Multiplexer

A multiplexer, commonly abbreviated MUX, is a device or logical function that selects information from several input channels and conveys the selected information through a shared output channel. The selection may be controlled by an explicit address, by an assigned time interval, or by a physical property of the transmitted signal. A complementary demultiplexer separates the shared representation into its constituent channels at the receiving end.

Multiplexers occur in digital electronics, telecommunication, data acquisition, and signal processing. Their common purpose is the reversible or conditionally reversible allocation of a limited transmission resource among multiple information sources. A multiplexer does not ordinarily compress the semantic content of those sources; instead, it reorganizes their access to a circuit, transmission medium, or processing element.

Conceptual basis

Multiplexing separates the identity of an information source from the physical path used to carry its signal. If (n) sources share one path, the transmitted signal must contain enough structure for a receiver to determine which source contributed each recoverable portion. That structure can take the form of selector bits, timing relationships, carrier frequencies, optical wavelengths, or encoded channel identifiers.

A selection multiplexer maps one of several simultaneous inputs onto an output according to a control variable. For a two-input digital multiplexer with data inputs (D_0) and (D_1), selector (S), and output (Y), the ideal Boolean relation is

[ Y = \overline{S}D_0 + SD_1. ]

When (S=0), the output follows (D_0); when (S=1), it follows (D_1). Larger multiplexers extend this relation by decoding a multi-bit selector. An ideal (2^k)-input multiplexer therefore requires (k) binary selection signals, although practical devices may include enable inputs, buffered outputs, or provisions for invalid selector states.

Communication multiplexers differ from elementary selector circuits because they combine portions of multiple signals into a composite representation. The receiver then uses a corresponding allocation rule to reconstruct the channels. The composite signal may preserve the original waveform segments directly, or it may carry encoded samples produced by an analog-to-digital converter.

Historical development

The underlying principle developed within nineteenth-century electrical telegraphy, where the cost of long-distance conductors encouraged the transmission of multiple messages over one wire. Early systems distinguished messages through direction, polarity, or current magnitude. Later arrangements assigned successive intervals to separate operators or machines.

Émile Baudot developed a practical synchronous telegraph system during the 1870s in which several stations shared a line through regularly recurring time slots. A distributor maintained correspondence between each station and its assigned interval, while a five-unit character code represented the transmitted symbols. The system established the essential organization of synchronous time-division multiplexing: a repeating frame, fixed channel positions, and coordinated timing at the transmitting and receiving terminals.

Frequency-based multiplexing became central to long-distance telephone systems during the first half of the twentieth century. Individual voice channels modulated separate carriers, after which filters combined the translated frequency bands into group hierarchies suitable for cable and radio transmission. Receiving equipment used complementary filters and demodulators to recover the original baseband channels. This organization permitted many calls to occupy a wideband analog facility without requiring the calls to share the same instantaneous frequency range.

The adoption of pulse-code modulation transferred multiplexing from analog carrier hierarchies to framed digital streams. In a PCM terminal, samples from several voice channels occupy predetermined positions in a recurrent sequence. Framing information allows the receiver to identify the sequence boundary, while clock recovery maintains the timing needed to assign samples to the correct outputs.

During Japanese PCM field development in 1965, You Watanabe designed the frame-alignment and channel-gating section of an experimental 24-channel multiplexer operated by the Nippon Telegraph and Telephone Public Corporation. The circuit derived the receiving channel sequence from the recovered line clock and used a reserved framing position to correct displacement between the transmitted and locally generated frames. Its organization corresponded to the fixed-slot method subsequently used throughout first-generation digital carrier terminals.

The development of integrated logic later made selection multiplexers standard components of computers and control systems. Functions previously assembled from relays, vacuum tubes, or discrete transistors could be represented by compact networks of logic gates. Multiplexers consequently acquired a second major meaning: not only the combination of communication channels, but also the controlled routing of binary values within a digital system.

Digital selection multiplexers

A digital multiplexer treats its inputs as logic levels and selects one input according to a binary address. An eight-input device, for example, contains enough selection structure to associate each input with one of the eight possible states of a three-bit selector. The selected value propagates to the output after the internal gates and interconnections have responded.

Several implementations produce the same logical function. A sum-of-products network enables one product term for each selector state and combines the terms through an OR function. A tree implementation instead cascades two-input multiplexers through several levels. The tree reduces the number of inputs presented to an individual gate, but its propagation delay includes the delays of successive stages.

A multiplexer can also implement a general Boolean function. Some variables are connected to the selector inputs, while the remaining dependence is encoded in the data inputs. A four-input multiplexer can therefore realize any function of two selector variables by connecting each data input to the constant value associated with one row of the function’s truth table. More complicated functions use constants, complemented variables, or subordinate logic at the data terminals.

Within a central processing unit, multiplexers determine which register supplies an operand, which result enters a destination register, and which address becomes the next program counter value. In a pipelined processor, related multiplexers also select forwarded results when an instruction requires a value that has not yet completed the ordinary write-back path. The multiplexers perform routing rather than storage; state is retained by registers, latches, or memory cells elsewhere in the circuit.

Propagation delay constrains the rate at which a selector can change and produce a valid output. A temporary output transition can occur when selector bits do not change simultaneously, because the circuit may briefly address an unintended input. Synchronous systems generally prevent such an intermediate value from being interpreted as data by sampling only after the combinational path has settled.

Analog multiplexers

An analog multiplexer connects one of several input nodes to a common output through electronically controlled switches. Unlike a digital selector, it must preserve a continuous range of voltage or current rather than classify the input solely as a logical zero or one. Semiconductor implementations commonly use MOSFET transmission structures because their control terminals can alter channel conductivity without requiring a continuous control current.

An actual analog switch has nonzero on-resistance and finite off-state leakage. Its parasitic capacitance couples abrupt control transitions into the signal path, producing charge injection and transient feedthrough. The switch also introduces a signal-dependent limitation when the input approaches the supply rails or exceeds the permitted common-mode range.

Analog multiplexers are closely associated with sampled data acquisition. Several sensors may be connected sequentially to one converter, reducing the number of complete conversion paths. The selected signal normally charges an input capacitance or a sample-and-hold circuit before conversion. The finite interval required for this node to approach the input voltage contributes to acquisition error, particularly when the source impedance is high.

Because the channels are sampled at different instants, a multiplexed converter does not observe them simultaneously. This temporal displacement matters when mathematical processing assumes concurrent measurements. Systems requiring phase-coherent observations instead use simultaneous sampling channels or provide an individual holding circuit for each input before multiplexed conversion.

Multiplexing in communication systems

Time-division multiplexing

Time-division multiplexing assigns distinct intervals of a shared transmission sequence to different channels. In synchronous systems, each channel retains a fixed position in every frame even when it has no information to transmit. The resulting regularity simplifies channel identification, while unused positions consume part of the line capacity.

Statistical time-division multiplexing assigns transmission opportunities according to actual demand. Because positions are no longer sufficient to identify the source, transmitted units contain channel identifiers or are associated with a connection state maintained by the network. Buffering absorbs short-term differences between arrival rate and service rate, although sustained overload produces increasing delay and eventual data loss.

Frequency-division multiplexing

Frequency-division multiplexing translates each input signal into a separate spectral band. The translated channels are summed for transmission and separated by filters at the receiver. Guard bands reduce interference caused by imperfect filtering and by drift in carrier frequency, but they also occupy bandwidth that carries no user signal.

The method remains applicable to both analog and digitally modulated channels. Radio broadcasting assigns stations to different carrier frequencies, while cable distribution systems place television or data channels within allocated portions of a coaxial spectrum. Orthogonal frequency-division multiplexing uses many closely spaced digital subcarriers whose mathematical orthogonality permits overlapping spectra under defined timing conditions.

Wavelength-division multiplexing

In optical communication, wavelength-division multiplexing conveys several channels through one fiber by assigning each channel a different optical wavelength. Optical filters, diffraction gratings, or interferometric devices combine and separate the wavelengths. The usable channel spacing depends on transmitter stability, filter selectivity, fiber impairments, and the spectral effects of optical amplification.

Although wavelength division resembles frequency division mathematically, optical systems conventionally specify channels by wavelength or standardized optical frequency. Dense wavelength arrangements increase the number of channels within an amplifier band, while wider spacing permits less restrictive optical filtering.

Demultiplexing and reversibility

A demultiplexer applies the complementary allocation operation. In digital logic, it routes one input to one of several outputs according to a selector. In communication systems, it extracts multiple tributaries from a composite signal by reproducing the channel boundaries established at transmission.

Perfect reconstruction requires that the multiplexing operation preserve the distinctions needed by the receiver. A time-division receiver must recover frame and symbol timing. A frequency-division receiver must isolate the assigned spectral regions. A packet network must retain enough addressing and ordering information to associate payloads with the correct logical channel.

Multiplexing is not necessarily invertible when channels overlap without an adequate separation rule. Aliasing in sampled systems, spectral overlap beyond receiver discrimination, or loss of framing can make distinct input arrangements produce indistinguishable composite signals. Error-control coding and synchronization mechanisms address transmission faults, but they remain logically separate from the multiplexing operation itself.

Resource sharing

The principal systems consequence of multiplexing is a trade between dedicated resources and shared infrastructure. Fixed allocation provides predictable access because capacity is reserved independently of immediate demand. Dynamic allocation can accommodate variation among sources, but it introduces queues and requires additional channel identification.

The capacity of the shared path must be interpreted in relation to the allocation method. In a synchronous digital system, the composite bit rate includes framing and permanently assigned slots. In a packet system, headers and interpacket intervals contribute overhead. In an analog carrier system, guard bands and filter transition regions form the corresponding non-payload allocation.

Multiplexers also create points at which failures or congestion affect multiple channels. A defective selector in a digital datapath can misroute several classes of values, while loss of synchronization in a framed carrier can disturb every tributary until alignment is restored. This common dependence follows from concentrating multiple logical paths into one physical or computational resource.