A transformer would not work correctly on a phone line due to talk pathYes it would work - otherwise hybrids, and the transformers in my Adtran interfaces, wouldn't work. The voice and ringing signals are AC voltages riding on top of a DC battery voltage and will pass the transformer quite nicely. However, that being said, don't count on a simple transformer doing the job. It would screw up other things in the interface which depend on the presence of the DC voltage (like line signaling) - and you wouldn't want a 1:1 transformer anyway.
being a DC voltage. 1:1 transformers only work with AC voltage.
Impedance matching of this kind is non-trivial. Impedance is frequency dependent, and matching the impedance over frequency is really difficult - especially since the phone line is a distributed impedance, i.e., the R, L and C that make up the impedance are not all in one place like they are in a coil or a capacitor. Phone lines are classical transmission lines, the theory for which was worked out by Lord Kelvin in the 1890's when planning the first transatlantic telegraph cable (and was later applied, amazingly, to the transmission of nerve impulses). Line impedance refers to the "characteristic" impedance of the transmission line. This is the transverse impedance, that is, the impedance looking across the line. It depends upon the longitudinal resistance per unit length and the capacitance per unit length between the wire pair. Inductance is usually not much of an issue (unless LOTS of the line is coiled up somewhere or unless frequencies over 100MHz are involved). If the line is terminated in its characteristic impedance, it will appear perfectly resisistive and will optimally transmit energy into the load. If it is not terminated properly, there will be reflections down the line (i.e., echo at the far end). It is constant at a given frequency because of the distributed nature of the RLC on the line - the more distant elements make a smaller and smaller contribution. On the other hand, the longitudinal resistance, that is, the resistance measured from one end of the line to the other, is not constant but depends upon the length of the line and the resistance per unit length. Line attenuation is highly dependent on longitudinal resistance.
However, none of this is really the issue with echo at the caller's end of the line. The impedance mismatch at the near end hybrid, while causing reflections and non-optimal coupling, really has its effect by introducing a phase shift in the transmitted signal. When the hybrid attempts to subtract the correct portion of the transmitted signal (the sidetone) from the received signal, echo cancellation is compromised owing to this phase shift. (As an exercise, try subtracting one sine wave from another when one of them is phase shifted. You cannot get a zero result no matter how you adjust the amplitudes.) In other words, to get your impedance matcher to work, you will need to match impedance over frequency in such a way as to eliminate any unexpected phase shift, otherwise cancellation will not be improved. In fact, if you are not very careful, you may just make things worse.
Stephen R. Besch
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