Appendix A: How the Interval Timer Works

The interval timer has basically 3 different parts:

1. A resistance-capacitance timing circuit
2. The 555 timer integrated circuit
3. An LED circuit
   

These parts are indicated in Figure A1.

Parts (1) and (2) are really not separate but interact with each other. They are important in determining how the circuit works so we will consider them in detail.

The Capacitor

The basic time interval that the circuit produces is accomplished by charging a capacitor. A capacitor is a device that can "separate" charge. It consists essentially of two conducting plates separated by an insulator as shown in Figure A2.

A current in the top lead, as shown, deposits positive charge on the top plate. The current in the bottom lead (which, at any time, must be equal to the current in the top lead) removes positive charge from the bottom plate and hence leaves a negative charge on the bottom plate. The amount of positive charge on the top plate, at any time, must equal the amount of negative charge on the bottom plate.

Whenever there is a positive charge on one plate (and an equal amount of negative charge on the other plate), there is a voltage across the plates which is proportional to the magnitude of the charge. This voltage will be a rise from the negatively charged plate to the positively charged plate. (The relation between the voltage and charge is: v=Cq where C is the capacitance of the capacitor. The capacitance of a capacitor depends primarily on the size of the plates, the distance between them, and the electrical properties of the insulator between the plates.)

The unit of capacitance is the "farad". It turns out a farad is a very large unit indeed. Real world capacitors that you will encounter usually have values between 10^-12 (a "picofarad") to 10^-3 farads. A common unit for capacitance is the "microfarad" which is 10^-6 farads.

Charging the Capacitor

The capacitor is placed in the simple circuit shown in Figure A3. Assume at first that there is no charge on the capacitor as shown in (a). Since the capacitor voltage is zero, the battery voltage, V_B, all appears across the resistor R, and a large current is produced. This current starts to charge up the capacitor by depositing positive charge on the top plate and removing negative charge from the bottom plate. As charge accumulates, the capacitor voltage, v, builds up. This voltage reduces the voltage across the resistor and the current gets smaller. Finally, after a long time, the capacitor charge will have increased to the point that the capacitor voltage is equal to the battery voltage and the current will be zero. We can say that the capacitor is fully charged.

(a)	(b)	(c)

The way the capacitor voltage looks as the capacitor charges is shown in Figure A4.

This time function is an "exponential" function, and it has form given in equation (1):

(1)

where t (tau) is the "time constant". The exponential function in Figure A4 has V_B=1 and t (tau) =1.

It turns out that the time constant for the series RC circuit is equal to the product of the resistor's value times the capacitor's value (t=RC) or (tau=RC). If R is in ohms and C is in farads, then the unit of the time constant will be seconds.

A circuit with a small time constant would charge faster than a circuit with a larger time constant. Figure A5 shows three exponential functions with different time constants.

MATLAB Interactive Demo Enter in R & C values to see calculated time response.

Figure A5. Three Time Constants

The 555 Timer

Now let's look at how the 555 timer is connected to the timing circuit. A portion of the 555 timer is shown in Figure A6.

Figure A6. How the 555 Timer is Connected to the Timing Circuit

The part of the 555 timer which causes the capacitor to charge and dischargd is basically a switch which is controlled by an input voltage. In this case, the voltage across our capacitor is the input voltage which is used to control the switch.

When the switch is open, the capacitor charges. The charging circuit is shown in Figure A7(a). (Since the switch is open, we don't have to show it.)

Figure A7. Charging and Discharging Circuits shown Separately

When the switch is closed, the capacitor is "shorted out" as shown in Figure A7(b). The voltage across the capacitor is zero.

So let's see what the switch control portion of the 555 timer does. The input to the switch control is the capacitor voltage, so that it is possible to switch between the charging and discharging circuits when the capacitor voltage reaches a certain level.

Assuming the capacitor voltage is initially zero, and the switch is open, then the capacitor will charge up to the battery voltage (9 volts in our case) exponentially with a time constant,t (tau), having the value RC as shown in Figure A8.

Figure A8. Switched Capacitor Voltage

The 555 timer switch control is such that when the capacitor voltage reaches a level which is 2/3 of the battery voltage (i.e., 6 volts), the switch will close and the capacitor voltage will then discharge rapidly to zero as shown.

Calculating the Interval Time

The equation for the charging waveform is given in equation (2)

v = 9(1 - exp[-^t/_t]) (2)

where t=RC.

Now T can be found from equation (2). T is the time at which v = 6 volts, so

9exp[-T/t] = 9 - 6 = 3

from which T = -t ln(1/3) = 1.098t or

T = 1.098RC (3)

The Circuit in More Detail

Figure A9 shows the interval timer in more detail.

Figure A9. The Interval Timer Circuit in More Detail

In particular the internal structure of the 555 timer is expanded. The portion of the timer called the switch control above is in reality a flip-flop and two comparators. A flip-flop is a common electronic circuit that has two stable states, and the device generally "flips" between them. The output of the flip flop is "high" (9 volts) or "low" (0 volts). It is this output that turns on and off the transistor switch which changes the mode between charging and discharging the capacitor. The output of the flip-flop is available on pin 3 of the 555 timer, and it is this signal which is supplied to the transistor-LED circuit.

Signals to switch the flip-flop are derived from the two comparators. These devices compare two input signals and indicate when one particular signal is higher than the other.

Initially, the trigger input, 2, is high, the flip-flop output is low and the 555 transistor switch is closed

The push button is pressed. When the trigger input, 2, is below V/3, it causes the flip-flop to be low (0 volts) and the transistor switch inside the 555 timer to be open. Hence the capacitor will be start to charge.

The signal which causes the internal switch inside the 555 timer to open so that the capacitor can charge, is used to control the 2N2222 transistor switch so that the LED lights during the time that the capacitor is charging.

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