ATLLC Examples
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.
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 |
|
|
© Copyright:
Owen Duffy 1995, 2021. All rights reserved. Disclaimer.
