                           TLINE
                          ver 1.3

             Copyright (C) 1993  Richard M. Hardy


1)  GENERAL

TLINE is a Shareware program for the IBM PC or compatible that
provides quick and accurate calculations of electrical
transmission line parameters.  The program uses the ABCD complex
matrix method for transmission line analysis.  It requires an IBM
PC or compatible with at least 640K RAM running MS-DOS release 3.1
or later.

A separate 2x2 matrix is calculated for each transmission line
element at the chosen temperature and frequency.  Each of the
matrix terms is complex with both real and imaginary components. 
For multiple elements, the overall network matrix is determined by
matrix multiplication.  The calculations take into account the
complicated interactions between cable pair elements and between
elements and terminations.

Available transmission line elements are 26, 24, 22, and 19 gauge
PIC or Pulp copper cable (based on AT&T Publication 62310 - see
Section 3), Bridged Tap, 88 or 44 mH Load Coils and Build Out
Capacitors.  User Defined Cable, based on Primary Constants, can
also be input (see Section 3).  Up to 20 elements can be entered. 
Terminations can be either resistive or complex.

Possible calculations include Transducer (Measured) Loss, Insertion
Loss, Input and Output Impedance, Characteristic Impedance, Primary
Constants, Propagation Constant and Total Length and Resistance. 
The ABCD Matrix can also be displayed.

Available frequencies are 1 Hz to 2 MHz (2,000,000 Hz).  Available
temperatures are 0 to 120 degrees Fahrenheit (-17.8 to 48.9
Celsius).  Either F or C can be input.


2)  OPERATING INSTRUCTIONS

To start the program, type TLINE at the DOS prompt and press
ENTER/RETURN.

The program is self explanatory.  It can be interrupted at any
point by simultaneously pressing CONTROL and BREAK.

Defaults are 900 to 600 ohm resistive terminations and 68 degrees
F (20 degrees C) temperature.

Impedances at the A and Z ends of the circuit are indicated by IMPA
and IMPZ respectively.
The initial calculation is loss at the chosen frequency.  After the
initial loss calculation, all other calculations can be done.

Circuit elements can be changed or corrected.  Blank elements can
be used to remove elements or to make it possible to insert
elements for subsequent calculations.

The PC may display some numbers in exponential format.  For
example, 2 MHz (2000000 Hz) may be displayed as 2E06.  This is the
same as 2x10^6.  Inputs can also be in exponential format.

Each time an element is entered, TLINE lists the circuit makeup. 
For User Defined Cable (UDC), TLINE lists the Primary Constants
plus the applicable frequency and temperature Fahrenheit.


3)  CABLE PAIR PRIMARY CONSTANTS

For 26, 24, 22, and 19 gauge PIC or Pulp cable, TLINE calculates
the Primary Constants R, L, G and C (Resistance, Inductance,
Conductance and Capacitance per unit length), by polynomial or
power fit to the PIC and Pulp cable Primary Constant tables
published in AT&T Publication 62310.  User Defined Cable (UDC)
requires the Primary Constants (per mile) to be input for the
chosen temperature and frequency.

Primary Constants are fundamental to transmission line calculations
and can be displayed with the "K" command.


4)  CHARACTERISTIC IMPEDANCE

TLINE calculates the Characteristic Impedance (Zo) according to
the formula 

        Zo = Sqr Rt [(R + jwL)/(G + jwC)]

where  w = 2*pi*frequency  is the radian frequency  and
       Sqr Rt = Square Root

Characteristic Impedance (Zo) is fundamental to transmission line
calculations and can be displayed with the "K" command.


5)  PROPAGATION CONSTANT

TLINE calculates the Propagation Constant (Gamma) according to the
formula

        Gamma = Alpha + j Beta = Sqr Rt [(R + jwL)*(G + jwC)]

where Alpha is the attenuation constant and Beta is the phase
constant).   The Propagation Constant is  fundamental to
transmission line calculations and can be displayed with the "K"
command.


6)  TWO-PORT LINEAR NETWORKS

A two-port linear network can be represented by an ABCD matrix
where A, B, C and D are complex numbers with both real and
imaginary parts dependent on frequency.

TLINE calculates an ABCD matrix for each element of the
transmission line at the chosen temperature and frequency.


7)  TRANSMISSION LINE  (CABLE PAIR)

For a transmission line of length l with propagation constant     
Gamma = Alpha + j Beta    and Characteristic Impedance  Zo, the 
ABCD matrix is given by

       A = cosh(Gamma*l)              B = Zo*sinh(Gamma*l)

       C = [sinh(Gamma*l)]/Zo         D = cosh(Gamma*l)
            
where cosh and sinh are the hyperbolic cosine and hyperbolic sine
respectively.

TLINE calculates an ABCD matrix for each gauge length of cable
pair at the chosen temperature and frequency.

Lengths can be input in feet, kilofeet, miles or meters.


8)  MULTIPLE ELEMENTS

For two-port networks connected in tandem, the overall ABCD matrix
is the matrix product of the original two-port matrices.

This can be done for any number of two-port networks connected in
tandem.  TLine will automatically multiply matrices for up to 20 
elements.


9)  INSERTION LOSS

Insertion Loss (IL) is defined as  (all logarithms to base 10)

        IL = 10 log (P1/P2) dB
              
where  P1 = Power delivered to load without network  and
       P2 = Power delivered to load with network inserted

In terms of the ABCD matrix this becomes

        IL = 20 log {[(C*Zl +D)Zs + A*Zl + B] / (Zs + Zl)}  dB

where Zs and Zl are the impedance of the source and load
respectively.

This is the formula that TLINE uses to calculate IL.  TLINE will
calculate IL for either resistive or complex terminations.


10)  TRANSDUCER LOSS

Transducer Loss (TL) is what is measured in the field.  For this
reason, it is sometimes referred to as Measured Loss.  Transducer
(Measured) Loss is defined as

        TL = 10 log (P1'/P2) dB

where  P1' = Maximum power available from the source  and
       P2  = Power delivered to load with network inserted

In terms of the ABCD matrix this becomes

        TL = IL + 10 log [(Zs + Zl)^2 / 4*Re(Zs)*Re(Zl)]  dB

Where IL is the Insertion Loss and Re means the real part of Zs and
ZL (impedance of source and load) respectively.

This is the formula that TLINE uses to calculate TL.

Note that Transducer (Measured) Loss is always equal to or greater
than Insertion Loss.

For resistive terminations, the 2nd term becomes zero when the
source and load impedances are equal.  For this special case, IL
and TL are equal.

Since transmission measuring sets and reference oscillators are
essentially resistive, TLINE will calculate TL only for resistive
terminations.


11)  INPUT IMPEDANCE
                          
Input Impedance Zin is defined as    Zin =  V1/I1

where  V1 = the network input voltage  and
       I1 = the network input current  when the network is 
terminated in Zt.


In terms of the ABCD matrix this becomes


        Zin = (AZt + B) / (CZt + D)

This is the formula that TLINE uses to calculate Zin.  Input
Impedance is displayed with the "Z" command.


12)  OUTPUT IMPEDANCE

Similar to the above, the Output Impedance (Zout) is defined as

        Zout = V2/-I2

where  V2 = the network output voltage  and
       I2 = the network ouptut current  when the input side is 
terminated in Zt.

In terms of the ABCD matrix this becomes

        Zout = (D*Zt + B) / (C*Zt + A)

This is the formula that TLINE uses to calculate Zout.  Output
Impedance is displayed with the "Z" command.


13)  BRIDGED TAP

To calculate the ABCD matrix for Bridged Tap, TLINE first
calculates the Input Impedance to the Bridged Tap length of cable
with an open circuit termination (Zbt).  This impedance is
connected across the circuit at the point where the Bridged Tap 
appears.

The ABCD matrix for Bridged Tap (BT) is

        A = 1           B = 0

        C = 1/Zbt       D = 1


14)  BUILD OUT CAPACITORS

The ABCD matrix for a Build Out Capacitor (BOC) is

        A = 1           B = 0

        C = jwC         D = 1

where w = 2*pi*frequency   is the radian frequency.

This representation is accurate within the voice band.


15)  LOAD COILS

Load coils can be represented by a pi network where the shunt  
elements are a parallel conductance (G) and capacitance (C) and the

series element is a series resistor (R) and inductor (L).
For a typical coil, G and C have small values within the voice
band.

When the matrices for these elements are successively multiplied
together the resulting ABCD matrix for a load coil is

 A = (1 + RG - w^2*LC) + jw(LG + RC)
 B = R + jwL
 C = G(2 + GR) - w^2*C(2GL + CR) + jw(2C + 2GCR + G^2*L-w^2*LC^2)
 D = (1 + RG - w^2*LC) + jw(LG + RC)

This representation is accurate within the voice band.  Either 44
or 88 mH load coils can be input.


16)  ABCD MATRIX

After the Loss (L) command is run, TLINE asks if you wish to
display the ABCD Matrix.  If requested, the Matrix will be
displayed.  The two numbers for each letter are the real and
imaginary components respectively.


17)  TOTAL LENGTH & LOOP RESISTANCE

The P command, which displays the circuit makeup, terminations and
temperature, also gives the total circuit length and loop
resistance.  For UDC (User Defined Cable), the Primary Constants
(per mile), frequency and temperature (Fahrenheit), are displayed. 
Loop resistance is not given if the circuit includes UDC.         


               **   THANK YOU !   **

If you find TLINE to be useful please register by sending a check
or money order, payable to Richard M. Hardy, for $25.00.  Please
add $6.00 for shipping outside the U.S.  Send to:

          Richard M. Hardy
          2800 N Lake Shore Dr #914
          Chicago, Illinois  60657

Registered users receive a copy of the latest version plus a
complete printed mathematical explanation.

Please specify 3.5" or 5.25" diskette size.

              **   THANK YOU !   **