21.3 Full Duplex on One Circuit
Modern modems are able to both send and receive signals simultaneously. One could call this "bidirectional" or "full duplex". This was once done by using one frequency for sending and another for receiving. Today, the same frequency is used for both sending and receiving. How this works is not easy to comprehend.
Most of the telephone system "main lines" are digital with two channels in use when you make a telephone call. What you say goes over one digital channel and what the other person says goes over the other (reverse) digital channel. Unfortunately, the part of the telephone system which goes to homes (and many offices) is not digital but only a single analog channel. If both modems were directly connected to the digital part of the phone system then bidirectional communication (sending and receiving at the same time) would be no problem because two channels would be available.
But the end portion of the signal path goes over just one circuit. How can there be two-way communication on it simultaneously? It works something like this. Suppose your modem is receiving a signal from the other modem and is not transmitting. Then there's no problem. But if your modem were to start transmitting (with the other received signal still flowing into your modem) it would drown out the received signal. If the transmitted signal was a "solid" voltage wave applied to the end of the line then there is no way any received signal could be present at that point.
But the transmitter has "internal impedance" and the transmitted signal applied to the end of the line is not solid (or strong enough) to completely eliminate the received signal coming from the other end. Thus while the voltage at the end of the line is mostly the stronger transmitted signal a small part of it is the desired received signal. All that is needed is to filter out this stronger transmitted signal and then what remains will be the signal from the other end which we want. To do this, one only needs to get the pure transmitted signal directly from the transmitter (before it's applied to the line) amplify it a determined amount, and then subtract it from the total signal present at the end of the line. Doing this in the receiver circuits leaves a signal which mostly came from the other end of the line.
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