🚀 go-pugleaf

Checksum: 1371419103 (verify with brik -cv)
Submitted-by: Mike Morgan <m00012@KANGA.STCLOUD.MSUS.EDU>
Posting-number: Volume 6, Issue 22
Archive-name: rlc_mm/part01

BEGIN_DOC rlc.doc

**************************
*                        *
*       FORM &           *
* RLC             FINDER *   Version: Last
*       FUNCTION         *
*                        *
* By:  Mike Morgan       *
**************************

Credit is due to Dr. B. W. Ellis, Chairperson, Department of
Electrical Engineering, College of Science and Technology,
St. Cloud State University, St. Cloud, Minnesota.  He taught
the Circuit Analysis course I took before I wrote this
program.  He is an excellent teacher--but he would probably
frown upon anybody using this program during exams.

Also, "ENGINEERING CIRCUIT ANALYSIS" by William H. Hayt, Jr.,
and Jack E. Kemmerly, chapter 7, pp. 194-228 of the Fourth
Edition was used as a reference.  This is the text many
students must use while taking their first courses in
Circuit Analysis, and this program helps solve the problems
for chapter 7.  These problems are difficult, and it is
easy to make dumb mistakes.

My program is best suited for checking your homework and
learning the method of solving these problems.  Also, please
note that these programs work *ONLY* on problems like those
found in chapter 7 of the above-cited text, i.e., simple
RLC circuit responses in the time domain.

DESCRIPTION:

This program finds a time domain response of a simple RLC
circuit. The response is either given explicitly or in
general terms with arbitrary contsants.  It prompts the user
for the required parameters.  Form Finder finds the general
form with arbitrary constants and Function Finder finds the
explicit form of a response.

This version is completely free and may be distributed,
modified, etc., so long as my name is attached to the
program in some way.  Also, I assume absolutely no
responsibility for any damages whatsoever.  Use these
programs at your own risk!!!

INSTRUCTIONS:

Download the programs, contained in a directory, as 'RLC'.
If you are using the version already in user RPL, you must
run the 'SETUP' program, which deletes itself, to get the
main program ready for running.  If you download the ASC
version, there is no need for this.

To run the programs, hit the 'RUNIT' menu key.  You will
then be presented with a menu screen.  Choose either Form
Finder or Funtion Finder by toggling between the two with
the up or down arrow, and hitting ENTER when the arrow on
the menu screen points to the program you want to run.  The
program then prompts the user for the required parmaters.
It is self explanitory from there.

HINTS:

One helpful feature, which may be obvious, is that when the
program requests the resistance, for example, and you want
to enter a 5 Ohm in parallel with a 15 Ohm, you may enter
the resistance as follows:

     5 INV 15 INV + INV <ENTER>

where INV is obtained by hitting the '1/X' key.

One bug is that you may not have any variables with the name
'A1' or 'A2' in any directory under the 'RLC' directory
without the possibility of obtaining incorrect answers.  So,
don't name anything A1 or A2.

This program saves the system and user flags and restores
them upon completion.  Interupt the program during execution
at the risk of screwing up your flag settings.

EXAMPLES:

Consider the following circuit:

              Is
             _____
            (     )      R1
     ------(  <--  )----/\/\/\---
     !      (_____)              !
     !                           !
     !               \/          !
     !               /\ @t=0     !
     !______________/ \/  _______!_______________
     !                           !               !
     !                           !               !
     !                          _!_ +            /
     (                        C ___  Vc(t)       \ R2
  L  )                           !  -            /
     (                           !               !
     !___________________________!_______________!

Where:  After being open for a long time, the switch closes
        at time t=0 seconds, and

          Is = 15 Amps
           L =  0.5 Heneries
           C =  1/32 Farads
          R1 = 50 Ohms
          R2 = 2 Ohms
       Vc(t) = desired response

Run Form Finder.

Enter the RLC directory, and hit the menu key marked
'RUNIT'.  Using the up and down arrow keys, chose Form
Finder and hit ENTER.  The program will prompt for the
resistance.  (Sorry if I'm explaining too much...)  Since
the 50 Ohm resistor is effectively cut out of the circuit
for time t >= 0 seconds, the only resistance is the 2 Ohm
resistor.  Hit 2 and then hit enter.  For the inductance
enter 0.5.  For the Capacitance, use the following key
strokes:  32 INV ENTER.  Then you will be prompted for
series or parallel.  Hit the menu key marked '(P)' for
parallel.

After a brief period, the stack will contain the following
data:

        6:  ( greek alpha): 8
        5: ( greek omega0): 8
        4: d/dt(f(t))|t=0+: 'A1-8*A2'
        3:       f(t)|t=0+: 'A2'
        2:        function: 'e^-(8*t)*(A1*t+A2)'
        1:  "Critically Damped"

This information represents, I hope, the major steps
required to solve such a problem.  Consequently, it would
be helpful if this program were used during an exam...if,
of course, your professor allows it.

Now run Function Finder for the same circuit.  Enter the
resistance, inductance and capacitance as before.  You will
then be prompted for the forced part of the responce you
desire.  The 15 Amp source will be isolated after the
switch closes, so there is no forcing function.  Therefore,
enter 0.  Next, you will be prompted for the initial value.
For this circuit, we want the voltage accross the capacitor,
plus to minus--top to bottom.  The entire 15 amps will flow
through the inductor ( a short to DC ), bypass the capacitor
( open circuit to DC), and through the resistor before the
switch closes  (Remember, capacitor voltages must be
continuous.)  Consequently, the resistor will have a voltage
of 15 Amps times 2 Ohms sensed positively at the bottom of
the resistor by the passive sign convention and Ohm's law.
The capacitor is in parallel with the resistor, so it will
have an equal voltage immediately before, and consequently
after, the switch closes.  However, this initial voltage
*must* be entered as a negative value because the desired
response is plus to minus--TOP to BOTTOM and the resistor
voltage is plus to minus--BOTTOM to TOP.  So enter the
initial value with:  15 2 * NEG ENTER.  Now you are prompted
for the initial deriviative (two hints are given).  For a
capacitor, dv/dt=i/C.  The current through the inductor must
be continous, and so the 15 Amps flowing through the
inductor must go through the resistor to keep the capacitor
voltage constant.   As a result, no current is passing
through the capacitor immediately after the switch closes,
so dv/dt=0/1/32=0*32=0.  Therefore, enter 0.  Finally, hit
the menu key marked '(P)' for parallel.

After a brief period, the stack will contain:

1:  'e^-(8*t)*(-(240*t)-30)'

Which is Vc(t).

This function may then be plotted using the plotter
application and setting the independant variable to 't'.

Excuse my poor example, I am not a good teacher...but I hope
it is helpful anyway.  (One thing is sure:  you still need
to know the concepts invlolved to use the Function Finder
program!)

HOW IT WORKS:

Let
   R=Resistance*
   L=Inductance*
   C=Capacitance*
   a=exponential damping coefficiant (neper frequency)
  w0=resonant radian frequency
  wd=natural resonant frequency
  S1=(first) complex frequency
  S2=(second) complex frequency
  A1=(first) arbitrary constant
  A2=(second) arbitrary constant
  fi=response funtion's initial value*
  fp=value function approaches as time approaches infinity*
  id=initial value of function's derivative*

* means value is supplied by user.

The program calculates:

        a=1/(2*R*C)        if circuit is in parallel
        a=R/(2*L)          if circuit is in series

        w0=1/SQRT(L*C)

Now, the response of a simple RLC circuit has three forms,
depending on the relative values of 'a' and 'w0'


If 'a' is greater than 'w0', the response is *overdamped*,
and it has the form:

        f(t)=A1*e^(S1*t)+A2*e^(S2*t)+fp (1)

Where S1 and S2 are calculated with:

        S1=-a+SQRT(a^2-w0^2) if a > w0
        S2=-a-SQRT(a^2-w0^2) if a > w0

and A1 and A2 are arbitrary constants.

At t=0, f(0)=fi=A1+A2+fp ==> A1+A2=fi-fp (2)

Where 'fi' and 'fp' are supplied by the user.  Taking the
derivative of (1) and evaluating it at t=0, you get:

f'(t)=S1*A1*e^(S1*t)+S2*A2*e^(S2*t)
f'(0)=id=S1*A1+S2*A2 (3)

Where, again, 'id' is supplied by the user.  Because the
program has already calculated 'S1' and 'S2', (2) and (3)
constitute two linear equations with two unknowns:

                   A1 +    A2 = fi-fp (2)
                S1*A1 + S2*A2 = id    (3)

'A1' and 'A2' can be found with matrices on the HP 48SX:

 [ [ A1 ]   = [ [ (fi - fp) ]     /  [ [  1  1 ]
   [ A2 ] ]     [    id     ] ]  /       S1 S2 ] ]

(Note:  No hate mail from mathematicians, please.)

If 'a' is equal to 'w0', then the response is *critically
damped*, the response is in the form:

        f(t)=e^(-a*t)*(A1*t+A2)+fp

Where 'A1' and 'A2 are given by:

 [ [ A1 ]   = [ [ (fi - fp) ]     /  [ [  0  1 ]
   [ A2 ] ]     [    id     ] ]  /        1 -a ] ]

If 'a' is less than 'w0', then the response is *under
damped*, and is in the form:

        f(t)=e(-a*t)*(A1*COS(wd*t)+A2*SIN(wd*t))+fp

Where:

        wd=SQRT(w0^2-a&^2) if w0 > a

And, where 'A1' and 'A2' are given by:

 [ [ A1 ]   = [ [ (fi - fp) ]     /  [ [  1  0 ]
   [ A2 ] ]     [    id     ] ]  /       -a wd ] ]

Thank you,

Mike Morgan
email:  M00012@KANGA.STCLOUD.MSUS.EDU
        mmorgan@solar.stcloud.msus.edu

mail:   K.H.K.
        428 7th Ave. S.
        St. Cloud, MN 56301
        (612) 654-6010

END_DOC


BEGIN_RPL rlc.rpl
%%HP: T(3)A(R)F(.);
DIR
  SETUP
    \<< Subs RLCP
OBJ\-> DROP 1 68
      FOR X +
      NEXT OBJ\->
'RLCP' STO RLCL
OBJ\-> DROP 1 3
      FOR X +
      NEXT OBJ\->
'RLCL' STO ERASE {
# 0h # 0h } PVIEW
PICT { # 0h # 0h }
RLCP GXOR 1 WAIT 1
3
      FOR Y PICT {
# 1Ah # 20h } RLCL
GXOR .3 WAIT 1 5
        FOR X 30
.05 BEEP 40 .05
BEEP
        NEXT PICT {
# 1Ah # 20h } RLCL
GXOR
      NEXT 5 WAIT
UPDIR 'SETUP' PURGE
    \>>
  RUNIT
    \<< Subs ERASE {
# 0h # 0h } PVIEW
PICT { # 0h # 0h }
RLCP GXOR RCLF
'OFL' STO {
# 40000000810FF0h
# 0h } STOF { # 23h
# 3h } { # 23h # 9h
} 0 \-> p1 p2 dy
      \<< PICT p1 ARR
GXOR
        WHILE dy
NOT
        REPEAT 0
WAIT IP \-> key
          \<<
            IF key
51 ==
            THEN 1
'dy' STO
            ELSE
              IF
key 25 == key 35 ==
OR
              THEN
IF 3 FS?
THEN PICT p1 ARR
GXOR PICT p2 ARR
GXOR 3 CF
ELSE PICT p2 ARR
GXOR PICT p1 ARR
GXOR 3 SF
END
              END
            END
          \>>
        END
      \>> PICT {
# 1Ah # 20h } RLCL
GXOR .3 WAIT PICT {
# 1Ah # 20h } RLCL
GXOR .5 WAIT
      IF 3 FC?C
      THEN FRMFD
      ELSE FNCFD
      END OFL STOF
UPDIR
    \>>
  Subs
    DIR
      FRMFD
        \<< GRAV GIAV
GCAV SOSOP CCFF
        \>>
      FNCFD
        \<< GRAV GIAV
GCAV GFP GIV GID
SOSOP CCFN
        \>>
      RLCP {
"GROB 131 64 "
"DFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"50400000000000000000000000000000"
"00107000000000000000000000000000"
"00007010000000000773111000000000"
"0000004010000000000155B920000000"
"00000000401000F40E00075351B000F9"
"31D1FD30004010001501100155194000"
"101152144000401000150100017511B0"
"00101354144000401000F40100000000"
"0000F01554FC30004010005401000759"
"CEAB4010195414100040100094011001"
"5B24AA501011521420004010001D7E00"
"075F24AA701831D1F540004010000000"
"00015D24AA6000000000000040100000"
"00000179C4AB40000000000000401000"
"00000000000000000000000000004010"
"070F1000000000000000000000000040"
"10E8F060081000808004000000000000"
"4018140181746000CD5D120000000000"
"00401408020A82810080416100000000"
"000040120000060102008C5180000000"
"00000040110000018001008180E00000"
"00000000401100008000020000001100"
"00000000004090000080000400000845"
"00000000000040900000000004000006"
"83300000000000409020666500040FFF"
"F701FFFFFFFFFFF14017201115008201"
"00060030200040000140941021250201"
"01000000002000400001409800414501"
"02010000000020004000014019003637"
"0202C700000000200040000140150000"
"00044138100000081000200001409000"
"000408B8012000000700001000014098"
"000064E7040140000008F008E0000140"
"9110009A1004C7400000000708130001"
"401A00289100A20180000038F04CE006"
"01401400280000A20180000057004813"
"09EF401810140000A20080600038F04C"
"E001004010E8230000420080A0005007"
"481309EF401007C00000420080600058"
"F0CDE0060140100000000004C740A000"
"070008130001401000000000040040A0"
"0008F008E00001401000000000080020"
"00000007001000014010000000000038"
"10111000C00020000140100000000000"
"C7001110002000400001401000000000"
"00010011100020004000014010000000"
"00000108AA2000200040000140100000"
"0000000108AA20002000400001401000"
"000000000FF7AA2FFFFFFFFFFFF14010"
"00000000000000AAA000000000000040"
"1000000000000000AAA0000000000000"
"40100000000000000044400000000000"
"00401000000000000000444000000000"
"000040100000000000000044400000E1"
"00000040100000000000000000000000"
"12000000409700001111000110000000"
"08C4807C1740980030B101000B100000"
"000429C882A8409822305919830593D9"
"3EC30428888228409722005115440554"
"344054042880FC36409822301113C701"
"54144E5404298080214098C330111540"
"015418715408C4804090409702001939"
"830193104E540012C13C8F4010C10000"
"0000000008300000E100000040700000"
"00000000000000000000000000704000"
"000000000000000000000000000010DF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFF50"
}
      RLCL {
"GROB 15 21 "
"0040002010201F40F840084004200420"
"0493047202010A3106A000A000700050"
"00300030081008100800"
}
      ARR
GROB 7 5 0102F70201
      GET1
        \<< { "" V }
INPUT OBJ\->
        \>>
      GRAV
        \<<
"Enter Resistance"
GET1
          WHILE DUP
0 \<=
          REPEAT
DROP
"Resistance > 0"
GET1
          END
        \>>
      GIAV
        \<<
"Enter Inductance"
GET1
          WHILE DUP
0 \<=
          REPEAT
DROP
"Inductance > 0"
GET1
          END
        \>>
      GCAV
        \<<
"Enter Capacitance"
GET1
          WHILE DUP
0 \<=
          REPEAT
DROP
"Capacitance > 0"
GET1
          END
        \>>
      GFP
        \<<
"Enter Forced Part"
GET1
        \>>
      GIV
        \<<
"Enter Initial Value"
GET1
        \>>
      GID
        \<<
"Enter Initial Deriv.
 di/dt=v/L
 dv/dt=i/C"
GET1
        \>>
      SOSOP
        \<< CLLCD
"Series or Parallel?"
1 DISP
"(S)  series  RLC"
3 DISP
"(P) parallel RLC"
4 DISP { "(S)" ""
"" "" "" "(P)" }
TMENU
          DO -1
WAIT
          UNTIL DUP
DUP 11.1 == SWAP
16.1 == OR
            IF
            THEN 1
            ELSE
DROP 0
            END
          END
          IF 11.1
==
          THEN 1 CF
          ELSE 1 SF
          END 0
MENU
        \>>
      CCFF
        \<< CLLCD
"Calculating" 4
DISP \-> r l c
          \<< r l c
CA l c COMEGA0 \-> \Ga
\Gw0
            \<< \Ga "\Ga"
\->TAG \Gw0 "\Gw0" \->TAG
              IF \Ga
\Gw0 >
              THEN
\Ga \Gw0 CS1S2 \-> s1 s2
\<< s1 "S1" \->TAG s2
"S2" \->TAG 's1*A1+s2
*A2' EVAL
"\.d/\.dt\166t=0+" \->TAG '
A1+A2' "f\166t=0+"
\->TAG 'A1*e^(s1*t)+
A2*e^(s2*t)' EVAL
"function" \->TAG
\>> "Overdamped"
              ELSE
IF \Ga \Gw0 <
THEN \Ga \Gw0 C\Gwd \-> \Gwd
  \<< \Gwd "\Gwd" \->TAG '-
\Ga*A1+\Gwd*A2' EVAL
"\.d/\.dt\166t=0+" \->TAG
'A1' "f\166t=0+" \->TAG
'e^(-\Ga*t)*(A1*COS(
\Gwd*t)+A2*SIN(\Gwd*t))
' EVAL "function"
\->TAG
  \>> "Underdamped"
ELSE 'A1-\Ga*A2' EVAL
"\.d/\.dt\166t=0+" \->TAG
'A2' "f\166t=0+" \->TAG
'e^(-\Ga*t)*(A1*t+A2)
' EVAL "function"
\->TAG
"Critically Damped"
END
              END
            \>>
          \>> 1 CF
        \>>
      CA
        \<< \-> r l c
          \<<
            IF 1
FS?
            THEN 2
r c * * INV
            ELSE r
2 l * /
            END
          \>>
        \>>
      COMEGA0
        \<< \-> l c
          \<< l c * \v/
INV
          \>>
        \>>
      CS1S2
        \<< \-> \Ga \Gw0
          \<< \Ga 2 ^
\Gw0 2 ^ - \v/ \-> r
            \<< \Ga NEG
r + \Ga NEG r -
            \>>
          \>>
        \>>
      C\Gwd
        \<< \-> \Ga \Gw0
          \<< \Gw0 2 ^
\Ga 2 ^ - \v/
          \>>
        \>>
      CCFN
        \<< CLLCD
"Calculating" 4
DISP \-> r l c fp fi
id
          \<< r l c
CA l c COMEGA0 \-> \Ga
\Gw0
            \<<
              IF \Ga
\Gw0 >
              THEN
\Ga \Gw0 CS1S2 \-> s1 s2
\<< fi fp - id { 2 1
} \->ARRY 1 1 s1 s2 {
2 2 } \->ARRY / OBJ\->
DROP \-> A1 A2
  \<< 'A1*e^(s1*t)+A2
*e^(s2*t)+fp' EVAL
  \>>
\>>
              ELSE
IF \Ga \Gw0 <
THEN \Ga \Gw0 C\Gwd \-> \Gwd
  \<< fi fp - id { 2
1 } \->ARRY 1 0 \Ga NEG
\Gwd { 2 2 } \->ARRY /
OBJ\-> DROP \-> A1 A2
    \<< 'e^(-\Ga*t)*(A1
*COS(\Gwd*t)+A2*SIN(
\Gwd*t))+fp' EVAL
    \>>
  \>>
ELSE fi fp - id { 2
1 } \->ARRY 0 1 1 \Ga
NEG { 2 2 } \->ARRY /
OBJ\-> DROP \-> A1 A2
  \<< 'e^(-\Ga*t)*(A1*t
+A2)+fp' EVAL
  \>>
END
              END
            \>>
          \>> 1 CF
        \>>
    END
  dtag
    \<< DTAG
    \>>
  up
    \<< UPDIR
    \>>
END

END_RPL


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MX*0"%0```@```````+`2`T@N0"#%-,1$3AXS*9"9```````P\'$:-N1!IP).
M*E`!`!H`````````3BI0`0`@`````````"LQ@.0"!%),0TSDY#&3`ID)````
M```%'Z<Q["+SH@)2'/HN@N0"!492349$M2^"Y`(%1DY#1D35+X+D`@-/1DQ_
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`
end
sum -r/size 49093/6544 section (from "begin" to "end")
sum -r/size 62057/4734 entire input file
END_UU