Do router and ethernet cables affect sound quality?

All digital equipment is subject to those factors because voltages, currents, etc. used to represent digital signals are analog quantities. Engineering makes it possible to detect and, where necessary, correct errors. In the case of Ethernet, if an error occurs in transit then it will be detected by means of a CRC and (normally) rejected by either the receiving Ethernet interface hardware or the device driver. When the Ethernet frames carry an audio stream this will be before any audio payload is extracted, and rejecting an errored frame may cause drop-outs (depending on the higher-level protocol). If a drop-out occurs this will be an obvious indication that something is broken, not a subtle change in sound quality.

Exactly, what about it? I’m not sure what you mean by jitter in this context, since the audio data is packetised and the inter-sample time is not contained in the packets (but is mutually agreed between the sender and receiver). Any protocol for streaming audio over a network has to handle the fact that the inter-frame time is variable, which as @Janne_Johansson pointed out is normally done by having a local buffer on the receiving side.

Well, that might be a concern if the DAC is not well-engineered.

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