a “black box” whose impedance is unknown. There are two types of black boxes as shown in Table 1 below. Table 1: Types of Black Boxes Type Impedance Description SRL Series RL Circuit PRC Parallel RC Circuit In addition, type SRL can consist of a nonideal inductor having a small series resistance and type PRC can consist of a single, almost ideal, capacitor with no shunt resistor in parallel with it. 2.0.1 Series RL Circuit- V 1 ~ +- V 2 ~ (a) (b) R s R s R c R c j L L s s ω + +- v (t) 1 +- v (t) 2 Figure 1: Series RL Impedance Determination Consider the series RL circuit shown in Figure 1 where R s and L s are unknown elements to be determined. This unknown series impedance is placed in series with a calibrating series resistor with known value R c . Assume that the sinusoidal input and voltages, v 1 ( t ) and v 2 ( t ), respectively, v 1 ( t ) = √ 2 V 1 cos( ωt ) v 2 ( t ) = √ 2 V 2 cos( ωt − ϕ ) = √ 2 AV 1 cos( ωt − ϕ ) (1) 1 are observed with a dual-trace oscilloscope. The transfer function between the output phasor voltage ˜ V 2 and the input voltage phasor ˜ V 1 is obtained as ˜ V 2 ˜ V 1 = R c R c + R s + jωL s = R c √ ( R c + R s ) 2 + ( ωL s ) 2 ̸ − tan − 1 ωL s R c + R s (2) On the other hand, ˜ V 2 ˜ V 1 = A ̸ − ϕ (3) Therefore, the amplitude ratio of the two waveforms can be determined from the rms or peak-to- peak voltage magnitudes as A = | ˜ V 2 | | ˜ V...
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- Fall '08