# Table 1.
# Octave code.
f = 7.01; # FREQUENCY IN MHz
d = 100; # LENGTH OF LINE IN FEET
a = 2.0; # ATTENUATION IN dB PER 100 FEET
v = 66; # VELOCITY FACTOR AS A PERCENTAGE
#Zo = 50;
Zo = 50 - 1j * 0.72; # CHARACTERISTIC IMPEDANCE IN OHMS
# Specify source (transmitter) and load (antenna)
VS = 2.0;
RS = 50;
Rt = 100;
Xt = 0;
# Convert inputs as required
a = a ./ 1e2; # convert dB per 100 feet to dB per foot
a = 0.1151 .* a; # convert dB to nepers
c = 9.836e8; # speed of light in feet per second
lambda = c ./ (1e6 .* f); # wavelength of signal in vacuum
lambda = (v ./ 1e2) .* lambda; # adjust lambda for velocity
B = (2 .* pi) ./ lambda; # calculate Beta
ZL = Rt .+ j .* Xt; # calculate complex terminating impedance
# Calculate elements of T-equivalent network
# ZA = input series element
# ZB = output series element
# ZC = shunt element
ZA = Zo .* tanh((a .+ j .*B) .* d ./ 2.);
ZB = ZA;
ZC = Zo ./ sinh((a .+ j .*B) .* d);
# Prepare matrices for solution of currents
right_side = [RS + ZA + ZC, -ZC; -ZC, ZB + ZC + ZL];
left_side = [VS; 0];
# Solve for currents
denom = det(right_side);
for m = 1: rows(right_side)
 numerator = right_side;
 for n = 1: rows(right_side)
 numerator(n, m) = left_side(n);
 endfor
 current(m) = det(numerator) / denom;
endfor
# Calculate T-network input impedance
Zd = ZA .+ (ZC .* (ZB + ZL)) ./ (ZC .+ ZB .+ ZL);
# Calculate input power to T-network from source
Pwr_in = abs(current(1)) ^ 2 * real(Zd);
# Calculate power delivered by T-network to load
Pwr_load = abs(current(rows(right_side))) ^ 2 * real(ZL);
# Calculate T-network line loss
Line_loss = 10 * log10(Pwr_in / Pwr_load);
printf("\n T-NETWORK LINE LOSS (in dB) = %-8.5g", Line_loss);
# Calculate coefficients of ABCD matrix and solve
# for input voltage and current
Vt = 1.0;
gamma_l = (a + 1j * B) * d;
A = cosh(gamma_l);
B = Zo * sinh(gamma_l);
C = sinh(gamma_l) / Zo;
D = cosh(gamma_l);
It = Vt / ZL;
Vi = A * Vt + B * It;
Ii = C * Vt + D * It;
# Calculate ABCD matrix input impedance
Zin = Vi / Ii;
# Calculate input power to line (ABCD matrix) from source
Pwr_in = abs(Ii ^ 2) * real(Zin);
# Calculate power dissipated in load
Pwr_out = abs(It ^ 2) * real(ZL);
# Calculate and print out ABCD matrix line loss
Line_loss = 10 * log10(Pwr_in / Pwr_out);
printf("\n ABCD MATRIX LINE LOSS (in dB) = %-8.5g\n", Line_loss);
# Calculate and print out ARRL Antenna Book Total Loss (Eq. 16)
refl_coef = (ZL - Zo) / (ZL + Zo);
SWR = (1 + abs(refl_coef)) / (1 - abs(refl_coef));
adB = a / 0.1151;
mllr = 10 ^ (d * adB / 10);
Total_loss = 10 * log10((mllr ^ 2 - abs(refl_coef) ^ 2) / ...
(mllr * (1 - abs(refl_coef) ^ 2)));
printf(" ARRL EQ. 16 TOTAL LOSS (in dB) = %-8.5g\n\n", Total_loss);

# Table 2.
# Octave code.
Zo = 50 ohms:
T-NETWORK LINE LOSS (in dB) = 2.3145
ABCD MATRIX LINE LOSS (in dB) = 2.3145
ARRL EQ. 16 TOTAL LOSS (in dB) = 2.315
Zo = 50 - j0.72 ohms:
T-NETWORK LINE LOSS (in dB) = 2.2907
ABCD MATRIX LINE LOSS (in dB) = 2.2907
ARRL EQ. 16 TOTAL LOSS (in dB) = 2.3151

# Table 3.
# Octave code.
graphics_toolkit gnuplot;
#gamma = 1j * 0.5; # Used to generate Figure 1
gamma = 0.01 + 1j * 0.5; # Used to generate Figure 2
V1 = 1.0;
V2 = 0.5;
rho = V2 / V1;
p = log(1 / sqrt(abs(rho)));
q = -0.5 * arg(rho);
l = 16 * pi;
z = linspace(0, l, 200);
d = l .- z;
Vdabs = sqrt((sinh(real(gamma) .* d .+ p)) .^ 2 + (cos(imag(gamma) .* d .+ q)) .^ 2); # (8.17)
scale_factor = abs(2 .* V1 * e .^ (-1j .* imag(gamma) .* l) .* sqrt(rho));
Vdabs = scale_factor .* Vdabs;
upper_bound = scale_factor .* cosh(real(gamma) .* d .+ p);
lower_bound = scale_factor .* sinh(real(gamma) .* d .+ p);
plot(d, Vdabs, d, upper_bound, d, lower_bound);
grid();
xlabel("DISTANCE ALONG LINE => TOWARD TRANSMITTER");
ylabel("LINE VOLTAGE: ABSOLUTE VALUE");
pause;