# Example 1

What is the loss in a three quarters wavelength phasing line of LMR240-75 at 144MHz with a load of 50+j0Ω, and what is the input impedance?

From the datasheet for LMR240-75, Ro=75, vf=0.84, and MLL/100'=(0.229100) • FMHz + (0.000330) • FMHz.

First step is to find k1 and k2 in metres and Hertz units.

k1=0.2291/1e3/30.48=7.516e-6

k2=0.000330/1e6/30.48=1.083e-11

Entering that data into ATLLC...

Fig 1:

# RF Arbitrary Transmission Line Loss Calculator

 Parameters Ro 75.00000 vf 0.840 k1 7.516000e-6 k2 1.083000e-11 Frequency 144.000 MHz Length 0.750 wl Zload 50.00+j0.00 Ω Yload 0.020000+j0.000000 S Results Zo 75.00-j0.21 Ω Velocity Factor, VF -2 0.840, 1.417 Length 270.00 °, 0.750 λ, 1.312 m Line Loss (matched) 0.120 dB Line Loss 0.130 dB Efficiency 97.05 % Zin 111.23-j0.62 Ω Yin 0.008990+j0.000050 S VSWR(50)in 2.22 Γ, ρ∠θ, RL, VSWR, MismatchLoss (source end) 1.945e-1-j1.326e-3, 0.195∠-0.4°, 14.2 dB, 1.48, 0.17 dB Γ, ρ∠θ, RL, VSWR, MismatchLoss (load end) -2.000e-1+j1.363e-3, 0.200∠179.6°, 14.0 dB, 1.50, 0.18 dB S11, S21 3.798e-1-j2.395e-3, -9.829e-4+j9.113e-1 Y11, Y21 1.847e-4+j5.246e-7, 3.786e-5-j1.333e-2 NEC NT NT t s t s 1.847e-4 5.246e-7 3.786e-5 -1.333e-2 1.847e-4 5.246e-7 'ATLLC, 0.750 wl, 144.000 MHz k1, k2 7.516e-6, 1.083e-11 C1, C2 2.377e-1, 1.083e-2 γ 1.847e-2+j6.283e+0

The loss under the specified mismatch is 0.13dB, and the input impedance is 111.23-j0.62Ω.

# Example 2

(Smith 2001) made a series of measurements of Zip cord and published his results on Usenet. Fig 2 above shows the measured matched line loss. A  regression matched line loss model was derived from the ten data points and is shown, the loss model is MLL/m=2.3e-5f^0.5+4.2e-9f (MLL in dB, f in MHz). The conductor and dielectric loss components of the model loss are also in Fig 7, and it can be seen that whilst dielectric loss is relatively low at 1MHz, it overtakes conductor loss at about 30MHz. Measurements made well above or well below this cutover might not capture well the effects of both kinds of loss.

The problem to be solved is: what is the loss of a wavelength of this line at 14.1MHz when terminated in 70+j0Ω, what is the physical length, and what is the input impedance?

Entering that data into ATLLC...

Fig 8:

# RF Arbitrary Transmission Line Loss Calculator

 Parameters Ro 105.00000 vf 0.660 k1 2.300000e-5 k2 4.200000e-9 Frequency 14.100 MHz Length 1.000 wl Zload 70.00+j0.00 Ω Yload 0.014286+j0.000000 S Results Zo 105.02-j0.73 Ω Velocity Factor, VF -2 0.660, 2.296 Length 360.00 °, 1.000 λ, 14.032 m Line Loss (matched) 2.043 dB Line Loss 2.152 dB Efficiency 60.93 % Zin 81.68-j0.22 Ω Yin 0.012242+j0.000033 S VSWR(50)in 1.63 Γ, ρ∠θ, RL, VSWR, MismatchLoss (source end) -1.250e-1+j2.090e-3, 0.125∠179.0°, 18.1 dB, 1.29, 0.07 dB Γ, ρ∠θ, RL, VSWR, MismatchLoss (load end) -2.001e-1+j3.345e-3, 0.200∠179.0°, 14.0 dB, 1.50, 0.18 dB S11, S21 1.446e-1-j1.453e-3, 7.499e-1+j7.556e-4 Y11, Y21 4.123e-2+j2.873e-4, -4.011e-2-j2.796e-4 NEC NT NT t s t s 4.123e-2 2.873e-4 -4.011e-2 -2.796e-4 4.123e-2 2.873e-4 'ATLLC, 1.000 wl, 14.100 MHz k1, k2 2.300e-5, 4.200e-9 C1, C2 7.273e-1, 4.200e+0 γ 2.352e-1+j6.283e+0

From ATLLC, the loss is 2.15dB, the physical length is 14.032m, and the input impedance is 81.68-j0.22Ω.