.


     APPENDIX B - EXAMPLE CIRCUIT
     ============================

     Circuit file PHASER.LIN is a model of a voice-band audio phase shift 
     network for a Single Sideband Transmitter Exciter.  Designed by Peter 
     Martinez, G3PLX, it appeared in the English magazine, RADIO COMMUNICATION,
     December 1973, p. 852, in the Technical Topics column hosted by Pat Hawker,
     G3VA.  The circuit is intended to provide four outputs, each having 90
     degree phase shift from one another.  With each output fed into one of four
     mixers, each mixer also fed with an R.F. carrier of appropriate phase,
     combinations of mixer outputs should be able to generate either an upper
     sideband, suppressed carrier signal or a lower sideband, suppressed carrier
     signal.  Amount of rejection of the unwanted sideband is inversely
     proportional to the accuracy of the 90 degree phase differential.

     Several attempts were made to "draw" this circuit using ASCII characters.
     None seemed satisfactory, but the following may show it.  Individual
     numbers are nodes.  Resistor strings in order R1x-R2x-R3x-R4x-R5x-R6x
     connected horizontally in each row, the 'x' denoting row A, B, C, or D.
     All resistors are 5.6 K.  Capacitors are on the diagonal.  Zero-phase input
     signal is at nodes 1 and 8, 180-degree phase input signal is at nodes 15
     and 22.  Relative 90-degree outputs are at nodes 7, 14, 21, and 28.  Each
     input node has a 300 Ohm resistor to ground, each output node has a 10
     Megohm resistor to ground.


            1    2    3    4    5    6    7      - A row
             \    \    \    \    \    \
              C1   C2   C3   C4   C5   C6        - capacitor "AB" group
                \    \    \    \    \    \
      I     8    9   10   11   12   13   14      - B row
      n      \    \    \    \    \    \
      p       C1   C2   C3   C4   C5   C6        - capacitor "BC" group
      u         \    \    \    \    \    \
      t    15   16   17   18   19   20   21      - C row
             \    \    \    \    \    \
              C1   C2   C3   C4   C5   C6        - capacitor "CD" group
                \    \    \    \    \    \
           22   23   24   25   26   27   28      - D row
             \    \    \    \    \    \
              C1   C2   C3   C4   C5   C6        - capacitor "DA" group
                \|   \|   \|   \|   \|   \|
              (completed connections on row A)

     This circuit is very calculation-intensive due to all the diagonal
     connections.  Using the Standard (non-coprocessor) version of LENA and
     a 20 MHz 386SX computer, 140 frequencies took about 117 seconds for each
     output node.  With the Numeric coprocessor version, 140 frequencies were
     solved in only 21 seconds!  The solution at Node 7 is included as file
     PHASER7.LNA in the program set.  Comparing solutions at nodes 14, 21, and
     28 shows that adjacent output phase is within quadrature by 2 degrees from
     500 Hz to 5 KHz.





                           LENA Appendix B - Page 1 of 2








     This is a special case for analysis-solution where _phase_ is the
     important criterion.  There is no easy way to output phase error between
     nodes, other than by a tabulation or graphical equivalent at each node.  It
     is possible to add to the circuit, using transconductance-specified
     dependent current sources, to see differences.  Adding the following
     branches to PHASER.CIR:

        61  GMS       29    0     1.0000  mho    Dep.Br.# 15, R7
        62  GMS       29    0     1.0000  mho    Dep.Br.# 22, R8
        63  R-SUM1    29    0     1.0000  Ohm
        64  GMS       30    0     1.0000  mho    Dep.Br.# 29, R9
        65  GMS       30    0     1.0000  mho    Dep.Br.# 36, R10
        66  R-SUM2    30    0     1.0000  Ohm

     ...creates a new Node 29 which has a "45 degree" phase (vector sum of
     voltages at Nodes 7 and 14), and a new Node 30 which has a "225 degree"
     phase (vector sum of voltages at Nodes 21 and 28).  Two more GMSs and
     another summing resistor, a new node (31), GMSs dependent on the
     above-listed summing resistors, will show the vector addition of the "45"
     and "225" phases...or vector subtraction if the node ordering is reversed
     or transconductance made negative in the second added GMS.

     There are many combinations of measurement-observation additions possible.
     Dependent current sources allow a variety of no-disturbance monitoring.

        Note:  These "polyphase" networks have appeared in several papers
        in the IEEE Circuits and Systems Transactions of the late seventies
        and early eighties.

     It is possible to re-arrange the node ordering versus connection points in
     the circuit to slightly reduce solution time, but this is difficult with
     more complex circuit arrangements.  It is usually better to translate a
     schematic to circuit list as it appears; this permits better understanding
     of the written (versus schematic) versions of the same circuit at a later
     time.





















 
                      LENA Appendix B - Page 2 of 2



.1/31/94