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Today I was told that something was causing Transmission Loss and not Insertion Loss. Can someone clarify what these two phenomena are? I always thought they were the same thing expressed in dB or dB/m.

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They can be the same thing. A transmission line will attenuate an amount (based on distance) whilst maintaining impedances so, it could be regarded as causing "insertion loss".

Here's what wiki says about cable attenuation: -

Insertion Loss

Insertion loss, also referred to as attenuation, refers to the loss of signal strength at the far end of a line compared to the signal that was introduced into the line. This loss is due to the electrical impedance of the copper cable, the loss of energy through the cable insulation and the impedance caused by the connectors. Insertion loss is usually expressed in decibels dB with a minus sign. Insertion loss increases with distance and frequency. For every 3 dB of loss, the original signal will be half the original power (\$\sqrt2\$ of amplitude).

Taken from here

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    \$\begingroup\$ Re: "For every 6dB of loss, the (resulting) signal will be half the original power...." That should say 3dB not 6dB. The Wikipedia article has been corrected. \$\endgroup\$ – user71928 Apr 10 '15 at 5:10
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    \$\begingroup\$ Thanks for that update on the error in the wiki article yes, it should say 3 dB and I will correct that. \$\endgroup\$ – Andy aka Feb 28 '20 at 13:19
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In what context? An acoustic system, or a transmission line or what? In general I would say insertion loss is the loss you get from adding some component or section into your system. Say for instance how much loss do we get from using this connector. Transmission loss to me would be what's the loss over my transmission medium. So maybe it's a long trace, or really long Coax cable where your loss is increasing with distance.

A quick search of the terms yields several articles about this in the acoustic domain, where they define transmission loss as the loss as the signal spreads out from the source.

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