ATLLC Examples
Example 1
What is the loss in a three quarters wavelength phasing line of LMR24075 at
144MHz with a load of 50+j0Ω, and what is the input impedance?
From the datasheet for LMR24075, 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=7.516e6
k2=0.000330/1e6/30.48=1.083e11
Entering that data into ATLLC...
Fig 1:
RF Arbitrary Transmission Line Loss Calculator
Parameters 

Ro 
75.00000 
vf 
0.840 
k1 
7.516000e6 
k2 
1.083000e11 
Frequency 
144.000 MHz 
Length 
0.750 wl 
Zload 
50.00+j0.00 Ω 
Yload 
0.020000+j0.000000 S 
Results 

Zo 
75.00j0.21 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 
111.23j0.62 Ω 
Yin 
0.008990+j0.000050 S 
VSWR(50)in 
2.22 
Γ, ρ∠θ, RL, VSWR, MismatchLoss (source end) 
1.945e1j1.326e3, 0.195∠0.4°, 14.2 dB, 1.48, 0.17 dB 
Γ, ρ∠θ, RL, VSWR, MismatchLoss (load end) 
2.000e1+j1.363e3, 0.200∠179.6°, 14.0 dB, 1.50, 0.18 dB 
S11, S21 
3.798e1j2.395e3, 9.829e4+j9.113e1 
Y11, Y21 
1.847e4+j5.246e7, 3.786e5j1.333e2 
NEC NT 
NT t s t s 1.847e4 5.246e7 3.786e5 1.333e2 1.847e4
5.246e7 'ATLLC, 0.750 wl, 144.000 MHz 
k1, k2 
7.516e6, 1.083e11 
C1, C2 
2.377e1, 1.083e2 
γ 
1.847e2+j6.283e+0 

The loss under the specified mismatch is 0.13dB, and the input impedance is
111.23j0.62Ω.
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=2.3e5f^0.5+4.2e9f (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 
2.300000e5 
k2 
4.200000e9 
Frequency 
14.100 MHz 
Length 
1.000 wl 
Zload 
70.00+j0.00 Ω 
Yload 
0.014286+j0.000000 S 
Results 

Zo 
105.02j0.73 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 
81.68j0.22 Ω 
Yin 
0.012242+j0.000033 S 
VSWR(50)in 
1.63 
Γ, ρ∠θ, RL, VSWR, MismatchLoss (source end) 
1.250e1+j2.090e3, 0.125∠179.0°, 18.1 dB, 1.29,
0.07 dB 
Γ, ρ∠θ, RL, VSWR, MismatchLoss (load end) 
2.001e1+j3.345e3, 0.200∠179.0°, 14.0 dB, 1.50,
0.18 dB 
S11, S21 
1.446e1j1.453e3, 7.499e1+j7.556e4 
Y11, Y21 
4.123e2+j2.873e4, 4.011e2j2.796e4 
NEC NT 
NT t s t s 4.123e2 2.873e4 4.011e2 2.796e4
4.123e2 2.873e4 'ATLLC, 1.000 wl, 14.100 MHz 
k1, k2 
2.300e5, 4.200e9 
C1, C2 
7.273e1, 4.200e+0 
γ 
2.352e1+j6.283e+0 

From ATLLC, the loss is 2.15dB, the physical length is 14.032m, and the input impedance is 81.68j0.22Ω.
Links / References
 Smith, J. Oct 2001. Postings to group rec.radio.amateur.antennas. Usenet
2001.
Changes
Version 
Date 
Description 
1.01 
10/10/2011 
Initial. 
1.02 


1.03 


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Owen Duffy 1995, 2021. All rights reserved. Disclaimer.