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Q of a Resonant Circuit
Experiment 1.10

Abstract

Experiment to determine Q of an LCR circuit using 2 methods. Basic LCR setup: L = 31μH, C = 680 pF and R = 3kΩ. The first method is plotting ln Vm against Peak No. and returned Q as 5x10-13. The second method used a capacitor of about ¼ pF to create a weak capacitive coupling and the plot of V0 /Vi gives Q = 2.5. The second experimental method returned the best result.


Introduction

The aim of this experiment is to measure the quality factor Q of a parallel LCR circuit. This will be achieved by two methods.

Simple harmonic motion is not achievable in real physical situations. There is always some energy loss with real physical oscillations. Oscillations can be driven by a driving frequency. This will eventually reach a steady state of oscillation where the amount of energy being lost by the system is equal to the energy being replenished by the driving frequency.

The quality factor Q is a measure of how efficient an oscillating system is. It is a measure of how much energy is lost from the system per cycle.

Parallel LCR circuits are used to produce a sharp frequency resonance. They are used in radio receivers [1].




Experimental Method 1



Figure 1 produces damped oscillations.


The circuit shown in Figure 1 is using L = 31μH, C = 680 pF and R = 3kΩ and is connected to the fixed frequency generator, which provides pulses at a rate of 600Hz. These pulses charge the capacitor (C) through a resistor and when the pulse ends, the charge on the capacitor decays via the resistor (R) and the inductor (L). The damped oscillations are viewable on the oscilloscope, set to a time base of 2.5μs/cm. The oscilloscope is used to measure the distance between peaks (1μs) and also the voltage of...