NEON BULB OSCILLATOR EXPERIMENT
When we combine a neon bulb with the circuit for charging up a capacitor through a resistor, we
obtain the worlds simplest active electronic circuit that does something useful. It oscillates, and
we can easily change its frequency of oscillation.
Charging Up a Capacitor
Let us first review the circuit for charging up a
capacitor through a resistor, shown in Figure 1.
When the switch is closed, the capacitor voltage
Vc rises exponentially toward the power supply
voltage Vo as shown in Figure 2.The formula for
the voltage rise is
V = Vo (1 - e-t/RC)
(1)
and the time constant for this rise is τ = RC.
Note that you can determine the time constant
RC by extending the initial slope of the charge
up curve until it reaches Vo is illustrated in
Figure 2.
Figure 1
Charging up a capacitor
Exercises
1) Look up the
dimensions for R
and C and show
that the product
RC has the
dimensions of time
(seconds).
2) Show graphically
on Figure 2 that
you can start at
any time t, extend
the slope of the
curve, and it will
intercept Vo one
time constant later
(at t + RC).
Figure 2
Exponential rise
Neon Oscillator
Neon Bulb Oscillator
Now we add a neon bulb
to the circuit of Figure 1
to get the neon bulb
oscillator circuit shown in
Figure 3. This circuit
gives a voltage that starts
out like the charge up
voltage of Figure 2, but
breaks into oscillation as
shown in Figure 4.
Figure 3
Neon Oscillator
Figure 4
Neon bulb oscillator waveform.
The neon bulb causes the oscillation in the following way. The capacitor voltage Vc is also
across the neon bulb. As the capacitor charges up, but Vc is less than Vf, the neon bulb is off.
(At this point, there is neutral neon gas in the bulb which does not conduct electricity between
the two post in the bulb.) When Vc gets up to the bulb firing voltage Vf, the neon gas becomes
ionized, starts to glow, and creates a short circuit that very quickly discharges the capacitor.
The capacitor continues to discharge until Vc drops to Vq where the glow stops (the bulb shuts
off); we again have a neutral neon gas and no electricity can be conducted between the posts
2
Neon Oscillator
inside the bulb. Now the capacitor again charges up through the resistor until Vc reaches Vf and
the bulb fires again. This process repeats, giving the wave form shown in Figure 4. Small neon
bulbs often have a firing voltage Vf around 100 volts, and a quench voltage Vq around 40 volts.
(Some work at lower voltages.)
Calculation of the Period of Oscillation
To calculate the period T of the oscillation in the neon bulb oscillator, we see from Figure 4 that
T = t2 - t1, where t1 is the time when Vc rose up through Vq and t2 is when Vc rose up to the firing
voltage Vf. During this time we have the simple charging of a capacitor given by equation 1:
Vc = Vo (1 - e-t/RC)
(1)
Applying Eq. 1 to times t1 (Vc = Vq) and t2 (Vc = Vf) gives
Vq = Vo 1 - e-t1/RC
(2)
Vf = Vo 1 - e-t2/RC
(3)
Equations (3) and (4) can be rewritten as
Vo e-t1/RC = Vo - Vq
(4)
Vo e-t2/RC = Vo - Vf
(5)
Dividing Eq. 4 by Eq. 5 gives
e-t1/RC = e t2
e-t2/RC
- t1 /RC
=
Vo - Vq
Vo - Vf
(6)
where we used ea/eb = ea-b.
Finally taking the logarithm of Eq. 6 gives
T = t2 - t1 = RC Ln
Vo - Vq
Vo - Vf
(7)
where Ln is the natural logarithm (Ln ea = a).
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Neon Oscillator
The Experimental Setup
Figure 5
Neon oscillator with voltage divider
We could use the experimental setup of Figure 3, putting an oscilloscope across the capacitor and
observing Vc directly. This works well with a cathode ray tube (CRT) oscilloscope that can
handle the over 100 volts needed to fire the neon bulb. However we will use the computer based
oscilloscope MacScope in order to save a record of the wave forms, and MacScope is limited to
input voltage in the range of +5 to -5 volts. To use MacScope, we add the voltage divider shown
in Figure 5, so that Vc is dropped by a factor of 1000 and can easily be measured by MacScope.
The Voltage divider consists of two resistors connected between points A and B of Figure 5.
The 107 ohm resistor is so large that very little current flows through it and thus the voltage
divider has very little effect on Vc which we wish to measure. MacScope is attached across the
104 ohm resistor, and therefore sees only .1% of the voltage Vc. (Since the same current goes
through both resistors, the ratio of the voltages equals the ratio of the resistances.) For safety
purposes we put the neon bulb and voltage divider in a single box to reduce the chance of
someone putting a finger on one of the high voltage leads.
Setting Up the Experiment
Since this is one of your first major wiring exercises, we will take you through it in easy steps.
Circuit 1
Making sure that the power supply is off, first
wire the power supply Vo, the resistance box R,
and capacitor box C as shown. The convention in
physics and engineering laboratories is that red is
positive (+) and black is ground (-). So that you
can see what you are doing, use a red wire to go
from the red post on the power supply to either of
the posts on the resistance box. You might as
well use a red wire to go from the other post of
the resistance box to the (not low) post of the
capacitor box. Finally, use a black wire to go
from the "low" post of the capacitor box to the
ground (black) post on the power supply. You
should now have the circuit shown in figure 6.
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Figure 6
Basic RC circuit
Neon Oscillator
Add Neon Bulb
We have built the neon
bulb and voltage divider
into a single box. The next
step is to attach the neon
bulb box to the RC circuit
as shown in Figure 7.
Again use a red wire for
the positive side and a
black wire for the negative
side.
Add Voltmeter
In Figure 8 we have added
a voltmeter to measure the
voltage Vo of the power
supply. This voltage Vo
can also be measured on
MacScope by pressing the
button on the neon
oscillator box which open
the switch and disconnects
the neon bulb. When this
is done, the voltage on the
capacitor rises to Vo and
stays there.
Figure 7
Attaching the neon bulb box to the RC circuit.
Figure 8
Add voltmeter
Initial settings
We want you to experiment with various voltage and RC settings. But for now we will give you
some initial settings so that you can get the oscillator working.
A) Resistor Box
Set the slide switch to HI (right) and the right knob to 220 kΩ.
B) Capacitor Box
Set the knob on the capacitor box to .15 microfarads (µf).
C) MacScope
•Connect the output of the neon bulb box to input #3 of MacScope.
•Select *20 from the Amp menu
•Select No Offset from the Hardware menu
•Turn MacScope on, then
•Adjust the T scroll bar so that the time scale goes from 0 to 150 milliseconds.
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Neon Oscillator
D) Power Supply
Turn the voltage knob all the way down (counter clockwise), and turn the power supply on.
Also turn the standby switch to on. Set the "Volts" - "MA" switch to volts.
Now slowly turn up the
voltage on the power supply
until the neon bulb comes on.
The bulb should be flashing.
If you turn the voltage up
more, it should flash faster.
If the voltage is too low, the
bulb shuts off, and if too
high, it stays on
continuously. The interesting
range is where it flashes.
You should see the saw tooth
curve of Figure 9 while the
bulb is flashing.
Figure 9
Saw tooth curve on MacScope
Reading MacScope
Remember that we have put a
1000 to 1 voltage divider in
the circuit, so that each
millivolt on the voltage scale
actually represents one volt.
In addition, in order to get the
true voltage values above
zero, we have selected No
Offset from the Hardware
menu as shown in Figure 10.
If we had left MacScope on
Figure 10
automatic offset, the curve
Selecting No Offset and Negative Trigger Slope
would have been centered
and the voltage scale would
not have a true zero. (The zero would be at the average of the curve.)
Reading Vo
The reason for the switch above the neon bulb (shown in Figure 8) is so that we can record the
power supply voltage Vo. If we press the button to open the switch, the neon bulb is
disconnected from the circuit and the capacitor charges all the way up to Vo. This is read by
MacScope. (If you push the button, you see the curve rise to a constant value which is just Vo,
corrected by 1000.)
Taking data
6
Neon Oscillator
We can use the trigger capability of MacScope to grab both
Vo and the oscillating curve in one data file. Set MacScope
on negative trigger as shown in Figure 10, hold down the
switch button so that the voltage Vo goes to MacScope, and
adjust the MacScope trigger button just below Vo as shown
in Figure 11. Now set MacScope on Trigger (as in Figure 12),
and start it. When you release the switch, current flows
through the bulb and the voltage drops. The dropping voltage
activates the negative trigger and MacScope starts recording
data.
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Figure 11
Neon Oscillator
In the resulting curve is shown
in Figure 12. The pretrigger
data (t < 0) shows Vo, while the
post trigger data t > 0 shows
the oscillation.
Figure 12
The MacScope trigger captures the curve just when we release
the disconnect switch, and the neon bulb is back in the ciorcuit.
The pre trigger data (t < 0) shows the power supply voltage Vo.
Analyzing MacScope Data
Once we have the MacScope
data, there are a number of
ways to get information from
it. In Figure 13, we used the
cursor to measure the height of
Vo. We do this by dragging a
rectangle whose height is equal
to Vo and reading the height in
the rectangle that appears while
we are dragging. The answer is
164 volts (remember the factor
1000).
Figure 13
Using the cursor to measure Vo.
8
Neon Oscillator
A more accurate
way to measure Vo
is to use the editor
as shown in Figure
14, where we have
selected data just
before and after
t = 0. Here we see
that Vo is 159.3
volts. The
accuracy of this
number depends
upon how well
your MacScope
was calibrated.
Figure 14
Using the numerical values to measure Vo.
In Figure 15 we
have used the
cursor to measure the period of
the oscillation and got 45.6
milliseconds or a frequency of
about 22 hz. We could also
use the editor and numerical
data as we did in Figure 14.
Figure 15
Using the cursor to measure the period. The amplitude of the
wave was increased using the "V" scroll bar at the top of the
control panel.
9
Neon Oscillator
Figure 16
Demonstration that the initial slope of the curve intersects Vo at one time constant RC.
Finally, we note that the time constant RC = 220 x 103 Ω * .15 x 10-6 F = 33 x 10-3 sec or 33 ms.
We drew a rectangle 33 ms wide going up to Vo as shown in Figure 16. Drawing the diagonal
we see that it accurately represents the initial slope as expected by theory. (The capacitor is on
exponential rise to Vo.)
The Experiment
The neon bulb oscillator is enormously flexible. By choosing different values of R and C, you
can easily have the period range from the order of a millisecond to many seconds. Changing Vo
changes the shape of the wave form and also changes the period.
What you should do is try different values of R and C to get a broad range of periods. Also
change Vo to get different shaped wave forms from the pointed saw tooth waves (Vo >> Vf) to
round top waves (when Vo is just above Vf). Record the results as MacScope files for later
analysis.
As an instructive exercise, adjust Vo down until it is just above Vf, so that the bulb barely fires.
Then the curve looks very much like Figure 2 for the charge up of a capacitor. Save this wave
form as a MacScope file, and use this as experimental data to (a) verify that the initial slope
intercepts Vo at one time constant RC down the T axis, and b) carry out exercise 2 with this data.
(Take your MacScope file of this curve home, bring up this curve on your own Macintosh, and
adjust the amplification and the time base so that the curve nicely fills the screen. Then do an
imagewriter screen dump and do your exercises on the screen dump.)
10
Neon Oscillator
Computer Analysis of RC Circuits
Earlier we considered the analytic solution, first of the discharge, then of the charging up, of a
capacitor through a resistor. The results:
V = Vo e-t/RC
(Discharge)
(1)
V = Vo (1-e-t/RC)
(Charge up)
(2)
were fairly easy to obtain for the discharge, but took us a whole page when we added one more
term to handle charging up. Analytic solutions have the advantage of giving general results that
cover a wide range of parameters, but it becomes difficult to obtain analytic solutions when the
problem becomes just a bit more complicated. In contrast, computer solutions can be
generalized with very little additional work. In this section we will first discuss a computer
program for capacitor discharge, show how it is easily modified for charge up, and then modify it
some more to describe the neon bulb oscillator.
Discharge
To analyze the capacitor discharge, we go back to Kirchoff's law and set the sum of the voltage
rises equal to zero:
Vc - VR = 0
q
- iR = 0
C
(3)
We now have one equation and two variables q and i. The other
equation is obtained by noting that i is the rate charge is leaving
the capacitor:
i=-
dq
dt
(4)
Equations 3 and 4 will be the basis of our computer program.
Equation 4 is a differential equation (it involves dq/dt), and therefore needs special handling.
First we "undo" the calculus by writing
dq = - idt
(5)
where we think of dt as a small but finite time interval.
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Neon Oscillator
The quantity dq is the change in the charge q during the time dt. If we call qold the amount of
charge in the capacitor before dt, and qnew the charge after dt, then qnew and qold can be related
by the command
LET qnew = qold + dq
(6)
Using equation 5 for dq, our command for calculating qnew becomes
LET qnew = qold - i *dt
(7)
At this point equation 7 is very close to being a command in the computer language BASIC. In
BASIC, we can think of each variable, like q, i, and dt as the name on a mailbox (the kind you
see in a post office). Inside the mailbox goes a number that is the current value of the variable.
When given a LET statement, the computer goes to the right hand side, looks up the values of the
variables, performs the indicated operations, and then stores the result in the mailbox whose
name is one the left hand side. In the case of equation 7, the computer will look in the mailboxs
labeld q, i, and dt, multiply the numerical values of i and dt together, and subtract that product
from the numerical value found in mailbox labled q. The computer then goes to the mailbox
labled q and replaces the contents with the value just calculated.
An automatic consequence of this procedure for a LET statement is that the computer must use
old values in order to calculate the right hand side, and the result automatically becomes the new
value on the left hand side. Thus it is not necessary to write down the subscripts new and old;
that happens automatically and Eq. 7, written as a BASIC statement becomes
LET q = q - i *dt
(8)
Once the computer calculates a new value of q, it needs a new value of i, which it can get from
Eq.3
i = q/RC
or as a let statement
LET i = q/(R*C)
(9)
Now that the computer has the new value of i from Eq. 9, it goes back and calculates the next
new value of q. This process is repeated over and over again in a calculational loop indicated
schematically in Eq. 10;
12
Neon Oscillator
(10)
13
Neon Oscillator
The Computer Program
Equation (10) is not a complete program for we have to tell the computer what values of R, C,
and dt to use; what initial value of q should be used, and how to plot the results as we go along.
Figure 1 is a complete program for discharging a 10-8 farad capacitor through a 106 ohm resistor.
Let us go through each piece of this program to see how it works.
In the first block we
tell the computer the
experimental
constants. Aside
from giving the
values for R and C.
we are saying that
we had a 150 volt
power supply
(V0 = 150).
In the initial
conditions we are
saying that the
capacitor is initially
fully charged (Vc =
Vo, q = CVo at time
T = 0).
From Ohms law we
get VR = iR or
Figure 1
Simple program for capacitor Discharge
i = VR /R
From the definition
of capacitancewe get q = CVc or
Vc = q/C
Kirchoff's Law gives Vc - VR = 0, Vc = VR = iR, or
i = Vc/R
The charge flows out of the capacitor to create the current i, thus i = dq/dt or
dq = - i*dt
qnew = qold + dq = qold - i*dt
The Time Step
14
Neon Oscillator
The point of the computer calculation is to break the discharge into small time steps dt, calculate
the amount of charge dq that leaves the capacitor during that time step (we had dq = - i*dt ), and
then subtract that charge from what remains in the capacitor (qnew = qold + dq). In order to get an
accurate calculation, the time step dt must be sufficiently small that the current i does not change
much during the time step (otherwise we would not know what value of i to use in dq = i*dt).
From our earlier discussion we know that the capacitor voltage drops to 1/e (1/2.7) of its original
value in one time constant T = RC. This is a big step, too big for our small time step dt. What
we have done in the time step section is choose one tenth of a time constant for our time step.
This is still a big time step, but it gives fairly accurate results. (The current i does not change too
much in one tenth of a time constant.)
The Discharge Loop
The discharge loop is bracketed by the commands
DO WHILE T < 3*R*C
---LET i = Vc/R
LET q = q - i*dt
LET Vc = q/C
LET T = T + dt
PRINT "T";TAB(40*Vc/V0);T
---LOOP
What the computer does when it meets such a loop command is to repeat what is inside the loop
while the condition (T < 3*R*C) is met. In this case the loop will be repeated while T is less
than 3 time constants (30 steps).
Inside the loop we have changed things a little bit from Eq. 10. We put the equation for i first,
and replaced q/C by VC since the capacitor voltage VC is what we can observe directly:
LET i = Vc/R [was LET i = q/(R*C) ]
The next line is our command
LET qnew = qold - i*dt
with the subscripts new and old dropped. Then we use the definitions of capacitance C = q/Vc to
calculate the new capacitor voltage Vc from the new q
LET Vc = q/C
15
Neon Oscillator
Then we update our clock with the command.
LET Tnew = Told + dt
since an amount of time dt elapses every time we go around the loop.
16
Neon Oscillator
Typewriter Plotting
It does not do any good to have the computer calculate all these new values for q and Vc is we
cannot see the results. In the last, rather peculiar looking line inside the discharge loop, we
PRINT out the results using BASIC's version of standard typewriter operations. In the
command
PRINT "T";TAB(40*Vc/V0);T
three printing steps are involved (separated by semicolons). In the first step the computer prints
the letter T; this gives us the vertical axis of T's seen in the output of Fig. 1. Next the computer
tabs over a number of spaces proportional to Vc. (If Vc = Vo, we go over 40 spaces; if Vc =
V0/2, we go over 20 spaces etc.) Finally we print out the numerical value of the time T so that
we can see in the plot how much time has elapsed for each step. There are much more precise
ways to plot the capacitor voltage Vc, but none give us the time scale as easily. We will discuss
other plotting techniques later, typewriter plotting will do for now.
Exercise 1
Directly on the output of Figure 1, show that that curve has a time constant of about .01 seconds.
Do this by showing that any tangent line intersects the axis one time constant later.
A More Accurate Program
An inherent weakness of the program in Figure 1 is that we used a relatively large time step
dt = RC/10. The computer is perfectly capable of calculating with a much smaller time step and
repeating the discharge loop many more times. But if we used a smaller time step in Figure 1,
and printed out the value of Vc every time, we would have to look through a very long plot
before we see much of a discharge of the capacitor.
In order to use a short time step but not print out too much, we have in figure 2 added the
following lines to the discharge loop.
FOR N = 1 to 10
-------
calculate for
one time step dt
NEXT N
now print out the results
17
Neon Oscillator
In this so called FOR NEXT statement the computer calculates new values of Vc for 10 time
steps before printing out the results. However we used a time step dt that was ten times shorter
than the time step in Figure 1, (.01 RC instead of .1RC), so that we got essentially the same
results. There is a slight difference because the calculation in Figure 2 is more accurate.
18
Neon Oscillator
Figure 2
Capacitor Discharge with a Shorter Time Step. This is the same calculation as in Figure 1, except
that we used a time step 10 times shorter, but then used the FOR NEXT loop to do 10 calculations
of Vc before printing the results.
Exercise 2
Type in the program of Figure 2 and run it to see that you get the same results. Then cut the
time step to one thousandths of a time constant and adjust the FOR-NEXT loop so that you get
essentially the same results.
19
Neon Oscillator
Capacitor Charge Up
In our analytic solutions there was a big change when we went from capacitor discharge to
capacitor charge up. In a computer program, the change is very small. In Figure 3 we show the
circuit, program, and output for the charging of a capacitor. The program of Figure 3 is identical
to the program of Figure 2 except for two lines in the charge up loop. In Figure 1, Kirchoff's law
required that Vc - VR = Vc - iR = 0 giving the command
LET i = Vc/R
In Figure 3, Kirchoff's law requires that V0 - VR - Vc = V0 - iR - Vc = 0 giving the new
command
LET i = V0/R - Vc/R
The only other change is that current is now flowing into the capacitor in Figure 3 where it
flowed out of C in the discharge of Figures 1 & 2. Thus the sign of i is now reversed in the
command
LET q = q + i*dt
In the output of Figure 3, we see our standard capacitor charge up curve.
20
Neon Oscillator
Exercise 3
Use graphical methods on
the output curve of Figure
3 to show that the time
constant for this capacitor
charge up is
approximately.01 seconds.
Show what your graphical
methods were.
Figure 3
Capacitor chargeup
21
Neon Oscillator
Neon Bulb Oscillator
One modification of our
charge up program of
Figure 3 and we end up
with a program for the
neon bulb oscillator
shown in Figure 4. To
effectively add a neon
bulb to our circuit, we
went to the
calculational loop and
watched the capacitor
voltage Vc. When Vc
got up over the bulb
firing voltage Vf, we
immediately dropped
Vc back to the bulb
shutoff or quench
voltage Vq, and reduced
the charge q in the
capacitor to the value
CVq that it should have
at this voltage. We then
let the capacitor charge
up again, discharge,
etc., and get the typical
neon bulb oscillator
voltage shown.
Lab Exercises
For several of your
experimental neon
oscillator results in this
weeks lab, use the
program of Figure 4 to
compare the prediction
of this program with
your experimental
results. This requires in
each case using your
experimental values for
R, C, V0, Vf, and Vq.
Then compare the
Figure 4
Neon Bulb Oscillator. We can effectively add a neon bulb to our
charge up program by monitoring the capacitor voltage Vc in the
charge up loop. When Vc gets up to the bulb firing voltage Vf, we drop
Vc back to the bulb shutoff voltage Vq and reduce the charge q to CVq.
22
Neon Oscillator
shape and timing of the output of your program with the curve you stored as a MacScope file.
(Use screen dumps of both to make the comparison). Comment on the results.
23
Neon Oscillator
24