ME 360 Lab Report
Dynamic Response
Salman Qali
Lab Partners: Tyler Pipkin, Logan Newcomb, and Sam Watson
Group number: 7
March 29, 2018
Objectives
In the lab experiment, a dynamic first-order RC circuit will be designed with the aim of calculating the time-constant theoretically and experimentally. The bandwidth will be calculated. The frequency response will be achieved by calculating the gain and the phase lag. Ultimately, the bode plots will be drawn.
Background
The RC circuit is defined as a first-order dynamic circuit, which has a time-dependent response. The dynamic system is defined as the system with the output dependent on time. In other words, the output of the dynamic system may change with the time, unlike the static system.
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• Frequency 0.5Hz.
The waveform was given to the circuit, and the output was observed. The LEDs were blinking at the input and output which meant that the circuit is working as expected.
The first part of the experiment deals with the construction of a first-order RC circuit on the provided breadboard. The resistor value will be kept constant while the capacitor values will be changed to 0.1,0.2 and 0.3uF. After construction, the voltage followers were used at the input /output of the circuit to provide isolation. This allowed us to nullify any chances of the loading due to impedance mismatch. Four LEDs were connected: two for the detection of input current in both directions, and two for the detection of output current in both directions.
In addition, the waveform was changed to the frequency of 2.5Hz. The signal was fed to the circuit, and the oscilloscope probes were connected to its input and output. The data was recorded for plots.
The time constant was calculated using point of 70.7% of the final value. The time constant was also found using the formula:
Time constant = R*C
The bandwidth was found using the
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Now, the data was plotted as a function of frequency. The results were studied to draw the certain conclusions. Results
Construction of first-order system and evaluation of time-constant:
On the application of the input signal, the LEDs were found to be blinking. However, a delay between the blink of input and output LEDs was observed. It was a result of the time constant. On switching towards the negative part of the waveform, the input LEDs immediately swapped. However, the output LEDs took time as the voltage took time to drop due to the time constant. Furthermore, the delay was directly proportional to the calculated time constant.
Another observation made was that the LEDs blinked with a sequence. The order of LED lighting was:
Input LED Output LED Input Opposite direction LED Output Opposite direction LED
This observation also verified the lag of output waveform relative to the input waveform. The time constants were compared along with the error analysis. The bandwidth was calculated by taking the inverse of the time constant.
Table 1. Time constant