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        Laboratory Experiment 2 EE348L
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1.   HSpice user manual  version 2001 4   is as  follows      tran resolution duration sweep parameter_name poi number_of_points valuel value           University of Southern California  EE348L page10 Lab 2    An example is shown below   KEKE K K K K K K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K KK        analysis section  FR FAS 2g K K K ie K K ig K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK os K K K K K K K KK     tran  Ins 200ns sweep r2 poi 3 1k 10k 100k    Exercise   Rerun the SPICE netlist in Figure 2 5 with the modification to sweep the parameter r2  through three values of 1k  10k  100k  Plot Vo  What should the amplitude for Vo be for each case     The transient analysis with the parameter sweep will produce multiple waveforms on the same panel in  WaveView Analyzer  To view which waveform corresponds to which parameter value  you can click on  the box next to the waveform name  Then you can separate each waveform by right clicking in the panel  the waveform names are located in     2 3 4    ALTER Statements   In HSPICE  embedded sweeps are not allowed  Thus the  ALTER statement can be used so that the same  simulation is repeated for a different value of another parameter  We will practice by changing the  parameter    opamp_gain    using the  ALTER statement  page 3 40 of HSpice user manual  version  2001 4      An HSpice simulation with n  ALTER statements produces n 1 output files  For a transient analys
2.   for example    options post 1 brief nomod alt999 accurate acct 1 opts    2 3 Voltage Controlled Voltage Sources  VCVS     In Exercise 2 of the laboratory exercises of laboratory  1  we modeled an operational amplifier using a  voltage controlled voltage source  VCVS   These dependent sources are represented in SPICE using the  E element     University of Southern California  EE348L page5 Lab 2    The syntax of the E element in SPICE is  Ename n  n  p  p  gain  lt MAX val gt   lt MIN val gt     Exxxis the name of the E element source  such as Elor E2  There are four nodes in the dependent  source command  The first two nodes of the voltage controlled voltage source  VCVS   n  and n    represent the node numbers for the positive and negative ports of the output  The second set of node  numbers  in  and in   represents the positive and negative nodes of source   s reference voltage     The gain of the VCVS is indicated by the value of gain  The value of the output is dependent on the  controlling voltage by a factor of the gain      lt MAX val gt  and  lt MIN val gt  are optional parameters that determine the maximum and minimum values  the E element can assume during the course of the simulation  In other words  they specify the upper and  lower limits on the voltage the dependent source can assume  These keywords are very useful in modeling  the limits placed by the power supplies on the output voltage of an op amp     2 3 1 Examples of VCVS statements   E1231050    In the a
3.  Gm  expressions for the effective input resistance  inductance   and capacitance  Reff  Leff  and Ceff  respectively     R L    S        Figure 2 12  Tuned circuit for VCCS problem 5  Zin s  is the input impedance of the entire circuit  to the right of the arrow     B     C     Let the resonant frequency of the input impedance be denoted as      What is    in terms of  inductances L   L  and capacitance Cin   The resonant frequency is the frequency at which the  imaginary impedances cancel each other out   What design condition must be satisfied at the  resonant frequency to achieve a purely real and matched impedance at the input port  that is   Zin j      Rs     Determine H s   Q    o  and H     and simplify for the case in part  B   You should be able to  show that the transfer function can be cast in the form of a second order bandpass filter     University of Southern California  EE348L page21 Lab 2          H s  H w         2  Ky Ky  1          Qw  W   What is the low frequency gain  What is the high frequency gain  What is the phase at resonant  frequency in degrees     D  Model the amplifier in Figure 2 12 in SPICE  using the SPICE Voltage Controlled Current  Source  VCCS  element  G  Represent the core element of the amplifier  as outlined by the  dotted line box in Figure 2 12  as a sub circuit in your netlist  Let G  2 5mmho  R  50 Ohms   C   50fF  L  5nH  and L  1nH  Let L  be a parameter with default value of InH    a  Perform an ac sweep from 100 MHz to 1THz  v
4.  K K K K K K K K K K K 2K K K    KEEK K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K KK K K K K K K K K K K K K K K 2 K K       begin output form section  KKE K K K K K K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K KK K K K K K K K K K K K K 2k K 2 K K     Before saving the file  make sure to press return once  and only once  after END  END    Note  Remember that SPICE is case insensitive     2 2 1 Options statements   Options statements      options     are control statements to specify various parameters associated with the  simulator  A description of HSPICE options can be found on page 8 14  Chapter 9  pages 10 22 to 10 36   pages 11 24 to 11 26  and page12 7 of the HSPICE manual  version 2001 4  December 2001   The  following options are a useful set of options for the beginner      options post  1 post output data associated with each node in the circuit  page 9 14     options brief stop printback of netlist until  options brief 0 is encountered  page 9 6     options nomod do not print model decks  which may be large  page 9 9      options alt999 generate up to 1000 unique output run files  page 9 5      options accurate useful for accurate simulation of large circuits  page 9 40      options acct 1 reports job accounting and runtime statistics  page 9 5      options opts print the current settings of all control options  page 9 10      Multiple options may be combined on one line  See
5.  K ok ok KK    vl inOac 1    KEKE K K K E K es K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K KK        probe statement section  KEEK fe fe 2g E K ae E K K K K fe K K K K 2S 2g K K K K K K K K K K K K K k K K K K K K KK k K K K K K K K og     probe ac gain par  v out  v in      probe ac gaindB par  20 log10 v out  v in       probe ac phase par  vp out  vp in       FEE K K E E K 2 K K K K K K K K k K K K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K KK        specify nominal temperature of circuit in degrees C  EKEK K K K E K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K k KK K K K K K K K K KK     TEMP 27    EEKE K K KE E K a K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K KK    x    analysis section  FEE K K 2g E K ae K K K K K fe K K is K 2S ag K K K K K K K K K K K K K k K K K K K K KK k K K K K K K K 2     ac dec 100 10k 10G sweep rpar1 poi 3 100 1e3 1e4       alter   param cpar1 100pF    END    Figure 2 8  HSPICE netlist highlighting ac analysis with parameter variation and user defined expression    2 3 5 6 Printing from HSPICE   See Laboratory Experiment 1  section 1 9 3 for printing with Wave View Analyzer    Another method is to use ctrl PrintScreen while a window containing the plot is open on your desktop   Then the entire window can be pasted  and edited before submitting      2 4 Voltage Controlled Current Sources  VCCS     University of Southern California  EE348L page
6.  and its phase in the  dc   ac or the  tran analyses  we have to be able  to specify an expression for the transfer function Vo s  Vin s   and the phase shift from input to the  output     We use the PAR command to do so  The syntax is described on page 7 8 of the HSpice user manual   version 2001 4  The  probe statement  used to specify the graphical output of node voltages  branch  current and user defined expressions for a particular analysis is described in page 8 10 of the HSpice user  manual  version 2001 4        2 3 5 1 Plotting the transfer function   We specify the ac plot of the transfer function   v out  v in   where out and in are the output and input  node names respectively  as follows  where gain is the user defined plot parameter     probe ac gain par  v out  v in       The ac plot of the transfer function  expressed in dB terms is 20 log10 v out  v in    is   probe ac gaindB par  20 log10 v out  v in        In the above expression  log10 is the logarithm to base 10  and gaindB is the user defined plot parameter     2 3 5 2 Plotting the phase of the transfer function  The phase of a node voltage or a branch current is specified by using vp node  or ip branch_current   as  described on page 8 30 of the HSpice user manual  version 2001 4     Accordingly  the phase difference from input to the output is   probe ac phase par  vp out  vp in       where phase is the user defined plot parameter    Note  the type of analysis specified in the  probe statements above m
7.  n  n     transresistance current flowing through vname    2 6 1 Examples of CCVS statements  H123V150    In the above example  the output voltage of the CCVS H1  is between nodes 2and 3  The controlling  or  reference current is flowing through voltage source V1 in the circuit  The gain of the CCVS is 50   Mathematically  V 2 3  50  I V1   Note that optional parameter MAX and MIN are absent     A CCVS can be used to model a device with finite gain and maximum and minimum limits on the value  of the output voltage     Hlimited out  out  V1 MAX 5V MIN 0V 1000             In the above example  Hlimited models a device where V out  out   1000 0 OI V1   with a maximum  voltage of 5 0V and a minimum voltage of OV    In many cases  it is useful to parameterize the transresistance of a CCVS so that simulations that check  the influence of varying transresistance can be run  This is specified in HSpice as follows         _param transres 2e5  Hlimited out  out  V1 MAX 5V MIN OV transres    In the above example  transresis a user defined parameter  It is important to note that user  defined       University of Southern California  EE348L page17 Lab 2    parameters should not be the same as SPICE commands or reserved keywords  They should also be less  than 16 characters in length  Unpredictable results can occur if user defined parameters are not different  from SPICE commands or reserved keywords           Of all the dependent sources  the CCVS is the least encountered source you  wil
8. 14 Lab 2    Voltage Controlled Current Sources  VCCS  are dependent sources that are represented in HSpice using  the G element  page 5 34 of the HSpice user manual  version 2001 4   The G element can also be used to  describe a Voltage Controlled Resistor  VCR  or a switch  page 5 35 of the HSpice user manual  version  2001 4      The syntax of the G element in HSpice is  Gxxx n  n  in  in   lt MAX val gt   lt MIN val gt  transconductance    Gxxx is the name of the G element source  such as G1 or G2  There are four nodes in the dependent  source command  The first two nodes of the voltage controlled current source  VCCS   n  and n    represent the node numbers for the positive and negative ports of the output  The second set of node  numbers  in  and in   represents the positive and negative nodes of source   s reference voltage      lt MAX val gt  and  lt MIN val gt  are optional parameters that determine the maximum and minimum  values the G element can assume during the course of the simulation  In other words  they specify the  upper and lower limits on the current the dependent source can assume  These keywords are very useful  in modeling the limits placed by the power supplies on the output current of the device     The gain of the VCCS is indicated by the value of transconductance  The value of the output  is dependent on the controlling voltage by a factor of the transcondutance     2 4 1 Examples of VCCS statements  G1231050    In the above example  the output curr
9. 2 inm 0 r2    PRS FAS 2g 2g K K 2 E K 2 K K K K K fe K K is K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K KK      k   Darameters section  KKK K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K K K     param r2 1k   param opamp_gain 1  FKK K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K 3K K K K K K K K K K K K K K K K K K K K     x   Sources section  2 2 2 KE K KE K K 2 K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K KK K K K K K K ok ok ok K    vl in 0 sin OV 60mV 10x 100ps 0     FEE K K K E E K E K K K K K K K K k K OK K K K K K K K K K K K K K k K K K K K K KK k K K K K K K K KK        specify nominal temperature of circuit in degrees C  KEKE EK K KE E K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K KK     TEMP  27    KEE KE K KE K E K K K K K K K K K K 2s K K a K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K KK    xxx analysis section  EEE K K KE E K 2 K K K K K K K K 2s K K K K K K K K K K K K K K K K K K K K K K Kk k K K K K K K K KK     tran  1ns 200ns sweep r2 poi 3 1k 10k 100k       alter   param opamp_gain 1e2  ealter   param opamp_gain 1e4    END    Figure 2 6  HSPICE netlist for op amp circuit in Exercise 2 of lab assignment  1 with  ALTER  statements    Exercise    Rerun the HSPICE netlist in Figure 2 6 and plot the different output waveforms corresponding to each  parameter value  You should plot a total of three  3  
10. K K K K K K 2 K K K K K K K K K K K K KK k K K K K K K K 2         options section  FKK K K K K K K K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K K K     options post 1 brief nomod alt999 accurate acct 1 opts    FEE K K KE K K 2 K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K KK k K K K K K K K KK         subcircuit section  2 2 2 KE K K K K K K K K K K K K K K K K E K K K K K K K K K K K K K K K K K K K K K of K K K K K K K ok ok KK     subckt my_opamp in  in  out gain opamp_gain  Rin in  in  1G  Rout out AOv Im    University of Southern California  EE348L page9 Lab 2    E1 AOv 0 in  in  gain MAX 5 MIN  5   ends    FE AS 2g 2g K K ie K K ie K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK os K K K K K K K KK         Circuit description  KEEK K K K K K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K KK    rs in inp 50   rl inp 0 1k   x1 inp inm out my_opamp gain opamp_gain  rf out inm 100K   r2 inm 0 r2    KEKE K K K K K K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K KK         Darameters section  KEEK K K K K K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K 2     param r2 1k   param opamp_gain 2e5    KEKE K K K K K K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K KK     k   Sources section  2 2k of KE KE KE K K E K K K K K K K K K K K K K K K K K K K K K K K 
11. K K K K K K K K K K K K K K K K K K K K KK K K K K K K K 2K KK K K K K K K K K K K KK K 2 K K K       begin description of top level circuit netlist  KKE K K K K K K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K KK K K K K K K K K K K K K K 2K 2 K K    KEEK K K ie K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K KK K 2s K K K K K K KK K K K K K K K K K K K K K K 2K K K       begin parameters section  KK K K K K K K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K 2K KK K K K K K K K K K K KK K 2K 2 K K    KEKE K K K ie 2s K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK K 2s K K K K K 2K KK K K K K K K K K K K K K 2k K 2K K K       begin source section  KKE K K K K K K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK K 2K K K K K K 2K KK K K K K K K K K K K K K K 2K K K K    KK K K K K K K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K KK K K K K K K K K K K K K K 2K 2K K K       begin analysis section  KEKE K K K K K K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K KK K K K K K K K K K K KK 2k K 2K K K    KKK K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K K K K K 2k K 2 K K       begin Model section  KKE K K K ie K K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K KK K K K
12. K K K K K K K K K K KK K K K K K K K ok K K    vl in 0 sin OV 60mV 10x 100ps 0     EKEK K K K K K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K KK    xk specify nominal temperature of circuit in degrees C  KEEK K K K K K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K K K     TEMP  27    KEEK K K K K K K K K K K K K K K 2 K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K KK         analysis section  KEEK K K 2s K K K K K K K K K K K is K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K KK     tran Ins 200ns    END    Figure 2 5  HSPICE netlist for op amp circuit in Exercise 2 of lab assignment  1 with supply limit of      5V for the op amp     2 3 3 Parameter sweep in DC AC TRAN analysis    In this section  we investigate parameter sweeping in the example netlist shown in Figure 2 5 for the  circuit in Figure 2 4  Our goal is to determine how the transient waveforms in the example netlist  changes as a function of the op amp gain that we parameterized using the parameter    opamp_ gain    in the  subcircuit    my opamp     This kind of analysis is called    sweeping a parameter    or    sweeping a variable      Although this example is done using a transient analysis  it can be done in both AC and DC analyses as  well     We change the analysis section in the above example to sweep the parameter r2 through three values   1k 10k  and 100k  The syntax  page 11 4  transient sweep
13. Laboratory Experiment 2  EE348L    B Madhavan  Revised by  Aaron Curry    University of Southern California  EE348L page1 Lab 2    Table of Contents    2 Experiment  2  SPICE Simulations IL                cccsccssssscssssccssssccssssccsssscssssssssssees 4  2 1 Introductionis hada chaise ane the cee ee a aun ial 4  2 2  Good SPICE netlist writing practice 0 0    cee eeceeeeseecseceseceeceseceseeeseecsaecaeeeeeseeseeeeaeeeaeee 4  221 Options statements   enei eiee e enea E E RE E A E A O A aE E 5  2 3 Voltage Controlled Voltage Sources  VCVS        ccccccessecsseceeseceeaeeceaeeceseeecaeceeaaeceeaeenaeeeaes 5  2 3 1 Examples of VCVS statement  eresie cee esceseceseceeeesecneceseceseeeseceseseneecaaeaeeaeeees 6  2 3 2 Subcircuit representations sosen icsse i iiini i ia 8  2 3 3 Parameter sweep in transient analysis    see eeeceeceseeereeeeeeseecaeeseeeseeeeeeenaeenaes 10  23 4 ALTER St  tementS ennn esi eal ede er ih Gas a 11  2 3 5 Using the PAR expression    cee n RE EE a a EE a E EE 12  2 3 5 1 Plotting the transfer fUNction             cece cee ee eee e erence e te eneeneenaes 13  2 3 5 2 Plotting the phase of the transfer function                 e cece eee ener e eee eens 13  2 3 5 3 Printing from HSPICE          0  cece EEE ATE ERNES 15  2 4 Voltage Controlled Voltage Sources  VCCS  oo    cee eeescssecsseceseceseeeseeeseeeseesaeceaeeeseeeaeenaees 15  2 4 1 Examples of VCCS statement iieis iiia ieat n nna 15  25 Current Controlled Current Sources  CCCS     ccccccccccsscccs
14. ain by using the following      probe tran gain par    v out  v s       What is the problem with plotting the gain this way  Hint  What vale  does the input equal periodically   C  Now  plot the gain by performing an  AC sweep with Vs having a magnitude of 1   i  If we want to sweep within 3 decades before and after frequencies of interest   what frequency range should we sweep   NOTE  you should sweep 3 decades  before the pole and 3 decades after the zero       Vee    Figure 2 10  A regular 741 op amp       Figure 2 11  Equivalent circuit model of an op amp    University of Southern California  EE348L page20 Lab 2    5     The linear  small signal model of a tuned amplifier which includes the input signal source is in    Figure 2 12  The output  or response  Vo   to the input signal  Vs  is developed across the output  inductance Lo  Gm models the transconductance of the amplifier  The inductance L  is a circuit element  that is exploited to achieve maximum power transfer between the applied input signal and the amplifier  input port  whose input impedance is delineated as Zin s   The inductance L  is a circuit element that  is used to tune the resonant frequency of the amplifier  The output inductance L  controls the gain at  resonant frequency     A     Show that the indicated input impedance  Zin s   the input impedance of the entire  circuit to the right of the arrow in Figure 2 12  can be expressed as    Zin s   R eet Let st   Cof S    Give  in terms of Cin  Ls  Lg and
15. arying the value of L  over three  3   values  1nH  5nH  10nH  Plot gaindB  phase  zin  and pin  input power  versus frequency  on a logarithmic scale on separate panels  As we alter L   which plots should change   refer to your answers in part  C    How should they change  Do your simulations  agree with your responses  Make sure you zoom in on the Rin  vertical axis so that the max value is 5000    b  Calculate the values of the resonant frequency  gain  dB  at resonant frequency  phase at  resonant frequency  zin at resonant frequency  and pin at resonant frequency for the  default values  the sweeps with L L  1nH   Verify these values in HSpice with a cursor  on your sweep     NOTE  zin and pin can be calculated as     probe ac zin par    v vs  i vs  rs        probe ac pin par    v inpAmp  i vs        Where vs is an AC source named vs between nodes vs and 0  and rs is a parameter that defines the value  for R   You should know that these are complex values whose magnitudes will be plotted  Zin and Pin  are only real at resonant frequency    As shown below  use a 1000 point decade sweep for the ac analysis    ac dec 1000 1OOMEG 1T       6  Switched capacitor circuits are very important circuits for analog design  They are used in filter  applications and also for analog to digital conversion  In these circuits  transistors are turned on and off  like switches  In this exercise  we will use the G element as a VCR model for transistors  Figure 2 13  shows the circuit of a sw
16. ay be ac  dc  noise or tran   permitting the graphical display of user defined expression in ac analysis  dc analysis  noise analysis and  transient analysis     SPICE netlist of circuit to demonstrate parameter sweep in ac analysis   Written Jan 24  2005 for EE348L by Bindu Madhavan    Edited July 10  2012 for EE348L by Aaron Curry     KEKEKE K K 2s E K K K K K K K K K K k K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K 2    xk options section    University of Southern California  EE348L page13 Lab 2    FES AS 2k E K K 2g E K 2 E E K K K K K K K K 2S 2g K K K K K K K 2g K K K K K k K K K K K k Kk k K K K K K K K 2   options post 1 brief nomod alt999 accurate acct 1 opts    EEK fe K 2 K K 2 K K K K K K K K K K 2S ag K K K K K K K K K K K K K K K K K K K K KK k K K K K K K K KK       Circuit description  KEKEE K K 2k E K ag is K K K K K K K K K KK K K K K K K K ig K K K K K K K K K K K K KK K K K K K K K K 2    R1 in out    rpar1     C1 out 0    cpar1       FES FAS 2g 2s K fe 2 E K 2 K K K K K fe K K k K 2S 2s K K K K K K K K K K K K K k K K K K K k Kk k K K K K K K K 2       parameters section  KEE KE K K KE E K K K K K K K K K K 2s K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K KK     param rparl 1k   param cparl 10pF  KEEK K K K E K K K K K K K K K K 2s K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K KK     x   Sources section  2 2 2 KE K KE K K KE K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K KK K K K K K
17. bove example  the output voltage of the VCVS E1  is between nodes 2and 3  The controlling  or  reference voltage is between nodes land 0  The gain of the VCVS is 50  Mathematically   V 2 3  50 V 1 0   Note that the optional parameters MAX and MIN are absent     A VCVS can be used to model an op amp with finite gain and maximum and minimum limits on the  value of the output voltage     Eopamp1 out  out  in  in  200000 0 MAX 5V MIN 0V    In the above example  Eopamp1 models an op amp where V out  out   200000 0  V in  in    with a  maximum voltage of 5 0V and a minimum voltage of OV     In many cases  it is useful to parameterize the gain of a VCVS so that simulations that check the  influence of varying gain can be run  This is specified in HSpice as follows      param opamp_gain 2e5  Eopamp  out  out  in  in  opamp_gain MAX 5V MIN 0V    In the above example  opamp_gain is a user defined parameter  It is important to note that user  defined  parameters should not be the same as SPICE commands or reserved keywords  They should also be less  than 16 characters in length  Unpredictable results can occur if user defined parameters are not different  from SPICE commands or reserved keywords              University of Southern California  EE348L page6 Lab 2       Rout    wv Vo    D   t I 7  ma ee NA i  AVK  Rin  gt  VS  e 5   I    Rin  gt  A o     Rout 0  a     Figure 2 1   a  VCVS conceptual representation of op amp   b  schematic representation              Conceptually  an ideal 
18. d C1l 5pF   Let tstep 1n and tstop 201n     a  Ifwe want     to have a delay of Ins  what should the delay of    be  We want no  overlap and maximum separation between the on states of each phase  What is the  gain of this circuit  What amplitude should V  have     b  Plot Vin and Vou  in separate panels  Does Vin look like you expect  What about  Vou  What happens to Vow in between     opening up and     closing  Why  Now  you can see why it is important to have a    reset    on the output voltage  It is also  important that your output is able to settle to the desired value before     opens        Figure 2 13  A switched capacitor amplifier for problem 6     University of Southern California  EE348L page23 Lab 2    closed    Figure 2 14  Timing diagram for the switched capacitor circuit in problem 6     C   P      v       a Vo    Figure 2 15  Switched capacitor circuit during phase         C   P   C  p Mo    Figure 2 16  Switched capacitor circuit during phase         University of Southern California  EE348L page24 Lab 2    29 General Report Format Guidelines  1  Introduction  Explain what the lab is about  Describe the circuits being built in terms of structure and purpose   Also talk about what is being investigated   2  Procedure  Step by step talk about what was done and show diagrams of the circuits   3  Data  Present all data taken during the lab  It should be organized and easy to read   4  Questions  Answer all the questions in the lab   5  Discussion  Discuss the 
19. d all panels in the same window     3  Use the netlist in Figure 2 8  section 2 3 5     AC sweep example     plot the user defined  gaindB and phase plot parameters on separate panels on the same page for cpar1 100pF and  rparl values of 100  1000 and 10000 ohms   A  What should the  3db frequency be for each rpar1 value   B  What should the phase at the  3db frequency be   C  Measure the    3 dB frequency of each LPF and the value of the phase of the transfer function  of the circuit at the    3 dB frequency of each LPF  Do your simulations agree with your hand  calculations     4  Recall the circuit used from lab 1 exercise 2 with an added feedback capacitor        University of Southern California  EE348L page19 Lab 2    Figure 2 9  Feedback amplifier circuit schematic for problem 4     A  Determine the new transfer function     i  How does the addition of C  alter the transfer function   Let R   gt  gt R  and  A  gt  gt Aj     ii  What is the low frequency gain in dB    iii  What is the high frequency gain in dB    iv  What is the time constant associated with pole caused by C     y  What is the time constant associated with the zero caused by C       B  Model the op amp using the models shown below  Let Vcc Vee 10V  Let A  80dB   100e6   Perform a transient analysis with Vs having amplitude of 100mV  and a    frequency of 1MHz   i  If we want to plot 10 periods  what should tstop be   ii  If we want 100 points per period  what should tstep be   iii  Attempt to plot the g
20. d keywords    They should also be less than 16 characters in length  Unpredictable results can occur if user defined  parameters are not different from HSpice commands or reserved keywords  See Chapter 7 of the HSpice  user manual  version 2001 4     Parameters and Functions                 2 5 Current Controlled Current Sources  CCCS     Current Controlled Current Sources  CCCS  are dependent sources that are represented in HSpice using  the F element  page 5 46 of the HSpice user manual  version 2001 4   In order to specify a current   controlled dependent source  we have to be able to specify the controlling current  This is done in HSpice  by using a voltage source of OV to measure the controlling current     The syntax of the F element in HSpice is  Fxxx n  n  vsens  lt MAX val gt   lt MIN val gt  currentgain    Fxxx is the name of the F element source  such as F1 or F2  There are two nodes in the dependent source  command  The two nodes of the current controlled current source  CCCS   n  and n   represent the node  numbers for the positive and negative ports of the output current source  The parameter vsens represents  the name of the voltage source element through which the controlling current flows      lt MAX val gt  and  lt MIN val gt  are optional parameters that determine the maximum and minimum values  of output current the F element can assume during the course of the simulation  In other words  they  specify the upper and lower limits on the current the depende
21. eaaaeseneeeseseaeeesaees 13    Figure 2 8  SPICE netlist highlighting ac analysis with parameter variation and user defined    ERAIK EL L PEETS A TE sot ties AT S N IA A E E A AE 14  Figure 2 9  Tuned circuit for VCCS problem 5            ccccceeeeeeceeeeeeeeceaeeeeeeeeeeseaeeseeneeeseaaeeseaeeeseaeeeseaeeeees 19  Figure 2 10  A regular 741 OP AMD       cee eeeceeeeeeeeneeeeeeeeaeeeeeeaaeeeeeeeaaaeeeeeeseaaeeeeeeeaaaeeeeseeaeeeeeeeaaeeeeeseaas 20  Figure 2 11  Equivalent circuit model Of AN OP AMP         eee eeeeeee cece eeee ee ee ee teen ee eee eeaaeeeeeetaeeeeeeeaeeeeene 20    Figure 2 12  Tuned circuit for VCCS problem 5  Zin s  is the input impedance of the entire circuit to the    right Of the  anw  nesenie aa e E E A es ane EE AOAN Lear AENEA 21  Figure 2 13  A switched capacitor amplifier for problem 6   ssssssssssssssssssserisssssrrrsssrirrssriirnssrnennsssrennnns 23  Figure 2 14  Timing diagram for the switched capacitor circuit in problem 6   sssseesssessersssesrsssree 24  Figure 2 15  Switched capacitor circuit during phase Dy    eeescccessesceeeeeeeeeeeeessneeeeeeseeesaeeeseesnsaeess 24  Figure 2 16  Switched capacitor circuit during phase Do    ceeecececeeeceeeeeeeeeeeeaeeeseeeeseaaeseeeeeeeeeeeeaas 24    University of Southern California  EE348L page3 Lab 2    2 Experiment  2  SPICE Simulations Part II    2 1 Introduction     The objective of this laboratory assignment is to familiarize the student with    1  Good netlist writing practice  A netlist is a text 
22. ent of the VCCS G1  is between nodes 2 and 3  The  controlling  or reference voltage is between nodes 1 and 0  The gain of the VCVS is 50   Mathematically  I 2 3  50 xV 1 0   Note that optional parameter MAX and MIN are absent     A VCCS can be used to model a device  such as a MOSFET  with finite transconductance and  maximum and minimum limits on the value of the output current     GMOSFET1 out  out  in  in  MAX 5e 6A MIN 0A 200000 0    In the above example  GMOSFET1 models a MOSFET where I out  out   200000 0x V in  in    with a  maximum current of 5e 6A and a minimum current of 0A     The G element can also be used as a switch by making it a Voltage Controlled Resistor  VCR    Gswitch 2 0 VCR PWL 1  1 0 Ov 10meg 1v 1m   The resistance between nodes 2 and 0 varies linearly from 10 meg to 1 m ohms when voltage across  nodes 1 and 0 varies between 0 and 1 volt  Beyond the voltage limits  the resistance remains at 10 meg  and 1 m ohms  respectively    In many cases  it is useful to parameterize the transconductance of a VCCS so that simulations   that check the influence of varying transconductance can be run  This is specified in HSpice as    follows      _param transconductance 2e5  GMOSFET1 out  out  in  in  MAX 5e 6A MIN 0A transconductance    University of Southern California  EE348L page15 Lab 2    In the above example  transconductance is a user defined parameter  It is important to note that  user defined parameters should not be the same as HSpice commands or reserve
23. file that contains a description of the circuit   including all the sources in the circuit  the type of analysis  ac  dc  transient  noise etc    simulator  control options to obtain a reasonable simulation of the circuit under consideration  A netlist is  generated by hand using a text editor in this course    Dependent sources   Subcircuit command   DC AC TRAN sweep command   Use of the  ALTER command   Use of PAR to define and plot user defined expressions for plotting gain and phase across  arbitrary nodes in a circuit   7  Use of the measure command in WaveView Analyzer     Ra i ee ed    This laboratory assignment will use the small signal linear models discussed in class as the vehicle for  highlighting the above  Please ensure that you read the lab questions carefully and turn in all the  requested material  derivations  SPICE simulation plots  and explanations      2 2 Good SPICE netlist writing practice    It is useful to learn to quickly get to the relevant section and page of the HSPICE manuals using the index  and the search function available in adobe acrobat when a pdf file is being viewed  The HSPICE user  manual and the HSPICE models manual are posted on the class web site     It is best to think of the netlist as comprising multiple sections  The first line is the one line description of the  circuit  Following this line  it is best to have a section that serves as the revision history of the netlist  Each  line begins with a comment character         and end
24. is of  netlist file mycircuit spice with 4  ALTER statements  transient output files mycircuit trO   mycircuit trl        and mycircuit tr4 are produced     Figure 2 6 shows the revised netlist of Figure 2 5 with ALTER statements  The modified netlist  statements are shown in bold  blue text     HSPICE netlist of Op amp circuit in Exercise 2 of lab  1   Written Jan 24  2005 for EE348L by Bindu Madhavan    Edited July 10  2012 for EE348L by Aaron Curry     KEEK K K ie K K ie K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK os K K K K K K K KK         options section  KEKE K K K K K K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K KK     options post 1 brief nomod alt999 accurate acct 1 opts    KEKE K K K K K K ig K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK os K K K K K K K 2    xk subcircuit section   KEKE K K K K K K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K KK    subckt my_opamp in  in  out gain opamp_gain   Rin in  in  1G   Rout out AOv Im   E1 AOv 0 in  in  gain MAX 5 MIN  5    ends    PES FAS 2g 2g K K K K K ie K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK os K K K K K K K 2         circuit description  KEKE K K K K K K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K KK    rs in inp 50  rl inp 0 1k    University of Southern California  EE348L page11 Lab 2    xl inp inm out my_opamp  rf out inm 100K  r
25. itched capacitor amplifier  During phase     the      switches are closed and the      switches are open  See Figure 2 15   During phase     the     switches are open and the     switches  are closed  See Figure 2 16   The two phases do not overlap  Their timing diagram is shown in Figure  2 14  For analysis  assume the op amp is ideal     A  During phase      what is the charge stored across C    Use figure 2 15   B  During phase      what is the charge stored across C2  Use figure 2 16     C  Using the conservation of charge  what is the gain of this amplifier     University of Southern California  EE348L page22 Lab 2    D  During phase      the current in C  flows to ground to the left to discharge the capacitor  This  current flows through capacitor C  in the same direction  At the end of   5  is V  positive or  negative  Is this an inverting or non inverting amplifier     E  During phase      what does V  equal   F  During phase      what does V  equal  Note  this value is sampled at the end of phase         G  Verify your answers by simulating the circuit using HSPICE  Use the model of an op amp from  problem 4  Perform a transient analysis with V  being a SIN wave with amplitude of 1V anda  frequency of 1OMHz  Let     and     be pulses with periods of Ins     on    times of  4ns  and rise  and fall times of lps  Use voltage controlled resistors to model the switches with impedances  going from 1MQ to  1mQ in the    off    and    on    states respectively  Let C2 1pF an
26. l find  The other three sources are encountered by the listed elements   VCVS  Op Amp   VCCS  MOSFET   CCCS  BJT    2 7 References     1  HSPICE user manual posted on EE348L class web site    3  EE348L Laboratory Experiment 1  Spring 2005  posted on EE348L class web site    4  J  Choma  EE348L Lecture Supplement 1     University of Southern California  EE348L page18 Lab 2    2 8 Lab Exercises    Note       In your lab report  include a clean printout of the SPICE netlist for each Lab  question and its parts       Take care that you do not make typographical errors  as this can result in  erroneous results and increase your debugging time  Ensure that you use the  correct dependent source  Refer to section 1 9 of laboratory assignment 1     HSPICE  Guidelines Review    to refresh up on the HSPICE Guidelines       When doing an  AC sweep  make sure the horizontal axis  frequency  is logarithmic     1  Perform the exercise in Section 2 3 3     Parameter sweep in DC AC TRAN analysis      Calculate the gain for these three resistance values  Justify that the results of the  transient analysis simulations for the three r2 values of 1k  10k  and 100k agree with your calculations  by including a cursor  Submit the plot of the transient analysis     2  Perform the exercise in section 2 3 4      ALTER Statements    using the netlist in Figure 3 6   Submit a plot of the transient analysis results with the transient analysis for each value of parameter  opamp_gain in a separate panel  an
27. ned parameters should not be the same as HSpice commands or reserved keywords    They should also be less than 16 characters in length  Unpredictable results can occur if user defined  parameters are not different from HSpice commands or reserved keywords  See Chapter 7 of the HSpice  user manual  version 2001 4     Parameters and Functions        2 6 Current Controlled Voltage Sources  CCVS     Current Controlled Voltage Sources  CCVS  are dependent sources that are represented in SPICE using  the H element  page 5 42 of the HSpice user manual  version 2001 4   In order to specify a current   controlled dependent source  we have to be able to specify the controlling current  This is done in  SPICE by using a voltage source of OV to measure the controlling current              The syntax of the H element in SPICE is  Hxxx n  n  vsens transresistance  lt MAX val gt   lt MIN val gt     Hxxxis the name of the H element source  such as Hlor H2  There are two nodes in the  dependent source command  The two nodes of the current controlled voltage source  CCVS   n  and n    represent the node numbers for the positive and negative ports of the output  The parameter vsens  represents the name of the voltage source element through which the controlling current flows     The gain of the CCVS is indicated by the value of transresistance  The value of the output is dependent on  the controlling voltage by a factor of the transresistance  The mathematical representation of the CCVS is    V
28. nputs less than 200 uV  the output voltage falls  below  200 uV x 60000    12V and is limited by the MIN statement to     12V     Revisiting exercise 2 of laboratory assignment  1  we would like to write a SPICE netlist incorporating    University of Southern California  EE348L page7 Lab 2    good netlist writing principles and the VCVS element we have reviewed so far  In addition  we would  like to add the condition that its power supplies  which are  5V and    5V  limit the output of the op amp   The idealized small signal model of op amp is shown in Figure 2 3        Figure 2 3  Idealized small signal model of op amp in Exercise 2 of lab assignment  1     The model in Figure 2 3 is represented as follows  with in and in being the input terminals and out  being the output terminal  The gain of the op amp is    opamp _gain        _param opamp_gain 2e5   Rin in  in  1G   Rout out vZ Im   El VZ 0 in  in  opamp_gain MAX 5V MIN  5V    2 3 2 Subcircuit representation    An element like the op amp can be used many times in a circuit  A hierarchical representation of the  circuit netlist is facilitated by the notion of a subcircuit  which is very similar to the concept of a function  in programming languages  The syntax of the subcircuit  with terminal n1  n2  n3  etc   is shown below   pages 3 12 to 3 19  HSpice user manual  version 2001 4       subckt subcircuit_name n1 n2n3        lt parameter_name value gt      subcircuit description   ends            Very Important Point     N
29. nt source can assume  These keywords are  very useful in modeling the limits placed on the output current     The gain of the CCCS is indicated by the value of currentgain  The value of the output is dependent on  the controlling voltage by a factor of the currentgain  The mathematical representation of the CCCS is    I n  n     currentgain X current flowing through vsens   currentgain X I vsens     2 5 1 Examples of CCCS statements  F123 V150    In the above example  the output current of the CCCS F1  is between nodes 2 and 3  The controlling  or  reference current is flowing through voltage source V1 in the circuit  The current gain of the CCCS is 50     Mathematically  1 2 3  50 xI V1   Note that optional parameter MAX and MIN are absent     A CCCS can be used to model a device with finite gain and maximum and minimum limits on the value  of the output voltage     Flimited out  out  V1 MAX 5A MIN 0A 1000    In the above example  Flimited models a device where I out  out   1000 0 xI V 1   with a maximum  current of 5 0A and a minimum current of OA     In many cases  it is useful to parameterize the currentgain of a CCCS so that simulations that check the  influence of varying currentgain can be run  This is specified in HSpice as follows     University of Southern California  EE348L page16 Lab 2     param currentgain 2e5  Flimited out  out  V1 MAX 5A MIN 0A currentgain    In the above example  currentgain is a user defined parameter  It is important to note that   user defi
30. op amp is nothing more than a voltage controlled voltage source  VCVS  with  infinite gain  infinite input impedance  and zero output impedance as shown in Figure 2 1  The op amp is  usually represented schematically as a triangle with two input terminals and one output terminal  the internal  VCVS is implied              Figure 2 2  Behavior of op amp output voltage  assuming power supply    12V     Practical op amps have finite  but large gain  with finite  but large input impedances  and finite  but small  output impedances  In addition  the power supplies of the op amp limit the maximum and minimum  steady state output voltage that the op amp can assume  The power supply is limited to a few volts  for  op amps in the lab  this may be  12 V  on integrated circuits  perhaps as low as  1V   The very large  gain is true only for very small inputs signals  and for input voltages greater than a certain value  greater  than 200 uV or less than  200 uV in Figure 2 2   the output simply clips at one of the supply rails   determined by whether the input signal is positive or negative  This value is determined by the open loop  gain of the operational amplifier  The SPICE model of the op amp in Figure 2 1  whose transfer  characteristic is shown in Figure 2 2  is represented below     E1 out 0 in  in  60000 0 MAX 12V MIN  12V  An input greater than 200 uV results in the output voltage greater than 200 uV x 60000   12V  which is    limited by the MAX statement to 12V  Similarly for i
31. ote that the subcircuit ends with a     ends    statement  The optional parameter_name value  specifies the default value of a parameter specified in the subcircuit description     The model in Figure 2 3 may be represented as a subcircuit as follows      subckt my_opamp in  in  out ref gain opamp_gain   Rin in  in  1G   Rout out A0Ov 1   El AOv ref in  in  gain MAX 5V MIN  5V   ends    A subcircuit is instantiated in a circuit as follows  Xyyy nl n2 n3      lt parameter_name value gt     University of Southern California  EE348L pages Lab 2    Where Xyyyis the name of the subcircuit  nl  n2  n3etc  are the node names or node numbers of  the particular instantiation of the subcircuit in the top level circuit  The optional parameter_name value  sets the value of a parameter in the subcircuit definition for that particular subcircuit instantiation     The subcircuit  my_opamp is instantiated as follows   X1 in  in  out vss my_opamp gain opamp_gain    Where in   in   out  and vss correspond to the terminals in   in   out and ref of the subircuit definition of  my_opamp        Figure 2 4  Op amp circuit in Exercise 2 of lab assignment  1     Using the subcircuit definition called my_opamp  we can write down the SPICE netlist of the op amp  circuit in Figure 2 4 as follows     HSPICE netlist of Op amp circuit in Exercise 2 of lab  1   Written Jan 24  2005 for EE348L by Bindu Madhavan    Edited July 10  2012 for EE348L by Aaron Curry    FEE fe fe 2 K K 2 K K K K K K K K k K 2S a K 
32. output waveforms  one for each of the   three opamp_gain parameter values of 1  100  and 2e5  Do the results match with your expectations     2 3 5 Using the PAR expression  In this example  we will review the use of the    PAR    expression in HSpice  see page 7 8 of the HSpice  user manual  version 2001 4  to plot user defined expressions in the netlist     R    ValS   C Vs     University of Southern California  EE348L page12 Lab 2    Figure 2 7  First order RC Low Pass Filter     The circuit used in Laboratory 1  exercise 4 is shown in Figure 2 7  The HSPICE netlist for the ac  analysis of Figure 2 7 is shown in Figure 2 8  Parameters rpar  and cparlare used in the netlist to  parameterize the value of resistance R and capacitance C in the first order RC LPF in Figure 2 7  These  parameters are shown in quotes to highlight that expressions within quotes may be used instead of simple  parameters  where each expression involves multiple parameters  see page 7 8 of the HSpice user manual   version 2001 4      Analyzing the circuit  we see that the circuit has a pole at  o 1 RC radians per second  rps     1  2mRC  Hz  In a first order LPF  this is the    3 dB bandwidth of the circuit  The transfer function   of the circuit  Vo s  Vin s   has a phase shift that begins to change from 0 to  45 degrees   7 4 radians   at approximately  o0 10 rps  becomes    45 degrees   2 4 radians  at   o rps  and    90 degrees at  approximately 10 o rps     In order to plot the transfer function
33. results you obtained  What significance is there in the results  How do they help your  investigation  Explain the meaning  the numbers alone aren   t good enough   6  Conclusion  Wrap up the report by giving some comments on the lab  Do the results clearly agree with what  the lab was trying to teach  Did you have any problems  Suggestions   7  Attachments  Attach all hand calculations and SPICE plots necessary     NOTE  You are turning in lab reports that are to be graded  If you want good marks  be sure to make the  reports as neat and aesthetically appealing as possible  If you refer to an attached plot  include the page  number  If you refer to a hand calculation  be sure to highlight what you are referring to on the page  containing the hand calculation  However  including equations  plots  figures  etc  in the body of your  report is good practice  Be sure to include plot titles  Be sure to include axis titles and units  Lab reports  are to be typed  HANDWRITTEN REPORTS WILL NOT BE ACCEPTED  LAB REPORTS ARE  DUE AT THE BEGINNING OF THE NEXT LAB  THEY WILL NOT BE ACCEPTED IF THEY ARE  MORE THAN 15 MINUTES LATE     University of Southern California  EE348L page25 Lab 2    
34. s with a carriage return  obtained when the    Enter    key on  the keyboard is pressed   It is best to include a time  date and time for each revision section  This will help in  debugging and communicating your circuit problems to another circuit designer     This is a model of a typical SPICE input file   Title  This must be the first line  It is used by WaveVeiw Analyzer when the results are displayed        Description of the circuit   s function including revision notes  time and date     KEKE K K K 2g K K K K K K K K K K K K K KK K K K K K K K ig K K K K K K K K K K K K KK K K K K K K K K KK K K K K K K K K K K K K K K K K K      HSPICE options statements to control HSPICE simulator behavior      Description of HSPICE options can be found on page 8 14  Chapter 9  pages 10 22 to 10 36      pages 11 24 to 11 26  and page12 7 of the HSPICE manual   version 2001 4  December 2001      KKE K K K K K K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K KK K K K K K K K 2K KK K K K K K K K K K K K K K K K K K     options post brief nomod alt999    KEE K K K E K K K K K K K K K K K K K KK K K K K K K K K K K K K K K K K K K K K K K K K K K K K K 2K KK K K K K K K K K K K K K K K 2K K K       begin description of sub circuits  KEK K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K KK K K K K K K K K KK K K K K K K K K K K K K K K 2K K K    University of Southern California  EE348L page4 Lab 2    PRS AS 2g K K K K K K K K K K K K K K K K K KK 
35. sssececsesseecsessececssseeeessseeeseneeeenes 16  2 5 1 Examples of CCCS statements  0        ec ceeceeesseeeseeeseceseceeeeeeeeeeeeeneeeseceaecaeenseeeeeeees 16  2 6 Voltage Controlled Current Sources  CCVS   o   cccecccccececsseeeeseceeaceeeeeeceeeeeaeceeaeceeaeseaeeeeaes 17  2 6 1 Examples of CCVS statement oeeie poia ai E V aaiae 17  2 7 Referentes    sits sanen cc sti Bas E T eee eens eae Mee a ea eae 18  2 8 Lab Exercises   icsvecs csvaciteecesteateieeey ined  asthe wei eles neds Shalala a ea eae 19  2 9 General Report Format Guidelines 0 0 0    ee eecseceeeceseeeeeeseeeseecsaeeseceseceseeeseeeaaecsaeneeeneeeaes 25    University of Southern California  EE348L page2 Lab 2    Table of Figures    Figure 2 1   a  VCVS conceptual representation of op amp   b  schematic representation                  7  Figure 2 2  Behavior of op amp output voltage  assuming power supply   12V  oe eeeeeeeeeeeees 7  Figure 2 3  idealized small signal model of op amp in Exercise 2 of lab assignment  1    8  Figure 2 4  Op amp circuit in Exercise 2 of lab assignment  1               cccccceseeeeeeeeeeeeeeeeseeeseeeeessaaeeeeees 9  Figure 2 5  SPICE netlist for op amp circuit in Exercise 2 of lab assignment  1                ccceeeeeee 10  Figure 2 6  SPICE netlist for op amp circuit in Exercise 2 of lab assignment  1 with  ALTER   st  teme  tS e a a a SEAT eds E E A cubes Che EA E EE 12  Figure 2 7  First order RC Low Pass Filter              cccccccececeseeeeeeeeeeeeeeeeeeeeeceaeeeseaeesecaeee
    
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