Transmission Line Impedance

This program calculates the input impedance of a transmission line across a user-specified range of electrical distances expressed in degrees. For each angular step, it computes the complex impedance by combining the load impedance (with a reactive “J” component) and the characteristic line impedance using the standard transmission line equation involving the tangent of the electrical length. Rectangular-to-polar conversion via SQR and ATN yields the magnitude and phase angle, with a quadrant correction applied when the denominator phasor falls in the negative-real half-plane. Results are printed to both the screen and the printer, with a demo mode triggered by holding ENTER at startup that bypasses user INPUT prompts and suppresses printer output. The program also POKEs address 23692 to prevent the “scroll?” prompt from interrupting a long table of results.

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Program Structure

The program is organized into a clear sequence of phases: initialization (lines 1–16), parameter input (lines 20–80), header output (lines 100–110), and a computation loop (lines 120–380), followed by a STOP at line 8999 and a SAVE at line 9000. The REM statements at lines 3, 4, 8, 14, 90, 130, 200, 220, 270, 290, 310, 330, and 350 are unusually verbose, serving as inline documentation for each logical section.

Demo Mode

A notable feature is the demo/bypass mode controlled by the FLAG variable. After a PAUSE 30 at line 12, line 16 checks INKEY$: if a key (specifically ENTER held from the RUN command) is still detected, the program skips all INPUT prompts and loads preset values (ZL=40, ZLJ=20, ZO=50, BS1=35, BS2=55, S=1), sets FLAG=1, and jumps directly to the output loop. When FLAG=1, lines 100, 360 use IF FLAG=1 THEN GO TO to bypass LPRINT statements, preventing spurious printer output during demo runs.

Transmission Line Calculation

The core formula implements the standard transmission line input impedance equation. For each angular distance L (in degrees), the tangent is computed at line 150 as TN = TAN(L * PI / 180). The numerator and denominator complex phasors are then assembled:

• JPI = ZO * TN — reactive part of line term
• JTN = JPI + ZLJ — imaginary part of numerator
• JTD = ZL * TN — imaginary part of denominator
• ZLD = ZO - (ZLJ * TN) — real part of denominator

The real part of the numerator is simply ZL, and the real part of the denominator is ZLD. Magnitudes are found via SQR at lines 230–240, and angles via ATN at lines 250–260.

Singularity Avoidance

Two guards prevent arithmetic errors. Line 140 skips L=90 and L=270 using NEXT L directly inside the FOR loop, avoiding the infinite tangent at those angles. Line 210 similarly skips iterations where ZLD=0, which would cause a division-by-zero when computing the denominator angle.

Quadrant Correction

Because ATN returns values only in the range −π/2 to +π/2, the angle of the denominator phasor AD is incorrect when the real part ZLD is negative (second or third quadrant). Line 280 corrects this by adding PI to AD when ZLD < 0, restoring the proper principal value for a phasor in the left half-plane.

Output Formatting

Both magnitude and phase are truncated (not rounded) to three decimal places using the INT(1000 * value) / 1000 idiom at lines 300 and 320. Line 340 POKEs the system variable at address 23692 with 255 inside the loop, resetting the scroll counter before each row is printed so the “scroll?” prompt never interrupts a long table.

Variable Summary

Variable	Role
ZL	Real part of load impedance
ZLJ	Imaginary (“J”) part of load impedance
ZO	Characteristic impedance of the line
BS1, BS2	Start and stop distances in degrees
S	Step width in degrees
FLAG	Demo mode flag (1 = demo, suppresses printer)
TN	TAN of current angle
MN, MD	Magnitudes of numerator and denominator phasors
AN, AD	Angles of numerator and denominator phasors (radians)
MAGNITUDE	Computed impedance magnitude, truncated to 3 d.p.
PHASE	Computed phase angle in degrees, truncated to 3 d.p.

Potential Anomalies

• The singularity check at line 140 handles only exact integer values 90 and 270. If BS1, BS2, and S are chosen such that those values are never hit as exact loop iterations (e.g., S=0.5 starting at 35), the guard still works correctly, but non-integer near-singularities will produce very large but finite results without warning.
• FLAG is initialized to 0 at line 10 each run, so the demo mode cannot persist across runs without re-triggering the INKEY$ check — this is by design.
• The SAVE at line 9000 is unreachable during normal execution due to the STOP at line 8999; it must be run manually or via direct GO TO 9000.