RC Studies Relaxation Oscillator Introduction A glass tube containing neon gas will give off its characteristic light when the voltage across the tube exceeds a certain value. The value corresponds to the geometry of the tube (and of course the energy levels of neon) and physically signals the breakdown of the gas - an electron free in the gas acquires enough energy between collisions that it liberates several more electrons when it does collide. As a result of this avalanche effect, a large number of atoms are excited to higher energy levels, from which they return to the ground state with the emission of visible, characteristic light. This study uses a small neon tube, together with an RC circuit to build a relaxation oscillator. The R and C combine to build the voltage across the tube with their characteristic time, but when the tube begins conducting it discharges the capacitor, and so shuts itself off. The cycle then repeats itself, producing a free running oscillator. Theory A neon tube consists of two electrodes separated by a gap of a few millimeters in an atmosphere of neon. As you might guess, a neon tube is not a simple circuit element obeying Ohm s law. In fact, it is a nonlinear device. On application of a small voltage to the tube, no current passes through the tube (it is like an open circuit with infinite resistance). As the voltage exceeds a certain threshold voltage, T1, the gas breaks down and a large current starts to pass through the tube (now it is like a wire with very small resistance). Once the current is started it may be maintained by a lower voltage than T1 and we will denote this minimum voltage necessary to maintain conduction by T2. The voltage current characteristics of the tube can therefore be represented as shown in figure 1. 140512 1
I I T1 T2 Ohmic Device Neon Tube Figure 1 Because of its peculiar voltage current characteristics, the neon tube may be used to make an oscillator. Consider the circuit shown in Figure 2. ( 0 is the voltage across the supply and is the voltage across the neon tube.) R o C Neon Tube Figure 2 140512 2
Suppose we have just switched on the power supply and the capacitor, C, is uncharged. The voltage will increase as the capacitor charges through the resistor R. When exceeds T1 the neon tube will suddenly start to conduct and will discharge the capacitor until T 2. This will happen in a very short time. The capacitor will then start charging again through R and the whole cycle will be repeated. 0 T1 T2 Figure 3 When a capacitor is being charged, the charge on it is given by: Q = C 0 (1-e -t/rc ) Since Q = C for a capacitor, we have = 0 (1-e -t/rc ) Using this we can easily obtain an expression for the period of the oscillator, τ. If we assume that the discharge is instantaneous, then τ will be equal to the time it takes to charge the capacitor from T2 to T1. Letting and solving for t 1 and t 2, T2 = 0 (1 e -t 2/ RC ) T1 = 0 (1 e -t 1/ RC ) 140512 3
t 2 = -RC ln (1- T2/ 0 ) t 1 = -RC ln (1- T1/ 0 ) we have for: τ = t 1 -t 2 = RC ln(( 0 - T2 )/( 0 - T2 )) Procedure volts. Set up the circuit shown in figure 2 with R = 150K, C = 0.1µF and 0 = 100 to 110 We will monitor the voltage across the neon tube with the oscilloscope. We want to use the scope to measure the period, T 1 and T 2. To measure voltages with respect to ground, use a digital scope such as the Tektronix 2012. The outer rings of its input terminals are internally grounded. It is recommended you review Introduction to the Oscilloscope in the Brown Physics 60 Lab Manual. Using the horizontal sensitivity, vertical sensitivity and the trigger level controls, obtain a stable wave form as in Figure 3. Measure the period of the oscillation and T1 and T2 with respect to ground, i.e., = 0. The expression for τ is rather sensitive to the values of R and 0. Using a digital multimeter, measure these. Substituting the measured quantities into the expression for τ, compare the theoretical and experimental values for τ. Note that you can save your waveform data by using the Tektronix Open Choice Desktop Software available on the lab computers (extremely useful for this experiment). Data and Calculations 0 T1 T2 R 140512 4
Periods of Oscillation: τ(measured) τ(theoretical) If your construction checks out, you can proceed to variations in R and C and observe how oscillators of different, or variable frequency could be made. 140512 5