EEEN 462 - Study Guide: Introduction to Analog Switching Telecommunication Systems

1. Learning Objectives

By the end of this study guide, the student should be able to:

Explain the need for switching in telecommunication networks and describe the evolution from manual to automatic exchanges.
Describe the three basic switching functions: concentration, distribution, and expansion.
Classify switching systems and distinguish space-division from time-division switching.
Describe the step-by-step (Strowger) switching system: line finder, selectors, connector, and its mode of operation.
Describe the crossbar switch: horizontal/vertical bars, crosspoints, markers, and its advantages over step-by-step.
Explain time-division switching, the time-slot interchange (TSI) principle, and T-S-T structures.
Define telephone traffic units (Erlang, CCS) and blocking probability.
Apply the Erlang B formula to size a trunk group for a given grade of service.

2. Introduction: Why Switching?

A telecommunication switching system interconnects transmission paths between users so that any subscriber can communicate with any other. Without switching, a fully-connected network of N subscribers would need N(N−1)/2 dedicated links — for 10,000 subscribers, nearly 50 million lines. Switching provides resource sharing: a small pool of shared trunks and switch paths serves many users with an acceptably small probability of finding no path free.

The role of an exchange (central office): detect a call request (off-hook), identify the caller, receive the called number (dial pulses or DTMF), establish a physical path through the switch, supervise the call, and release all equipment on hang-up. In analog switching, the path carries the actual voice waveform (a continuous signal), as opposed to digital switching, which interconnects digitized samples.

2.1 Historical Evolution

1878 — Manual exchange: human operators connected pairs of cords on a switchboard (e.g. New Haven, Connecticut).
1891 — Step-by-step (Strowger) automatic exchange: an electromechanical system directly controlled by the subscriber's dial pulses; the first automatic telephone exchange was installed at La Porte, Indiana (1892).
1938 — Crossbar exchange: common-control switching with a matrix of electromagnetic crosspoints; far more flexible and faster than step-by-step.
1960s–70s — Electronic analog and digital exchanges: reed-electronic and time-division (PCM) switches, leading to stored-program-control (SPC) digital exchanges.

Analogue vs digital switching: this unit concerns analog switching — space-division paths that pass the voice-frequency signal unchanged, and the analog-era systems (Strowger, crossbar, TDM analog buses) that predate or accompany PCM digital switching. Understanding them is essential because modern digital switches evolved from exactly these structures.

3. Basic Switching Functions

A switch performs three basic functions on the traffic passing through it:

Concentration: many input lines are served by fewer internal or output paths — e.g. 128 subscriber lines feeding 16 trunks. The concentration ratio reflects that only a small fraction of subscribers call simultaneously.
Distribution: connecting inputs to outputs without concentration or expansion — e.g. within a switching stage where the numbers of inlets and outlets are equal.
fewer input paths are fanned out to many outputs — the reverse of concentration, used at the terminating side of a call.

A (offered traffic, Erlangs) = λ · h (λ = call arrival rate, h = mean holding time)

Fig. 1Space-division switching: a dedicated physical path (crosspoint) is established between an inlet and an outlet for the duration of the call; several simultaneous connections coexist in space. [TutorialsPoint, TSSN]

3.1 Classification of Switching Systems

Basis	Types
Signal carried	Analog switching (passes the voice waveform) · Digital switching (interconnects PCM samples)
Path sharing	Space division (separate paths in space) · Time division (shared path, separate time slots)
Control	Direct control (step-by-step) · Common control (crossbar, SPC)
Blocking behaviour	Blocking (may fail under load) · Non-blocking (Clos networks)

4. Step-by-Step (Strowger) Switching

The step-by-step (SxS) system is a direct-control, space-division switch: the subscriber's own dial pulses drive the switch directly, stage by stage, digit by digit.

4.1 System Structure

Line finder (or preselector): on off-hook, hunts for and seizes a free first selector, connecting the calling subscriber to it.
Selectors (1st, 2nd, …): each has 10 (or more) outlets and a wiper that steps vertically (digit value) then hunts (rotary motion) for a free outlet.
Connector (final selector): the last stage, whose outlets terminate on subscriber lines within the exchange.

Fig. 2Step-by-step exchange for 1000 lines: preselectors, group selectors and final selectors interconnect to route a dialed 3-digit number. [ExpertsMind]

Fig. 3Switch train for a call between step-by-step subscribers: line finder, five selectors and a connector advance one digit at a time. [Mark Csele collection]

4.2 Operation

Caller lifts handset → line finder rotates to find the calling line and seizes a first selector; dial tone returned.
Each dial pulse (10 pps, 39–59% break) steps the selector's wiper one position. First digit → vertical rise to level = digit; then the wiper rotates (self-hunting) to a free outlet.
Second digit operates the second selector; and so on for n digits.
Final (connector) stage rings the called party; on answer, the through path is complete.

Fig. 4Detail of a step-by-step call: line finder finds the active line; 1st selector takes the first digit (3), 2nd selector the second (1), connector the last digits (2,3). [neilrieck.net telephony notes]

Limitations of step-by-step: (1) direct control ties up switch equipment for the whole call and is slow (10 pps dialing); (2) the equipment is blockingly arranged and not very efficient; (3) poor for trunk and international routing; (4) maintenance-intensive with many moving parts. These motivated common-control crossbar systems.

Animation — Step-by-Step Selector in Action

Dial a number (rotary simulation): each digit produces a burst of pulses (10 pulses/second) that steps the selector vertically to that level, then the wiper auto-hunts to a free outlet. Watch the stages progress digit by digit.

Number to dial:

Enter a number (1–4 digits, no 0 as first digit) and press Dial.

5. Crossbar Switching

The crossbar switch is a space-division matrix of crosspoints operated by two sets of electromagnetic bars: horizontal bars (H) select the inlet and vertical bars (V) select the outlet; energizing one H and one V bar closes the crosspoint at their intersection.

A marker (common control) receives the dialed digits, then within ~1 second selects a free path through the switch and closes the required crosspoints.
Unlike step-by-step, control is separated from the speech path: the marker sets up the call and is released for the next call.

Fig. 53×3 crossbar switching: electromagnets M₁, M₂, M₃ (verticals) and M'₁, M'₂, M'₃ (horizontals) operate the crosspoints at bar intersections. [TutorialsPoint, TSSN]

Fig. 6Crossbar matrix concept: each crosspoint is a tri-state buffer; switching logic connects input i to output j on request. [Emory University CS course notes]

5.1 Advantages over Step-by-Step

Common control (marker): faster setup, sophisticated routing, register-translator for number translation.
No hunting: any free crosspoint can be chosen — more efficient trunking and lower blocking.
Modularity: matrices stack easily; N×M growth is straightforward.
Better maintenance: fewer moving parts per path; markers can be duplicated for reliability.

Crosspoint count: a single square N×N matrix needs N² crosspoints, but only N can be active at once (utilization ≤ 1/N) — very wasteful for large N. Practical designs therefore use multi-stage (e.g. three-stage Clos) networks that reduce crosspoints toward O(N log N) at the cost of possible internal blocking.

Simulation — Interactive Crossbar Matrix

Click an input (left) then an output (top) to close a crosspoint and carry an animated call (green). Click an active crosspoint to release it. Try "Load test" to add random calls and observe blocking when an input or output is busy.

Size N×N:

6. Time-Division Switching

In time-division (TDM) switching, inlets share a single high-speed path by transmitting in assigned time slots; the switch moves a sample from inlet i in slot s to outlet j in slot s' — a time-slot interchange (TSI) implemented with a speech store (buffer) and a control store (connection memory). Although the modern form is digital (PCM), the concept originated as analog time-division multiplex switching.

Fig. 7Time-division switch: control memory (CM) of M words addressed cyclically writes the connection pattern; the speech path is time-shared by N inlets/outlets in M time slots. [TutorialsPoint, TSSN]

Speech store: sequentially written by inlets; read out in permuted order so each outlet receives its slot.
Control store: written by the processor at call setup; holds the slot-interchange map.
T-S-T structure: large digital exchanges combine time stages (TSI) and space stages (crosspoint lattices) to keep costs low while remaining effectively non-blocking.

Simulation — Time-Slot Interchange

Eight inlets share one TDM bus in slots 1–8 (top row). The TSI reorders samples into output slots (bottom row). Press "Randomize map" for a new interchange, and watch the frames circulate.

Frame rate:

7. Telephone Traffic and Blocking

7.1 Traffic Units

Erlang (E): the average number of simultaneously occupied circuits; 1 Erlang = one circuit 100% busy.
CCS (cent call seconds): 1 Erlang = 36 CCS (CCS used with the "busy-hour" convention in some administrations).
Busy-hour: the continuous 1-hour period of maximum traffic; engineering is done on this basis.

A = C · T / 3600 (Erlangs) C = calls in busy hour, T = mean holding time in seconds

7.2 Grade of Service and the Erlang B Formula

A blocking system offers calls to N servers (trunks, timeslots, crosspoint paths). If all N are busy, an arriving call is lost (cleared). The blocking probability B is the grade of service (GoS):

B = (A^N/N!) / ∑_k=0^N A^k/k! (Erlang B, lost-calls-cleared)

Recursion for computation: B₀ = 1; B_k = A·B_k−1 / (k + A·B_k−1).

Carried traffic = A(1 − B); utilization per server = A(1 − B)/N.

Fig. 8Erlang B chart: blocking probability vs offered traffic A for N = 1…100 trunks. Higher N gives better trunk efficiency (economy of scale). [Chegg / standard Erlang-B chart]

Simulation — Erlang B Trunk Sizing Calculator

Given offered traffic A (Erlangs) and number of trunks N, this computes blocking probability B, carried traffic and per-trunk utilization — then recommends the minimum N for a target GoS.

Offered traffic A (E): Trunks N: Target GoS:

Example: A = 10 Erlangs, GoS 0.5% ⇒ minimum N = 18 trunks (B ≈ 0.42%). Utilization = 10(1−0.0042)/18 ≈ 55%. With N = 15, B jumps to 3.8% — poor service. Trunk dimensioning is done from Erlang B tables/charts like Fig. 8.

8. Comparison of Analog Switching Systems

Feature	Step-by-Step	Crossbar	Time-Division (TDM/TSI)
Switching principle	Space division	Space division	Time division
Control	Direct (dial pulses drive switches)	Common (marker/registers)	Stored program (SPC)
Path for a call	Dedicated physical path, wiper contacts	Crosspoint closure	Shared bus, assigned time slots
Setup speed	Slow (10 pps dialing)	Fast (< 1 s)	Very fast (< 100 ms)
Blocking	High (fixed hierarchical route)	Lower (any free crosspoint)	Low (large slot pool)
Crosspoints / moving parts	Many, wear-prone	N² per matrix (reduced by multi-stage)	None in speech path (L-C filters)
Services	Basic calls only	Routing translation, better trunking	Rich (billing, IN, ISDN ancestry)
Maintenance	Heavy	Moderate	Low

9. Self-Test (Click to Reveal Answers)

Q1. Why is switching necessary in a telephone network? What would a non-switched network require?

Switching lets a small pool of shared trunks serve many subscribers (resource sharing). A fully connected network of N subscribers needs N(N−1)/2 dedicated links — impractical for large N.

Q2. Distinguish concentration, distribution, and expansion.

Concentration: many inlets to fewer outlets (e.g. 128 lines → 16 trunks). Distribution: inlets to outlets in equal numbers. Expansion: few inlets to many outlets (terminating side).

Q3. Describe the sequence of events when a subscriber makes a call on a step-by-step exchange.

Off-hook → line finder seizes a free first selector and returns dial tone → each dial pulse steps the selector wiper; the digit value selects the vertical level, then the wiper hunts to a free outlet → successive digits operate successive selectors → connector rings the called party and completes the path on answer.

Q4. What is common control, and why is crossbar's marker an example of it?

Common control separates the control (decoding digits, path selection) from the speech path; one control unit (marker) serves many calls and is freed after setup. In crossbar, the marker chooses free crosspoints and releases them, enabling fast flexible routing.

Q5. An N×N single-stage space switch has how many crosspoints, and why is this wasteful?

N² crosspoints, of which at most N (typically far fewer) are active at once — utilization ≤ 1/N. Multi-stage (Clos) networks reduce the count toward O(N log N).

Q6. Explain the time-slot interchange principle in time-division switching.

Inlets share one bus in cyclical time slots; samples are written sequentially into a speech store, and a control-store map dictates the read-out order so inlet i's slot is delivered to outlet j in the desired slot. The map is rewritten at each call setup.

Q7. Define the Erlang and compute the offered traffic of 180 calls in the busy hour with mean holding time 120 s.

1 Erlang = one circuit continuously busy = 1 call-hour/hour. A = C·T/3600 = 180×120/3600 = 6 Erlangs.

Q8. Using Erlang B, how many trunks are required to carry 8 Erlangs at 1% GoS?

From Erlang B tables/recursion: N = 15 trunks give B ≈ 0.96% ≤ 1%; N = 14 gives ≈ 1.9% (too high). So N = 15.

10. Summary of Key Points

Switching enables resource sharing; exchanges detect, set up, supervise and release calls. Analog switches pass the voice waveform itself.
Switching functions: concentration, distribution, expansion. Systems are space-division or time-division, blocking or non-blocking.
Step-by-step: direct dial-pulse control, line finder → selectors → connector; simple but slow, blocking, maintenance-heavy.
Crossbar: H/V bars + crosspoints under marker (common) control; fast, flexible, modular; N² crosspoints per matrix motivate multi-stage designs.
Time-division switching interchanges time slots via speech + control stores (TSI); the basis of PCM digital exchanges (T-S-T).
Traffic A = λh Erlangs; Erlang B gives blocking probability for lost-calls-cleared systems; size trunks from A and target GoS.

Recommended References

T. Viswanathan, Telecommunication Switching Systems and Networks, PHI — Chs. 1–4.
S. Haykin & M. Moher, Communication Systems, 5th ed. — telephone switching fundamentals.
J. C. McDonald (ed.), Fundamentals of Digital Switching, Plenum.
R. A. Thompson, Telephone Switching Systems, Artech House.
Flood, J. E., Telecommunications Switching, Traffic and Networks, Prentice Hall.