An impedance matcher for matching the impedance of a high bit rate transmission channel of a copper-wired terminal installation comprising a high bit rate x-DSL modem (M) and a jack (P; P1; P2, P3), which automatically matches the impedance of the high bit rate transmission channel according to whether a modem is plugged into the jack of the installation or not. The impedance matcher comprises an adjustment module (10) adapted to insert a terminating impedance into the jack (P; P1, P2, P3) when it is not connected to said high bit rate modem (M), and a coupling module (20) adapted to be combined with said adjustment module (10) when said high bit rate modem (M) is connected to said jack (P; P1, P2, P3) to transform the impedance inserted into said jack to make it transparent to high bit rate transmission of broadband services.