SVGVector Architecture Diagram (SVG)

Time Division Multiplexing (TDM)

Q: Calculate the line rate of a TDM system combining four $100\text{ kbps}$ channels where 1 bit is interleaved from each channel and 1 framing bit is added per frame.

- Frame contains: 4 \times 1\text{ bit} + 1\text{ framing bit} = 5\text{ bits}. - Each input produces 100,000 bits/sec, so frame rate = 100{,}000\text{ frames/sec}. - Line rate = 5\text{ bits} \times 100{,}000\text{ frames/sec} = 500\text{ kbps}.

Q: Calculate the T-1 carrier bit rate.

A T-1 frame carries 24 channels \times 8 bits = 192 bits plus 1 framing bit = 193 bits. At 8,000 frames/s the rate is 193 \times 8000 = 1.544\text{ Mbps}.

1. Concept of Time Division Multiplexing

Time Division Multiplexing (TDM) is a digital multiplexing technique that combines multiple low-rate digital data streams into a single high-speed digital link.

Unlike FDM (which divides channel bandwidth across frequencies simultaneously), TDM allocates the entire bandwidth of the physical channel to each transmitting source for a brief duration of time (called a Time Slot).

MermaidDiagram

Rendering diagram…

There are two primary classifications of TDM:

Synchronous TDM
Statistical (Asynchronous) TDM

2. Synchronous TDM

In Synchronous TDM, each input connection is assigned a fixed, dedicated time slot in round-robin fashion within every transmission frame.

If an input device has data to transmit, its data occupies its designated slot.
If an input device has no data (idle), its time slot is transmitted empty, leading to wasted channel capacity.

SVGVector Architecture Diagram (SVG)

Mathematical Characteristics & Framing:

Frame Duration: Equal to the unit duration of one input data unit:

T_{\text{frame}} = T_{\text{input\_unit}}

Time Slot Duration: If there are $n$ input connections:

T_{\text{slot}} = \frac{T_{\text{frame}}}{n}

Data Rate of Multiplexed Link:

\text{Link Rate} = n \times (\text{Data Rate of each input channel}) + \text{Framing Overhead}

Framing Bit: A synchronization bit (pattern 101010...) appended to each frame to ensure receiver demultiplexers stay locked to slot boundaries.

Solved Numerical Example (T-1 Carrier / Synchronous TDM):

Problem: In a standard telephone T-1 carrier system, 24 voice channels are digitized via PCM (sampled at $8{,}000\text{ samples/sec}$ , 8 bits per sample). 1 framing bit is added to each frame.
Calculate: (a) Frame size, (b) Frame rate, (c) Output bit rate.
Solution:
- (a) Frame Size:

\text{Payload} = 24\text{ channels} \times 8\text{ bits/sample} = 192\text{ bits}

\text{Frame Size} = 192\text{ bits} + 1\text{ framing bit} = 193\text{ bits}

(b) Frame Rate: Must equal the sampling rate = $8{,}000\text{ frames/second}$ $8, 000 frames/second$ .
- (c) Bit Rate of T-1:

\text{Bit Rate} = 193\text{ bits/frame} \times 8{,}000\text{ frames/sec} = 1.544\text{ Mbps}

3. Statistical (Asynchronous) TDM

Statistical TDM (also known as Asynchronous TDM or Intelligent TDM) dynamically allocates time slots only to active devices that currently have data to transmit.

MermaidDiagram

Rendering diagram…

Addressing Overhead: Because slot positions are no longer fixed, each slot must carry an address/channel identifier so the demultiplexer knows which output line to route the data to.
Buffer Queues: If more stations transmit than there are available slots in a frame, extra data is held in input FIFO buffers.
High Efficiency: The total data rate of all input lines can exceed the physical capacity of the multiplexed link ( $\sum R_i > R_{\text{link}}$ ) based on the statistical reality that not all stations transmit simultaneously.

4. Comparison: Synchronous TDM vs. Statistical TDM

Parameter	Synchronous TDM	Statistical (Asynchronous) TDM
Slot Allocation	Fixed, predetermined round-robin	Dynamic, on-demand for active sources
Empty Slots	Yes (wastes bandwidth when idle)	None (only active data sent)
Addressing Overhead	None (position identifies source)	Required (Address header prepended to each slot)
Link Capacity	$\geq \sum \text{Input Channel Rates}$	Can be significantly less than $\sum \text{Input Rates}$
Buffering	No buffering required	Requires input FIFO buffers
Complexity & Cost	Simple, inexpensive	More complex, requires intelligent controller

Frequently Asked Questions

QWhy does Statistical TDM require addressing in its slots while Synchronous TDM does not?

In Synchronous TDM, the slot index within the frame is fixed and rigidly mapped to a specific input channel. In Statistical TDM, slots are allocated dynamically; without an explicit channel ID header, the demultiplexer cannot determine the intended destination.

QWhat is a Framing Bit in Synchronous TDM?

A single bit inserted at the beginning of each frame following a strict alternating sequence (0101...) that enables the receiver's demultiplexer to maintain clock synchronization and identify frame boundaries.

QCalculate the line rate of a TDM system combining four $100\text{ kbps}$ channels where 1 bit is interleaved from each channel and 1 framing bit is added per frame.

Frame contains: $4 \times 1\text{ bit} + 1\text{ framing bit} = 5\text{ bits}$ .
Each input produces 100,000 bits/sec, so frame rate = $100{,}000\text{ frames/sec}$ .
Line rate = $5\text{ bits} \times 100{,}000\text{ frames/sec} = 500\text{ kbps}$ .

QCalculate the T-1 carrier bit rate.

A T-1 frame carries 24 channels $\times$ 8 bits = 192 bits plus 1 framing bit = 193 bits. At 8,000 frames/s the rate is $193 \times 8000 = 1.544\text{ Mbps}$ .

Multiplexing — Time Division (TDM)