The purpose of this experiment was to observe the response of an RLC circuit and analyze the resulting graphs to find missing variables.
PRE-LAB
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| Figure 1 |
To begin our lab, we sought to find the damping ratio (ζ) and the natural frequency (ωo) based on the given circuit elements (Figure 1). However, in order to do so, we had to first measure the actual resistance values of the resistors. These measured values are included in the schematics of the circuit in Figure 1. From these values and the other circuit elements, we found the neper frequency (α) and the natural frequency (ωo). Finally, we found the ratio of these two values to find the damping ratio (ζ)
PROCEDURES
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| Figure 2 |
After the pre-lab, we constructed the circuit as shown in Figure 2. We had the analog discovery connected to the second resistor (R2) to measure the voltage across it, which we considered to be Vout. Then, we applied a 2 V step input to the circuit at varying frequencies until the circuit was able to reach steady-state in between pulses.
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| Figure 3 |
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| Figure 4: Close up of Figure 3 |
The resulting graphs are shown above in Figures 3 and 4. From Figure 4, it can be seen that the the overshoot (Mp) was approximately 35 percent. This is because the initial voltage was around 40 mV and the voltage decayed past 0 mV by 14 mV (Mp = 14/40 * 100% = 35%)
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