Pages created and updated by Terry Sturtevant Date Posted: March 27, 2015

Maple Kirchhoff's Law Tutorial

Maple is a commercial program. It is a computer algebra system (CAS) like Maxima or Mathematica.
There are various tutorials out there on how to use Maple; this one is designed to focus on its use for circuit analysis; i.e. lots of use of Kirchhoff's Laws, and including complex numbers for AC analysis with capacitors and inductors.

Sample DC Circuit

Here is a simple circuit:

sample circuit

It gives us the following three Kirchhoff's Law equations ( See the complete analysis here. ) :
-I1 R1 + I3 R3 = -V1

-I2 R2 -I3 R3 = -V2

-I1 + I2 -I3 = 0

A computer algebra system can be very useful for analyzing circuits like this.
  1. Opening Maple

  2. Solving Equations

  3. Saving a Session

  4. Quitting Maple

  5. Loading a Previous Session

  6. Redefining Variables

  7. Getting Resistor Voltages

  8. Using Phasors

  9. Getting DC and High Frequency Limits

  10. Links


  1. Opening Maple:
    • Open Maple from the menu or the desktop icon.

  2. Solving Equations:
    • To solve a set of Kirchhoff's Law equations, use the solve command, solving for I1, I2, and I3:

      At the prompt, type in the the commands as shown:
      sample equation 
            input

      The solve command gives the solution vector.


    • The solution is a vector of currents. We can pick off a single current by using an index with the previous result:

      single 
            element

    • You can substitute in specific component values:

      value substitution

      If numbers are not integers, results will also be non-integer
      Note that as soon as we use scientific notation, values become non-integer.

    • We can get the voltage across a resistor by multiplying the current times the resistance, and assigning it to a new variable:

      sample equation input

      Important tip: To combine two elements of two different arrays of the same size, just put a tilde after whatever operation you choose (such as +, -, etc.).

  3. Saving a Session:
    • This allows you to come back to it later with all of the variables the same.

      To save a session:

      save session

  4. Quitting Maxima:
    • Quitting maxima:
      Choose Exit from the menu.

  5. Loading a Previous Session:
    • It's nice to be able to pick up where you left off, so you can keep developing an analysis over time.

      To load a previous session:

      load session

      Everything should be as you left it.

    • Previous statements can be re-executed and/or edited.


    • Statements can be re-evaluated with different numbers.

  6. Redefining Variables:
    • Variables can be changed.


  7. Getting Resistor Voltages:
    • We can pick off individual current equations as well as just the results for each current:
      elementwise multiplication

  8. Using Phasors:
    • You can use phasors for circuits where there are capacitors and inductors.
      So for an inductor
      Zl = i ω L
      and for a capacitor
      ZC = 1/( i ω C):

  9. Getting DC and High Frequency Limits:
    Taking the limit as the frequency goes to zero will give the DC behaviour of a circuit; taking the limit as the frequency goes to infinity will give the high frequency behaviour of a circuit.
  10. Links:

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