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 ! **