HP 48G/GX stuff

HP 48G/GX series calculator is an extremely powerful tool. Most of the people actually don't know much about the possibilities it offers.
Here are some utilities I wrote and used at some of the exams at the faculty. By using these short programs the time spent for solving circuit analysis or tranmission line problems can be cut to a third or even less.

All of these utilities are in the package EEng-10. The package is in .zip format. Unpack it and upload it to your calculator's memory. If the upload is successfull a directory is created containing utilities described below.

• Top level directory - name it whatever you want
• j - Imaginary unit
• EENG - Utilities for electrical engineering
• WAWE - Utilities for transmission line analysis
• MAG - Calculates the magnitude of a complex number. Also found in MTH CMPL as ABS. This is a shortcut that saves you some typing.
• PHASE - Calculates the argument (phase) of a complex number. Also found in MTH CMPL as ARG.
• GSUM - Calculates the sum of an infinite geometric series. Put the first and the second element on the stack. Then select GSUM.

The geometric series:
a(1+x+x^2+x^3+..).=a/(1-x)
First two elements are a and ax.
This utility in intended for summarizing wave magnitudes in a zig-zag diagram.
• Zn->G - Calculates the reflection coeficient of a load with normalized impedance Zn. Put the value of Zn on the stack and select Zn->G.

G=(Zn-1)/(Zn+1)
• ->Gkl - Calculates the factor exp(-2jbx), where x=kl. Put the value of k on the stack and select ->Gkl.

Multiplying the reflection coeficient of a load by this factor gives the reflection coeficient at the distance kl measured from the load.
• G->Zn - Calculates the equivalent load from the reflection coeficient. Put the value of G on the stack and select G->Zn.

Zn=(1-G)/(1+G)
• Re - Returns the real part of a complex number. Also found in MTH CMPL as RE.
• Im - Returns the imaginary part of a complex number. Also found in MTH CMPL as IM.
• Matrix - Contains utilities for manipulatig matrices describing circuits.
• ->Yn - Adds a row and a column to the matrix so that the sums of elements in each row and each column equal 0. This operation is required when the conversion from one orientation to another is required.

Let-s say you have a transistor with its Y-parameters for common emitter orientation and you want to convert them to Y-parameters for common base orientation. First put the 2x2 matrix with Y-parameters for common emitter orientation on the stack.
Row 1 and column 1 belong to node 1 (base). Row 2 and column 2 belong to node  2 (collector).
Now select ->Yn. The 2x2 matrix is expanded to a  3x3 matrix where row 3 and column 3 belong to node 3 (emitter).
Since you want to extract the parameters for comon base orientation, you have to delete the row and column that belong to the base node. Therefore you have to delete row 1 and column 1. You can do that with the built-in matrix editor.
Now you have a 2x2 matrix with row 1 and column 1 for the collector and row 2 and column 2 for the emitter.
Since the input port is the emitter, nodes must be swapped by swapping rows 1 and 2 and columns 1 and 2. This operation can be performend by using the NSWP utility.
This procedure can be used for larger circuits, not just those with 3 nodes like the transistor.
• Eliminate - Eliminates the node that belongs to the last row in the matrix.

Let's say you have a 5-node (4 port, 4 nodes+ground) circuit and you want to obtain the Y-parameters for a certain pair of ports. Write it's reduced node admitance matrix (4x4) and put it on the stack. Then swap nodes with the NSWP utility so that the node that belongs to the input port is in the first row and the node that belogs to the output port is in the second row. Press Eliminate twice to eliminate the inner two nodes represented by rows 3 and 4 and columns 3 and 4. The result is the Y-parameters matrix (2x2).
• MCF - Calculates the matrix cofactor. The matrix cofactor is the determinate that belongs to the matrix with the row i and the column j removed, multiplied by (-1)^(i+j). Put the matrix, the row number i and the column number j on the stack and select MCF.
• NSWP - Swaps nodes in the Y-matrix. Put the Y matrix followed by two node numbers (i and j) on the stack and select NSWP. This will swap nodes i and j by swapping rows i and j and columns i and j.
• MCSW - Swaps columns in a matrix. Put the matrix along with the two column numbers (i and j) on the stack and select MCSW.
• MRSW - Swaps rows in a matrix. Put the matrix along with the two row numbers (i and j) on the stack and select MRSW.
• MCCI - Multiplies a column by a scalar factor. Put the matrix, the scalar and the column number on the stack and select MCCI.
• MCCIJ - Adds the source column multiplied by a scalar factor to the target column. Put the matrix, the scalar factor, the number of the source collumn and the number of the target column on the stack and select  MCCIJ.
• MRCI - Multiplies a row by a scalar factor. Put the matrix, the scalar and the row number on the stack and select MRCI.
• MRCIJ - Adds the source row multiplied by a scalar factor to the target row. Put the matrix, the scalar factor, the number of the source row and the number of the target row on the stack and select  MCCIJ.
• Y->A - Two-port network parameters conversion. Converts Y matrix to A matrix. See the definitions below. Put a 2x2 (compex) matrix containing Y parameters to stack and select Y->A.
• A->Y - Two-port network parameters conversion. Converts A matrix to Y matrix. Put a 2x2 (compex) matrix containing A parameters to stack and select A->Y.
• Z->A - Two-port network parameters conversion. Converts Z matrix to A matrix. Put a 2x2 (compex) matrix containing Z parameters to stack and select Z->A.
• A->Z - Two-port network parameters conversion. Converts A matrix to Z matrix. Put a 2x2 (compex) matrix containing A parameters to stack and select A->Z.
• H->A - Two-port network parameters conversion. Converts H matrix to A matrix. Put a 2x2 (compex) matrix containing H parameters to stack and select H->A.
• A->H - Two-port network parameters conversion. Converts A matrix to H matrix. Put a 2x2 (compex) matrix containing A parameters to stack and select A->H.
• K->A - Two-port network parameters conversion. Converts K matrix to A matrix. Put a 2x2 (compex) matrix containing K parameters to stack and select K->A.
• A->K - Two-port network parameters conversion. Converts A matrix to K matrix. Put a 2x2 (compex) matrix containing A parameters to stack and select A->K.
• K - Boltzman's constant. 1.380658E-23 J/K
• s - Stefan-Boltzman constant in the black-body radiation formula. 5.67051E-8 W/(m^2 K^4)
• e0 - Permittivity of vacuum. 8.85418781761E-12 As/Vm
• m0 - Permeability of vacuum. 1.25663706144E-6 Vs/Am
• h - Planck's constant. 6.6260755E-34 Js
 

Transmission line:

  ======================================--+
                                          I
                                         [ ]
G(x)           Zk                   G ->  [ ] Zn
                                         [ ]
                                          I
  ======================================--+
                                       x
  <=====================================
G(x)=Gexp(-2jbx)
 
Matrix manipulation:
Reduced node admitance matrix:
         node 1   node 2    ...     node n
node 1  [  x        x       ...       x   ]
node 2  [  x        x       ...       x   ]
 ...    [ ...      ...      ...      ...  ]
node n  [  x        x       ...       x   ]

Diagonal elements (i,i) are sums of all admitances connected to the node i.
Other elements are negative sums of all admitances between nodes i and j.
Node n+1 is ground node and is not contained in the reduced matrix. However it is contained in the expanded node admitance matrix. The reduced matrix can be converted to the expanded matrix by by the ->YN utility.
By deleting node l (row and column) from the expanded node admitance matrix a new reduced matrix is obtained. This matrix belongs to the circuit with node l grounded and node n+1 not grounded.

 

Matrix definitions:

 
     I1  [================]  I2
  + ==>==[                ]==<== +
         [    two-port    ]
 U1      [                ]      U2
         [    network     ]
  - =====[                ]===== -
         [================]

Z-matrix - Impedance matrix

[ U1 ]   [ Z11   Z12 ] [ I1 ]
[    ] = [           ] [    ]
[ U2 ]   [ Z21   Z22 ] [ I2 ]
Y-matrix - Admitance matrix
[ I1 ]   [ Y11   Y12 ] [ U1 ]
[    ] = [           ] [    ]
[ I2 ]   [ Y21   Y22 ] [ U2 ]
H-matrix - Hybrid matrix I
[ U1 ]   [ H11   H12 ] [ I1 ]
[    ] = [           ] [    ]
[ I2 ]   [ H21   H22 ] [ U2 ]
K-matrix - Hybrid matrix II
[ I1 ]   [ K11   K12 ] [ U1 ]
[    ] = [           ] [    ]
[ U2 ]   [ K21   K22 ] [ I2 ]
A-matrix - Chain matrix
[ U1 ]   [ A11   A12 ] [  U2 ]
[    ] = [           ] [     ]
[ I1 ]   [ A21   A22 ] [ -I2 ]
 
All of the matrix conversion utilities work with complex matrices. The result is always a complex matrix, even if the input matrix was real. However in this case all the imaginary parts equal 0.
To perform conversions that are not implemented: e.g. for Z->K execute Z->A and then A->K.