Loss - a review

[VK2OMD]

The general meaning of loss is PowerIn/PowerOut, or in decibels 10log(PowerIn/PowerOut).

Transmission Loss is an equivalent term, ie PowerIn/PowerOut, or in decibels 10log(PowerIn/PowerOut).

Two other terms widely used in relation to RF applications are Insertion Loss and Return Loss.

1. To review the meanings of these terms, lets find for a half wave of lossless 75Ω line at 10MHz with a 50+j0Ω load find (wrt 50Ω):
a - Insertion Loss;
b - Transmission Loss;
c - Return Loss;
d - power converted to heat in the coax with 100W developed in the 50Ω load.

2. Then find for a quarter wave of lossless 75Ω line at 10MHz with a 50+j0Ω load find (wrt 50Ω):
a - Insertion Loss;
b - Transmission Loss;
c - Return Loss;
d - power converted to heat in the coax with 100W developed in the 50Ω load.

For the adventurous, repeat the whole thing for RG6 coax (I will use Belden 1694A RG6 which uses a solid copper centre conductor).

What did you get? Answers for those interested later.

Owen

[VK5ZLR]

I am at a loss to know what this is all about.......

[VK2OMD]

...

1. To review the meanings of these terms, lets find for a half wave of lossless 75Ω line at 10MHz with a 50+j0Ω load find (wrt 50Ω):
a - Insertion Loss;
b - Transmission Loss;
c - Return Loss;
d - power converted to heat in the coax with 100W developed in the 50Ω load.

2. Then find for a quarter wave of lossless 75Ω line at 10MHz with a 50+j0Ω load find (wrt 50Ω):
a - Insertion Loss;
b - Transmission Loss;
c - Return Loss;
d - power converted to heat in the coax with 100W developed in the 50Ω load.

The answers:

1.

Lets do the easy ones first:

b - since the cable is by definition lossless, there is no Transmission Loss, 0dB.

d - since the cable is by definition lossless, there is no conversion of RF energy to heat, 0W.

Now it gets harder...

c - the input Z of a half wave of lossless line is equal to its load impedance, 50+j0Ω in this case, so the 50Ω source is terminated in a matched load, there is no reflected wave so Return Loss is ∞dB.

a - since the source has a matched load and there is no loss in the cable, the power in the load is equal to that of a matched load and so Insertion Loss is 0dB.

2.

Lets do the easy ones first:

b - since the cable is by definition lossless, there is no Transmission Loss, 0dB.

d - since the cable is by definition lossless, there is no conversion of RF energy to heat, 0W.

Now it gets harder...

c - the input Z of a quarter wave of lossless line is Zo^2/Zload=75^2/50=112.5+j0Ω, so we have a 50Ω source with load of 112.5Ω and so Return Loss is 8.30dB.

a - the power delivered by the 50Ω source into 112.5Ω load relative to a 50Ω load is 0.695dB lower, and since the cable is lossless, the power in the load is 0.695dB lower and therefore Insertion Loss is 0.695dB.

Some key points:
- Insertion Loss of the shorter cable was higher;
- RF energy converted to heat is not implied by Insertion Loss.

So, if you are reading specs for a coax relay, a balun, etc, read them carefully (though the specs for a lot of product aimed at hams are amateurish).

For the adventurous, repeat the whole thing for RG6 coax (I will use Belden 1694A RG6 which uses a solid copper centre conductor).

I will post those answers later if anyone is really interested.

Owen

[VK2OMD]

...
For the adventurous, repeat the whole thing for RG6 coax (I will use Belden 1694A RG6 which uses a solid copper centre conductor).

The answers for RG6:

...

1. To review the meanings of these terms, lets find for a half wave of
lossless 75Ω line at 10MHz with a 50+j0Ω load find (wrt 50Ω):
a - Insertion Loss;
b - Transmission Loss;
c - Return Loss;
d - power converted to heat in the coax with 100W developed in the 50Ω load.

2. Then find for a quarter wave of lossless 75Ω line at 10MHz with a
50+j0Ω load find (wrt 50Ω):
a - Insertion Loss;
b - Transmission Loss;
c - Return Loss;
d - power converted to heat in the coax with 100W developed in the 50Ω load.

1.

b - from a line loss calculator, Transmission Loss (under standing waves) is 0.26dB

d - input power is 0.26dB higher than 100W, 106.2W, so there is 6.2W heating of the cable.

c - input Z is 51.13-j0.03Ω, Return Loss is 39.0dB.

a - from a line loss calculator, S21 is -0.260dB.
Insertion Loss is 0.260dB.

In this case, there is very small mismatch at the source and almost all of the Insertion Loss is due to Transmission Loss.

2.

b - from a line loss calculator, Transmission Loss (under standing waves) is 0.13dB

d - input power is 0.13dB higher than 100W, 103.0W, so there is 3.0W heating of the cable.

c - input Z is 111.23-j1.90Ω, Return Loss is 8.41dB.

a - from a line loss calculator, S21 is -0.807dB.
Insertion Loss is 0.807dB.

In this case, there is very significant mismatch at the source and most of the Insertion Loss is due to mismatch (Mismatch Loss at the source is 0.68dB), loss that directly causes heating is 0.13dB. You cannot make any inferences about changes in heat generation inside the source from this information.

Mismatch Loss features in ham mythology which holds that the 'lost power' is reflected back into the transmitter and will burn your PA up.

Owen