The problem of using shunt and series sections of transmission line as matching devices is here investigated mathematically. By making use of hyperbolic functions the condition of match for both cases can be expressed in a very simple way. Both devices when used alone have a limited range with regard to the impedance to be matched. The exact range within which matching is possible is shown graphically. By using one additional matching network each device can be designed to match impedance of any value. The complete systems still preserve their simplicity in structure.