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[answered] ABSTRACT An unknown circuit in a black box was studied in t

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ABSTRACT

An unknown circuit in a black box was studied in this laboratory experiment, a procedure

was developed to identify the components in the black box and the equivalent circuit in the black

box.

INTRODUCTION

The purpose of this experiment is to develop and use a procedure to determine (identify) the

equivalent circuit for an unknown linear, passive circuit. In engineering, an unknown system is

often referred to as a Black Box.

THEORY

The components in the black box could include resistors, capacitors, and inductors. By

testing the features of each component, the equivalent circuit of the black box could be

identified.

Resistor:

Series and parallel combination of resistors:

The equivalent resistance of N resistors in series is: Fig.1. Resistors in series

The equivalent resistance of N resistors in parallel is: Fig.2. Resistors in Parallel

Ohm?s law states that the voltage, V, across a resistor, R, is equal to the current, I, following

through the resistor multiplied by the resistance of the resistor

V= I ? R 1 Capacitors:

Impedance of capacitor: Variable frequency-response of capacitor: Fig. 3. Fig. 4. 2 Inductors:

Impedance of inductor:

Variable frequency-response of inductor: Fig. 6. Fig. 5. 3 As the impedance of the inductor and capacitor vary as the frequency changes, the voltage

across them vary, as well. Therefore, the variable-frequency response features of the capacitor

and inductor can be used to identify the component in the Black Box.

METHODS

Experimental Procedure

Check if the Black Box contains any capacitor or inductor.

1. The function generator was used to generate the AC power of V s = 10sin(?t) V, the value

of ? was variable, and the circuit as shown in Fig.3 was built.

2. The voltage across the black box was measured at different frequencies, and the data of

the experimental RMS value was compared to see if the voltages changed as the

frequency changed. The frequency range was from 10 Hz to 100 kHz.

3. The change of voltage along the increasing frequency across all the combinations of two

ports on the black box observed, and recorded.

4. As the lab team observed the voltage across all two-ports combination did not change as

the frequency of the source changes. The lab team made a relevant conclusion that the

equivalent circuit in the black box was a resistive circuit. Therefore, the voltage across all

the two-port combinations did not change as the frequency of the source changed.

Basing on the conclusion that the black box contained a resistive circuit, the lab team

designed the following steps to find out the equivalent circuit in the black box.

1. The four ports on the black box were marked as ?A?, ?B?, ?C?, and ?D?, the

combinations of every two ports are ?AB?, ?AC?, ?AD?, ?BC?, ?BD?, and ?CD?.

2. The resistance of every two-port combination was measured, and recorded.

3. The equations for solving the equivalent circuit were written down, and solved.

4. The equivalent circuit in the black box was sketched according to the calculation.

Experimental Apparatus 5 Fig.7. Circuit model in black box provided by instructor

Equipment List

Digital multi-meter, Agilent 34401A;

Function Generator, Agilent 33220;

Oscilloscope, Agilent 54622A;

Cables;

Black Box RESULTS

Table 1: Measured Resistance between Ports

Port Combinations Measured Resistance RAB (k?) 23.74 RAC (k?) 24.70 RAD (k?) 36.64 RBC (k?) 0.967 RBD (k?) 12.90 RCD (k?) 13.87 6 Table 2: Measured and Actual Values of Resistances in Black Box

Measured

Actual

Percent Error

Resistance

Resistance (k?) Resistance (k?)

(%)

R1

23.74

24

1.08

R2 0 0 0 R3 0 0 0 R4 0.967 1 3.3 R5 12.90 13 0.77 Fig. 8. Experimental model for the equivalent circuit in the black box Discussion

The experimental results were in agreement with theory with the error generally remaining

around 3% for most of the data points. There was one data points with high error of 15.55%, but

after solving the equations of finding the resistance of individual resistor, the high error turned

out did not affect the result much, and the biggest error for the individual resistor in the black

box was 5.05%, which was acceptable for this experiment.

The lab team encountered few difficulties during the experiment. At the beginning of the

experiment, as the measurement value given by digital multi-meter was not stable, the lab team

figured the voltage across one of the two-ports changed along the change of the frequency of the

source. Then, the lab team spent about an hour to find out the components in the black box, 7 however, as the more measured had been done, the lab team realized there was not any capacitor

or inductor in the black box.

After identifying the circuit in the black box was resistive circuit and the learning the circuit

model from the instructor, the measurement became easier. The resistance across every two-ports

was measured, and the equations were established and solved. The equivalent circuit could be

identified by solving the equations.

CONCLUSIONS An unknown circuit in a black box was studied in this laboratory experiment, a procedure

was developed to identify the components in the black box and the equivalent circuit in the black

box. The equivalent circuit in the black box was identified as a resistive circuit, and the

resistance across every two-ports was measured to calculate the equivalent resistive circuit

components. Finally, the equivalent circuit of the black box was identified. 8

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