YOUR

 NAME:           YOUR  SID:  

Lab  4:  RC  Oscillators   EE43/100  Spring  2012   V.  Lee,  T.  Dear,  T.  Takahashi  
YOUR  PARTNER’S  NAME:         YOUR  PARTNER’S  SID:  

  Pre-­‐Lab  Score:  ___/40  

In-­‐Lab  Score:  ___/60  

  Total:  ____/100  

 
RC  Oscillators  
LAB  4:  RC  Oscillators  

ELECTRICAL  ENGINEERING  43/100  

INTRODUCTION  TO  DIGITAL  ELECTRONICS  

University  Of  California,  Berkeley  

Department  of  Electrical  Engineering  and  Computer  Sciences  

Professor  Ali  Niknejad,  Professor  Michel  Maharbiz,    

Vincent  Lee,  Tony  Dear,  Toshitake  Takahashi  

Lab  Contents  

I. Lab  Objectives  
II. Background  
III. Pre-­‐Lab  Component  
a. The  Relaxation  Oscillator  
b. The  Triangle  Wave  Generator  
IV. Lab  Section  
a. Your  Oscillator  
b. Building  the  Oscillator  
V. Lab  Report  Submissions  
a. Image  Citations  

   

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Lab  4:  RC  Oscillators   EE43/100  Spring  2012   V.  Lee,  T.  Dear,  T.  Takahashi  

Lab  Objectives  

In  this  lab  we  will  learn  to  analyze  and  build  RC  oscillators  that  may  be  used  as  one  of  the  modules  in  the  
final  project.  This  oscillator  primarily  functions  as  a  signal  generator  for  a  test  signal.  In  short,  you  are  
basically  building  a  very  simple  function  generator.  

Background  

Many  circuit  applications  that  require  precision  timing  or  PWM  (pulse  width  modulation)  control  need  
an  input  waveform  that  oscillates  between  two  voltages.  To  accomplish  this,  we  exploit  the  properties  
of  capacitors  to  create  these  oscillating  circuits.  Often  times  we  will  have  to  settle  for  triangle  or  square  
waveforms,  since  sinusoidal  waveforms  are  notoriously  difficult  to  produce  from  simple  RC  oscillators.  

These  waveforms  are  used  in  mechanical  applications,  such  as  motors  that  require  PWM  control  or  
timing  circuits  for  synchronous  digital  applications.  One  of  the  advantages  of  PWM  is  that  it  draws  less  
power  than  a  DC  input.  

However,  in  our  application,  we  will  simply  exploit  the  fact  that  it  can  function  as  a  signal  generator.  

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Lab  4:  RC  Oscillators   EE43/100  Spring  2012   V.  Lee,  T.  Dear,  T.  Takahashi  

Pre-­‐Lab  Component  

The  Relaxation  Oscillator    

Reproduced  below  is  a  schematic  of  the  relaxation  oscillator.  We’ll  use  this  as  a  square  wave  generator.  
Notice  that  it  is  configured  in  a  positive  feedback  configuration.  

  R1   R1
 

Fig  1.  Relaxation  Oscillatori  

Initially  the  relaxation  oscillator  will  start  off  with  zero  output.  But  the  world  isn’t  perfect,  and  random  
fluctuations  will  eventually  cause  one  input  terminal  to  be  higher  than  the  other.  Due  to  the  positive  
feedback,  the  output  will  then  saturate  to  the  corresponding  rail.  Once  this  happens,  the  capacitor  that  
is  connected  to  the  inverting  terminal  will  begin  to  charge  or  discharge  through  the  feedback  loop  
depending  on  the  state.      

Remember,  negligible  current  flows  into  the  operational  amplifier  input  terminals.  Also  the  supplies  to  
the  operational  amplifier  are  𝑉!!  and  𝑉!! = −𝑉!! ,  so  the  output  of  the  operational  amplifier  is  always  
either  +𝑉!!  or  – 𝑉!! ,  giving  us  really  only  two  states  to  analyze.  Intuitively,  the  square  wave  comes  
primarily  from  the  abrupt  saturation  from  the  positive  rail  to  the  negative  rail  or  vice  versa.  But  what  
about  frequency  and  duty  cycle?  Good  question…  

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Lab  4:  RC  Oscillators   EE43/100  Spring  2012   V.  Lee,  T.  Dear,  T.  Takahashi  

In  the  space  provided  below,  prove  that  the  frequency  𝑓  of  the  output  signal  of  the  relaxation  oscillator  
is  given  by  

1
𝑓=    
2 ln 3 𝑅𝐶

Show  all  relevant  mathematical  derivations  and  work.  

   
S core:__/ 20  

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Lab  4:  RC  Oscillators   EE43/100  Spring  2012   V.  Lee,  T.  Dear,  T.  Takahashi  

  More  workspace…  

The  Triangle  Wave  Generator  

The  triangle  wave  generator  is  actually  just  a  simple  integrator  shown  below.  

Fig  2.  Inverting  Integratorii  

In  the  space  provided  below,  prove  that  the  output  of  the  above  circuit  actually  integrates  and  inverts  
the  input  signal  by  showing  the  output  signal  is  given  by  the  following.  Assume  all  initial  conditions  are  
zero.  
!
𝑉!!
𝑉!"# = − 𝑑𝑡  
! 𝑅𝐶

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Lab  4:  RC  Oscillators   EE43/100  Spring  2012   V.  Lee,  T.  Dear,  T.  Takahashi  

Then  prove  how  this  generates  a  triangle  wave  from  the  square  waveform.  What  conditions  for  the  
square  input  waveform  must  be  satisfied  for  this  to  actually  produce  a  triangle  wave?    If  Vin  is  a  10-­‐Hz  
square  wave  with  5-­‐V  amplitude,  how  would  you  pick  the  value  of  R  and  C  to  generate  a  triangle  
waveform  with  4-­‐V  amplitude?    

 
Score:  __/20  
 

     Again  simulate  this  circuit  in  Multisim  and  attach  it  to  the  lab  report.  Simulation  is  worth  extra  10  
points.  

   

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Lab  4:  RC  Oscillators   EE43/100  Spring  2012   V.  Lee,  T.  Dear,  T.  Takahashi  

Lab  Section  

So  why  exactly  do  we  care  about  an  RC  oscillator  that  produces  a  square  and  triangle  wave?  

Glad  you  asked.  Square  waves  and  triangles  waves  make  excellent  test  signals,  because  they  are  periodic  
and  predictable,  unlike  real  world  analog  signals  that  you  may  be  measuring.  

In  this  lab  component,  you  will  be  building  the  appropriate  oscillator  for  your  final  project  to  act  as  you  
test  signal  source.  A  list  of  specifications  as  to  what  exactly  your  generator  will  need  is  explained  in  
detail  in  the  next  section.  

Your  Oscillator  

Obviously  we  can’t  just  use  any  arbitrary  oscillator  with  arbitrary  specifications.  Some  test  signals  are  
better  than  others.  Let’s  start  by  taking  a  look  at  the  application.  Suppose  we  need  to  pick  up  signals  on  
a  microvolt  level  through  a  pair  of  electrodes.  In  addition,  the  frequency  that  we  are  primarily  interested  
in  lies  around  10𝐻𝑧,  so  we  want  to  be  able  to  produce  at  least  that.  

However,  we  will  be  using  the  oscillator  as  a  test  source,  so  we  might  as  well  be  able  to  sweep  multiple  
frequencies.  This  will  enable  us  to  both  simulate  the  frequency  we  are  looking  for  as  well  as  test  if  our  
circuit  appropriately  rejects  undesired  frequencies.  

Thankfully,  you’ve  done  all  of  the  derivations  already  for  both  of  the  oscillators,  so  adjusting  the  design  
to  fit  the  following  parameters  should  be  fairly  simple.  

In  the  space  provided  below,  pick  appropriate  component  values  for  the  relaxation  oscillator  so  that  its  
minimum  frequency  is  10𝐻𝑧.  You  may  use  one  potentiometer  in  your  design.    

  Score:__/10  

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Lab  4:  RC  Oscillators   EE43/100  Spring  2012   V.  Lee,  T.  Dear,  T.  Takahashi  

  More  workspace…  

Building  the  Oscillator  

Now  that  you  have  calculated  the  component  values,  it’s  time  to  build  this  on  your  breadboard.    Before  
we  implement  that  microvolt-­‐level  signal  generation,  you  will  first  want  to  test  if  your  oscillator  is  
working  properly.  

As  always,  some  useful  tips  before  you  start  breadboarding  it  up:  

• Set  current  limits.  Anything  greater  than  a  reasonable  amount  of  current  will  destroy  your  
circuit,  and  you  and  your  chips  will  be  very  sad.  
• If  components  are  getting  hot,  make  sure  your  wires  are  not  shorting  and  things  are  connected  
correctly.  Check  supplies  to  make  sure  the  high  and  low  supplies  are  not  swapped.  
• The  multimeter  and  oscilloscope  are  your  friends.  Use  them  to  test  if  you  are  getting  expected  
value  on  your  circuit.    
 

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Lab  4:  RC  Oscillators   EE43/100  Spring  2012   V.  Lee,  T.  Dear,  T.  Takahashi  

i)  Build  the  relaxation  oscillator  (Fig  1).  Pick  R  and  C  based  on  your  previous  calculation.  You  can  use  a  
100-­‐kΩ  potentiometer  for  R.  Use  a  20-­‐kΩ  resistor  for  R1.  What  is  the  oscillation  frequency?  Tune  the  
potentiometer  until  the  frequency  of  the  square  wave  is  10  Hz  and  show  it  to  your  GSI.        
 
Your  GSI  Signs  Here  (15  Points)        

ii)  Build  the  triangle  wave  generator  (Fig  2).  The  input  comes  from  the  square  wave  generated  by  the  
relaxation  oscillator.  Pick  R,  C  based  on  your  previous  calculation.  You  can  use  a  100-­‐kΩ  potentiometer  
for  R.  What  is  the  amplitude  of  the  triangle  waveform?  Tune  the  potentiometer  until  the  amplitude  is  4  
V  and  show  it  to  your  GSI.    
 
Your  GSI  Signs  Here  (15  Points)        

Note:  you  may  want  to  put  a  100  kΩ  resistor  across  C  to  discharge  excess  charge.  

iii)  Once  you  have  finished  building  the  oscillator,  it  would  be  nice  to  see  some  indication  that  it  works.  
To  accomplish  this,  we  can  attach  an  LED  to  the  outputs.  

Add  an  LED  to  the  output  of  your  relaxation  oscillator  in  series  with  an  appropriate  resistor.  Usually  
resistor  between  200  Ω  and  1  kΩ  should  do  the  trick.  You  should  now  have  a  blinking  LED  at  10  Hz.  Turn  
the  potentiometer  and  show  the  LED  blink  at  different  frequencies.  Now  connect  a  second  LED  and  
resistor  to  the  output  of  your  triangular  wave  generator.  Does  the  intensity  of  the  LED  change  with  
time?  Show  your  se  up  to  you  GSI  for  check  off  

   
    Your  GSI  Signs  Here  (10  Points)        

Lab  Report  Submissions  

This  lab  is  due  at  the  beginning  of  the  lab  section.  Make  sure  you  have  completed  all  questions  and  drawn  all  the  
diagrams  for  this  lab.  In  addition,  attach  any  loose  papers  specified  by  the  lab  and  submit  them  with  this  
document.  

These  labs  are  designed  to  be  completed  in  groups  of  two.  Only  one  person  in  your  team  is  required  to  submit  the  
lab  report.  Make  sure  the  names  and  student  IDs  of  BOTH  team  members  are  on  this  document  (preferably  on  the  
front).Image  Citations  

                                                 
i
 http://en.wikipedia.org/wiki/File:OpAmpHystereticOscillator.svg  
ii
 http://en.wikipedia.org/wiki/File:Op-­‐Amp_Differentiating_Amplifier.svg  

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