[Asterisk-Users] Re: Chaining more than one zap echo canceller?

[Stephen R. Besch]

Henry Devito wrote:
> A transformer would not work correctly on a phone line due to talk path
> being a DC voltage.  1:1 transformers only work with AC voltage.  
> 
Yes 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.

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