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i posted a tweet asking about why TRS balanced audio jacks can accept TS unbalanced plugs and have it “just work”, but i had to delete it because i immediately found out why:

TS plug -> TRS jack
(mono signal) T -> T (complement 1)
(ground) S -> R (complement 2)
(ground) S -> S

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the noise reduction works like

output = complement₁ - complement₂

because the TS ground gets routed to complement 2, the result becomes basically

output = complement₁ - 0

so It Just Works! yay!

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oh and to explain what balanced audio is: on professional audio equipment, you often use a TRS “stereo” jack to carry a “mono” signal as a differential pair. i'm calling the two signals in the pair the “complements”. it is like:

T = original signal
R = inverted signal or 0
S = 0

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i'm getting a real kick out of finally understanding this. it seems like this complicated topic and then like… no, it is ridiculously simple and intuitive. it's a very, very simple technology that works super well. the world is so cool

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in the balanced audio case btw the equation

output = complement₁ - complement₂

becomes

output = original - -original
output = original + original
output = 2 × original

and indeed, that's how balanced audio systems behave, the signal level is doubled :3

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