[ECEN 1400]
Introduction to Digital and Analog Electronics
R. McLeod
HW #2: Capacitors and the 555 Timer
1
RC Circuit Charging (15 pts)
1.1
Assuming that the capacitor is initially uncharged (that is, the voltage across it is zero),
find the voltage across the resistor AND the capacitor as a function of t > 0 assuming
the switch J1 is closed at t = 0.
1.2
Plot these two functions. At what time does the capacitor voltage reach 9 V?
C1 = 2 µF
R1 = 1 kΩ
V1 = 10 V
J1
2
Capacitors in Parallel (15 pts)
Using the I/V relation of the capacitor, derive the equivalent capacitance of two capacitors in parallel. Hint: You
have two possible forms of the relation, one a derivative and one an integral. Given the layout of the circuit, one
is more natural to use than the other.
V1 (t)
Version 2.2, September 11, 2014
C1
C2
Page 1
[ECEN 1400]
3
3.1
Introduction to Digital and Analog Electronics
R. McLeod
An RC Circuit Driven by a Square Wave (30 pts)
Create the following RC circuit in multisim
The function generator on the left and scope on the right are from the Simulations → Instruments menu.
Note that both instruments are assumed to be grounded by multisim, which is why this circuit seems to have no
return current path to ground. It is through the function generator. Include a screenshot of your circuit.
3.2
Get your bearings
Set the function generator to produce a square wave with 1 kHz frequency and 2 Vpp amplitude (Figure 1a).
Then, set the oscilloscope to show both traces and capture this view. Trace 1 should be the square-wave
source and trace 2 should be the voltage across the capacitor. Check both the amplitude and the frequency of the
square wave by setting the voltage (Vertical) scale and time (Horizontal) scale (Figure 1b).
(a) Basic operation of function generator.
(b) Basic operation of oscilloscope.
Figure 1: Multisim equipment set up.
Version 2.2, September 11, 2014
Page 2
[ECEN 1400]
3.3
Introduction to Digital and Analog Electronics
R. McLeod
Plot Capacitor Voltage as a function of input frequency
1. Capture several capacitor voltages below 1 kHz, several in the range of 1 kHz and several above 1 kHz to
show the shape. A good range would be between 100 Hz and 20 kHz.
2. Plot the capacitor voltage versus frequency on a log-log plot (Excel can do this right click on the axis to
change it from a linear to a log plot).
3. At what frequency does the voltage drop to about half of the driving waveform? How does this compare to
the inverse of the RC time constant?
This is a hint of how filters work your RC circuit is a simple low-pass filter in that passes frequencies lower than
a certain cutoff frequency. Music passed through this filter, for example, would lose the highest notes. A female
singers voice can be separated from the base line this way (yes, youve made a Karaoke machine).
4
A 555 oscillator (40 pts)
The 555 IC is a very common chip used for a wide variety of simple timing and oscillation functions. Your blinking
bike light is very likely built with a 555 timer. We will learn later in the class what is inside, but right now, well treat
it as a black box. Read the Wikipedia entry on the 555 timer http://en.wikipedia.org/wiki/555_timer_IC as
an introduction. The pin definitions and the astable mode section are most relevant. Dont worry that you dont
understand all of this we will come back to it in the digital portion of the class.
Look at the circuit below. Ignore the 555 chip for a moment and you see two resistors in series (so they act as
a single equivalent resistance of 4.4 kΩ) in series with a 4.7 nF capacitor. The R and C are connected between 5 V
and ground so will charge with a time constant of 20.68 µs. When the voltage on the capacitor (connected to pin
6 Threshold and pin 2 Trigger) grows to 23 of 5 V, the 555 chip will ground pin 7 (Discharge). Now the capacitor
will discharge through the 2.2 kΩ resistor with a time constant of 10.34 µs. When the capacitor voltage falls to
1
3 of 5 V, the 555 timer disconnects pin 7 from ground and the process repeats. This circuit thus operates as an
oscillator, switching back and forth between charge and discharge stages. The OUT pin indicates which stage the
chip is currently in and thus provides a binary (low or high only) wave which could be used to drive, say, a digital
clock.
Version 2.2, September 11, 2014
Page 3
[ECEN 1400]
4.1
Introduction to Digital and Analog Electronics
R. McLeod
Create the Circuit in Multisim
• 555 chip is under MIXED → Timer → LM555CM.
• Battery component is under Sources → POWER SOURCES → DC POWER.
4.2
Confirm that the oscillator is working as expected by verifying that the voltage on pin
6 is at 31 and 23 of the source voltage when the timer switches. Observe the OUT pin
(PIN3) with your scope. Include a screenshot of your schematic.
Version 2.2, September 11, 2014
Page 4