Repeater Insertion

Repeater insertion is a technique for reducing the time delay associated with long wire lines in integrated circuits. The technique involves cutting the long wire into one or more short wires and inserting a

repeater In telecommunications, a repeater is an electronic device that receives a signal and retransmits it. Repeaters are used to extend transmissions so that the signal can cover longer distances or be received on the other side of an obstruction. Some ...

between each new pair of short wires. The time it takes for a signal to travel from one end of a wire to the other end is known as ''wire-line delay'' or just ''delay.'' In an integrated circuit, this delay is characterized by RC, the

resistance Resistance may refer to: Arts, entertainment, and media Comics * Either of two similarly named but otherwise unrelated comic book series, both published by Wildstorm: ** ''Resistance'' (comics), based on the video game of the same title ** ''T ...

of the wire (''R'') multiplied by the wire's

capacitance Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are ...

(''C''). Thus, if the wire's resistance is 100

ohm Ohm (symbol Ω) is a unit of electrical resistance named after Georg Ohm. Ohm or OHM may also refer to: People * Georg Ohm (1789–1854), German physicist and namesake of the term ''ohm'' * Germán Ohm (born 1936), Mexican boxer * Jörg Ohm (b ...

s and its capacitance is 0.01 microfarad (μF), the wire's delay is one microsecond (µs). To first order, the resistance of a wire on an

integrated circuit An integrated circuit or monolithic integrated circuit (also referred to as an IC, a chip, or a microchip) is a set of electronic circuits on one small flat piece (or "chip") of semiconductor material, usually silicon. Large numbers of tiny ...

is directly proportional, or ''linear'', according to the wire's length. If a 1 mm length of the wire has 100 ohms resistance, then a 2 mm length will have 200 ohms resistance. For the purposes of our highly simplified discussion, the capacitance of a wire also increases linearly along its length. If a 1 mm length of the wire has 0.01 µF capacitance, a 2 mm length of the wire will have 0.02 µF, a 3 mm wire will have 0.03 µF, and so o Thus, the time delay through a wire increases with the square of the wire's length. This is true, to first order, for any wire whose cross-section remains constant along the length of the wire. wire resistance capacitance time delay length R C t 1 mm 100 ohm 0.01 µF 1 µs 2 mm 200 ohm 0.02 µF 4 µs 3 mm 300 ohm 0.03 µF 9 µs The interesting consequence of this behavior is that, while a single 2 mm length of wire has a delay of 4 µs. Two separate 1 mm wires only have a delay of 1 µs each and cover the same distance in half the time. By cutting the wire in half, one can double its speed. To make this science trick work properly, an active circuit must be placed between the two separate wires so as to move the signal from one to the next. An active circuit used for such a purpose is known as a ''

.'' In a

CMOS Complementary metal–oxide–semiconductor (CMOS, pronounced "sea-moss", ) is a type of metal–oxide–semiconductor field-effect transistor (MOSFET) fabrication process that uses complementary and symmetrical pairs of p-type and n-type MOSFE ...

integrated circuit, the repeater is often a simple inverter. Reducing the delay of a wire by cutting it in half and inserting a repeater is known as ''repeater insertion''. The cost of this procedure is the additional new delay through the repeater itself, plus power cost because the repeater is an active circuit that must be powered, whereas the plain unrepeated wire was originally an unpowered

passive component Passivity is a property of engineering systems, most commonly encountered in analog electronics and control systems. Typically, analog designers use ''passivity'' to refer to incrementally passive components and systems, which are incapable of po ...

. For more details, see for example Anikreddy and Burleson's paper, ''Repeater Insertion in deep sub-micron CMOS: Ramp-based '' ''Analytical Model and Placement Sensitivity Analysis,'' in ISCAS 2000, the IEEE International Symposium on Circuits and Systems, May 28–31, 2000, Geneva, Switzerland (http://ieeexplore.ieee.org/iel5/6910/18588/00856173.pdf). Integrated circuits