Hybrid, balancing network and singing

A hybrid (four-wire/two-wire termination set) is a bridge transformer that joins the two-wire subscriber line to the four-wire transmission path (separate GO and RETURN pairs). Together with a balancing network it passes signals from the 2-wire line to the 4-wire GO path and from the 4-wire RETURN path to the 2-wire line, while keeping the RETURN path isolated from the GO path.

Construction and operation

   4-wire RECEIVE (in)          2-wire line
   ---------+                  +---------- Z_L
            |   +----------+   |
            +---|  hybrid  |---+
                | (bridge  |
   4-wire SEND  |  transf.)|---+
   <--------+---|          |   |
            |   +----------+   +---------- Z_B
                              balancing network

The hybrid has a centre-tapped (differential) winding. One half connects to the two-wire line (impedance $Z_L$), the other half to the balancing network $Z_B$, which is designed to copy the impedance of the line over the voice band.

1. 2-wire to 4-wire (transmit): speech from the subscriber enters the line winding and divides equally between the send winding (4-wire GO pair) and the receive winding; the part reaching the receive side is absorbed by the one-way RETURN amplifier output and does no harm. The GO pair therefore gets half the power (about 3 dB loss). The line and the balancing network are conjugate ports, so ideally none of this power goes into $Z_B$.
2. 4-wire to 2-wire (receive): the incoming signal enters the centre tap and splits into two equal currents, one into $Z_L$ and one into $Z_B$. Since the currents flow in opposite senses through the two halves of the winding, their fluxes cancel in the send winding when $Z_B = Z_L$. So no receive signal leaks into the GO path; the subscriber still gets half of it (3 dB loss).
3. The loss from the receive port to the send port is called the transhybrid loss. With perfect balance it is very large (ideally infinite); in practice it is set by the balance return loss (transhybrid loss ≈ BRL + 6 dB for the two 3 dB hybrid losses)

$$BRL = 20\log_{10}\left|\frac{Z_L + Z_B}{Z_L - Z_B}\right|\ \text{dB}$$

Singing and how it is eliminated

A four-wire circuit with a hybrid at each end forms a closed loop: GO amplifier – far hybrid – RETURN amplifier – near hybrid – GO amplifier.

        G1 (amplifier) -->
 hyb A ===================== hyb B
        <-- G2 (amplifier)
 leak through A (L_A)   leak through B (L_B)

If the hybrids leak, part of the signal goes round the loop. When the total loop gain is $\geq 0$ dB, i.e.

$$G_1 + G_2 - (L_A + L_B) \geq 0\ \text{dB}$$

the circuit oscillates (sings), producing a howl. Smaller leakage that does not cause oscillation still produces echo and a hollow sound ("near-singing").

The balancing network prevents singing by making $Z_B \approx Z_L$, which keeps the transhybrid losses $L_A, L_B$ high. The loop then has a net loss (a singing margin, typically a few dB) and cannot oscillate. Further aids are compromise networks for varying line lengths, a fixed net loss inserted in the four-wire circuit, and echo suppressors/cancellers on long circuits.