Thông tin thiết kế mạch P8

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THE TELEPHONE NETWORK The early history of the telephone system has been outlined in Chapter 1. The growth of the telephone system has been truly phenomenal and forecasts show a continuing growth as new services such as data transfer, facsimile and mobile telephone are added. The telephone differs from the broadcasting system in two basic ways: (1) In broadcasting, a few people who, in theory, have information send it out to the many who are presumed to want the information; it is one-way trafﬁc....

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  1. Telecommunication Circuit Design, Second Edition. Patrick D. van der Puije Copyright # 2002 John Wiley & Sons, Inc. ISBNs: 0-471-41542-1 (Hardback); 0-471-22153-8 (Electronic) 8 THE TELEPHONE NETWORK 8.1 INTRODUCTION The early history of the telephone system has been outlined in Chapter 1. The growth of the telephone system has been truly phenomenal and forecasts show a continuing growth as new services such as data transfer, facsimile and mobile telephone are added. The telephone differs from the broadcasting system in two basic ways: (1) In broadcasting, a few people who, in theory, have information send it out to the many who are presumed to want the information; it is one-way trafﬁc. The communication link provided by the telephone is two-way trafﬁc. (2) The basic idea of broadcasting is to make the message available to anyone who has the equipment and the interest to tune in. This is in contrast to the norm in the telephone system where the privacy of the message is guaranteed by law. Because of these differences, the two systems handle very different types of information – public versus private – and their patterns of development have been different. 8.2 TECHNICAL ORGANIZATION For a telephone system to work, there must be a minimum of two people who wish to communicate. It is then possible to install the circuit shown in Figure 8.1. This would be quite adequate except for the fact that these two people may not want to talk to each other all the time and therefore some additional system has to be set up for either person to indicate to the other that they wish to talk. What was 213
  2. 214 THE TELEPHONE NETWORK Figure 8.1. The basic elemental telephone system. added was a bell on the called party’s premises which can be rung from the calling party’s premises. Presumably the success of this prototypical communication system would soon attract the attention of other people who would want to set up similar systems. It is clear that soon the situation depicted in Figure 8.2 would develop where every subscriber would have to be wired up to every other subscriber. That would be prohibitively expensive and quite impractical. Evidently, the way to deal with the situation is to connect every subscriber to a central location and arrange to have an attendant to interconnect the various subscribers in whatever combination that is required. That central location is, of course, the central ofﬁce which has and continues to have a central role in the telephone system. The system conﬁguration would then be as shown in Figure 8.3. Assuming that the system has six subscribers then each subscriber has access to the other ﬁve subscribers. But in the meantime, a group, also of six, in the next town have heard of the success of the system and have set up a similar system of their Figure 8.2. The connection diagram for six subscribers showing all the 15 possible telephone lines.
  3. 8.2 TECHNICAL ORGANIZATION 215 Figure 8.3. The concept of a central ofﬁce reduces the number of lines to six. own. Now there is a possibility of reaching eleven other subscribers if a connection can be made between the two systems. This brings up two very important points: (1) The greater the number of people on the communication network, the more attractive it is for other people to join. (2) There has to be some level of compatibility between the two systems. The system would have evolved, as shown in Figure 8.4. Continuing with the story, the distance between the two towns is quite long and the initial cost and upkeep are high but if this line can be made to carry more than one conversation simultaneously, the cost per conversation will be substantially Figure 8.4. The connection of a trunk or toll line between two central ofﬁces increases the number of subscribers that can be reached from 5 to 11.
  4. 216 THE TELEPHONE NETWORK reduced. It is also very likely that because of the length of the line, the quality and the reliability of the system may be degraded. This brings up an important point: The greater the number of communication channels that can be established over the same link, the less the cost per message. Multiplex and the conservation of bandwidth will become goals of several generations of communications engineers. The telephone system that started with people talking to each other has acquired more than people for a clientele. Increasingly, the network is being used to supply services to machines such as computers, facsimile devices, security guard services and access to the Internet. 8.3 BASIC TELEPHONE EQUIPMENT The basic telephone has surprisingly very few parts. These are shown in Figure 8.1. When the microphone is connected in series with the battery, it produces a current proportional to the pressure of the sound impinging on it. The transformer eliminates the dc and sends the ac portion of the current through the line. The earphone at the receiving end changes the variation of the current into sound. Obviously, the system works in the reverse direction. 8.3.1 Carbon Microphone Figure 8.5 shows a cross-section of the carbon microphone [1]. It has a light-weight aluminum cone with a ﬂexible support around the periphery so that it will deﬂect (vibrate) due to the changing sound pressure level. Attached to the apex is a disc which acts as a piston when the cone deﬂects. A plastic housing with an electrode attached to the bottom contains a loose pile of carbon granules. When the pressure on the cone is increased, the carbon granules become Figure 8.5. A cross-sectional view of the carbon microphone.
  5. 8.3 BASIC TELEPHONE EQUIPMENT 217 compressed, the resistance goes down and more current ﬂows. The opposite happens when the pressure is released. Assuming that the sound pressure level on the carbon microphone is a sinusoid then the resistance of the device is rðtÞ ¼ r0 ð1 þ k sin otÞ ð8:3:1Þ where r0 is the mean resistance, k is a coefﬁcient less than unity, and o is the frequency of the sound pressure. When the microphone is connected to a battery of electromotive force E (volts) in series with a load R, as shown in Figure 8.6, we have E I¼ ð8:3:2Þ R þ r0 ð1 þ k sin otÞ E 1 I¼ ð8:3:3Þ R þ r0 kr0 1þ sin ot R þ r0 E r0 I¼ ð1 þ k sin otÞÀ1 : ð8:3:4Þ R þ r0 R þ r0 Using the binomial expansion,    2 E kr0 kr0 I¼ ½1 À sin ot þ sin2 ot À . . .: ð8:3:5Þ R þ r0 R þ r0 R þ r0 Let E I0 ¼ ð8:3:6Þ R þ r0 Figure 8.6. The carbon microphone with dc supply E and load resistance R.
  6. 218 THE TELEPHONE NETWORK then    2  2 kr0 I kr0 I kr0 I ¼ I0 À I0 sin ot þ 0 À 0 cos 2ot þ Á Á Á : ð8:3:7Þ R þ r0 2 R þ r0 2 R þ r0 Because kr0 =ðR þ r0 Þ is smaller than unity higher order terms can be ignored. If it is desirable to reduce second harmonic distortion, kr0 =ðR þ r0 Þ can be reduced, but in doing so the amplitude of the fundamental will be reduced as well. A compromise between distortion and signal amplitude has to be made. The carbon microphone has the following attractive properties: (1) It is simple and therefore inexpensive to manufacture. (2) It is robust; it is not likely to need attention even in the hands of the public. (3) It acts as a power ampliﬁer; under normal bias conditions, (the electrical power output far exceeds the acoustic power input. It does not normally require additional ampliﬁcation. (4) Its input–output characteristics are shown in Figure 8.7. The non-linearity at low input levels helps to suppress background noise and that at high levels acts as an automatic gain control. 8.3.2 Moving-Iron Telephone Receiver A cross-section of the moving-iron telephone receiver is shown in Figure 8.8. It consists of a U-shaped permanent magnet that carries a coil as shown. In front of the open face of the U, a thin cobalt iron diaphragm, is held by an annular ring support with a short distance between them. With no current in the coil, the diaphragm has a ﬁxed deﬂection towards the magnet. The signal current is passed through the coil and, assuming that it is sinusoidal, then for one-half of the cycle the ﬂux generated by the current will aid the pull of the Figure 8.7. The input–output characteristics of the carbon microphone.
  7. 8.3 BASIC TELEPHONE EQUIPMENT 219 Figure 8.8. A cross-sectional view of the moving-iron telephone receiver. permanent magnet on the diaphragm and it will deﬂect accordingly. During the other half of the cycle, the coil ﬂux will oppose that of the magnet and the diaphragm will deﬂect much less. The force between two magnetized surfaces is given by B2 F¼ ðN=m2 Þ ð8:3:8Þ 2m0 where B is the ﬂux density in teslas ðTÞ and m0 is the permeability of free space, that is, 4p Â 10À7 . Let A be the area of the pole face ðm2 Þ, B0 the ﬂux density due to the permanent magnet (T), and b0 sin ot the ﬂux density due to the current (T). The force in newtons is then 2A F¼ ðB þ b0 sin otÞ2 ð8:3:9Þ 2m0 0 A 2 ðB þ 2B0 b0 sin ot þ b2 sin2 otÞ ð8:3:10Þ m0 0 0 A 2 1 2 F¼ ðB þ b þ 2B0 b0 sin ot À 1 b2 cos 2otÞ ð8:3:11Þ m0 0 2 0 2 0 The second harmonic component can be reduced by making B0 large compared to b0 . This will increase the direct component of the force, which is likely to cause the diaphragm to touch the magnet. Note that when B0 is zero (no permanent magnet), the device produces only the second harmonic. This is to be expected since both the
  8. 220 THE TELEPHONE NETWORK positive and negative halves of the sinusoid will exert an equal force of attraction on the diaphragm. 8.3.3 Local Battery – Central Power Supply The system as depicted in Figure 8.1 is powered from batteries that are located on the customer’s premises. The batteries are of interest because they are a hazard to the customer and they pose a very difﬁcult problem for the maintenance staff. Furthermore, their reliability is questionable because of their location among other considerations. The solution to the problem is to have a common power supply located at the central ofﬁce (out of the way of the telephone subscriber) and readily available to the maintenance personnel. The reliability of the service can then be improved by installing a backup power supply. The scheme for achieving this end is illustrated in Figure 8.9. The central ofﬁce battery in series with two inductors is connected to the lines of the calling and called party as shown. The inductors have a high inductance and therefore appear to be open-circuits at audio frequency but short-circuits at dc. Every call requires two such inductors to complete the connection. 8.3.4 Signalling System The signalling system consisted of a magneto and a bell which responded to high ac voltage input. The magneto was a hand-operated alternator whose ﬂux was produced by a permanent magnet. The calling party turned the crank to produce about 100 V ac. The current travelled down the telephone line and caused the bell at the called party’s end to ring. To avoid damage to the telephone receiver and to conserve Figure 8.9. The local batteries are replaced by a central power supply.
  9. 8.3 BASIC TELEPHONE EQUIPMENT 221 Figure 8.10. The elemental telephone with signalling devices (magneto and bell) shown. battery power, the hook switch was disconnected them from the line when the telephone was not in use. A simpliﬁed diagram of the signalling system is shown in Figure 8.10. 8.3.5 The Telephone Line Physically, the telephone line consists of a pair of copper wires supported on glass or porcelain insulators mounted on wooden poles. Electrically, an inﬁnitesimally short piece of line can be modelled as shown in Figure 8.11 [2,3]. The elemental series resistance and inductance are represented by dR and dL and the elemental shunt capacitance and conductance are represented by dC and dG, respectively. The analysis of the model is beyond the scope of this book. However, the analysis shows that the telephone line, at voice frequencies, can be approximated by an RC Figure 8.11. (a) The equivalent circuit of the telephone line showing series resistance R and inductance L and shunt capacitance C and conductance G. (b) An elemental equivalent circuit of the telephone line.
  10. 222 THE TELEPHONE NETWORK low-pass ﬁlter whose cut-off frequency is a function of its length. The longer the line is, the lower the cut-off frequency. The frequency response of a typical telephone line is shown in Figure 12.1. 8.3.6 Performance Improvements From Figure 8.9 it can be seen that the dc required to power the carbon microphone has to ﬂow through the receiver. This is not a good idea since it will make B0 , the ﬂux density of the permanent magnet (see Equation (8.3.11)), larger or smaller than it should be. A second disadvantage is that all the ac current generated by the carbon microphone has to ﬂow through the receiver. This produces a very loud reproduction of the speaker’s own voice in her receiver. The psychological effect is that the speaker lowers her voice, making it difﬁcult for her listener to hear what she is saying. This phenomenon is called sidetone. The two problems can be solved by using the circuit shown in Figure 8.12. It is an example of a hybrid. The Hybrid. The carbon microphone is connected to the centre-tap of the primary of the transformer. One end is connected to the telephone line and the other to an RC network which approximates the impedance of the line. The secondary is connected to the receiver. There is still a path for dc from the central ofﬁce battery to ﬂow through the carbon microphone. In the transmit mode, the ac produced by the microphone divides up equally, with one half ﬂowing through the telephone line and the other half in the line-matching impedance. Since these currents are in opposite directions in the primary of the transformer, no net voltage appears across the secondary. The speaker cannot hear himself. In the receive mode, the current IR ﬂows through the ﬁrst half of the primary winding and then splits at node X with Im ﬂowing through the carbon microphone where the energy is safely dissipated. The remainder (IR À Im ) ﬂows through the second half of the primary into the line-matching impedance. This time, the Figure 8.12. The use of a hybrid transformer to control sidetone.
  11. 8.3 BASIC TELEPHONE EQUIPMENT 223 directions of the two currents in the primary are the same; a net voltage appears across the receiver. In practice, the level of sidetone fed back to the speaker has to be carefully controlled. When it is too low, the telephone appears dead to the speaker and her normal reaction is to raise her voice. When the sidetone is too high, it has the opposite effect. The Rotary Dial. The rotary dial came with the invention of the automatic central ofﬁce. Evidently, the automatic central ofﬁce offered several advantages over the manual ofﬁce. There was increased security of the messages since there was no human interface in setting up calls. The time for setting up and releasing a call was substantially reduced and the probability of operator errors decreased. It guaranteed 24-hour service with fewer more highly trained personnel. The dial is simply a method of issuing instructions to the central ofﬁce and it does this by producing a binary coded message by mechanically opening and closing a switch in series with the circuit. The basic dial is as shown in Figure 8.13. It has a ﬁnger wheel with ten ﬁnger holes and it is mechanically coupled by a shaft to a second wheel which has ten cam lobes as shown. The shaft is mounted so that both wheels can rotate about the axis. The wheel assembly is spring loaded so that, when it is rotated in a clockwise direction, it will return at a constant speed under the control of a mechanical governor. Figure 8.13. The essential features and operation of the rotary dial.
  12. 224 THE TELEPHONE NETWORK To operate the dial, the caller inserts his or her index ﬁnger into the hole corresponding to the number and pulls the ﬁnger wheel to the ﬁnger stop and then releases it. While the ﬁnger wheel is rotating in the clockwise direction, the lever X is free to move out of the way of the cam lobes without disturbing the switch lever Y. When the wheel assembly is rotating in the counter-clockwise direction, every cam lobe that passes X will cause the switch lever Y to open the switch. If current is ﬂowing through the switch, the current ﬂow will be disrupted the number of times corresponding to the number of the ﬁnger hole. The current pulses can be used to operate a device (to be discussed later) at the central ofﬁce to effect the required connection. The return spring, cam lobes and mechanical governor are designed to produce 10 pulses per second with approximately equal mark-to-space ratio. Since it is bound to take the subscriber much longer then 1=10 seconds to rotate the ﬁnger wheel again, a pause longer than 1=10 seconds can be recognized by the central ofﬁce as an inter-digit pause. It is then possible to send a second and subsequent string of pulses to effect a connection which requires a multi-digit code. Note that when the digit ‘‘0’’ is dialled, ten pulses are produced. Telephone Bell. The telephone bell has two brass gongs with a clapper which is operated by an electromagnet. It is mechanically and electrically tuned to respond optimally (resonance) to current at 20 Hz. It is left connected to the telephone line at all times but the high impedance of its electromagnet coil ensures minimal effect at voice frequencies. Also the 10 Hz pulse from the rotary dial has no signiﬁcant effect on it. Nominally, it operates on 88 V, 20 Hz ac supplied to it from the central ofﬁce in the ring-mode. 8.3.7 Telephone Component Variation The telephone components described in this section are meant to be a representative sample of what can be found within the territory of any telephone operating authority or company. For each component there are several possible variations, some made to get around patents rights granted to others, and some to lower cost and improve reliability. The subscriber telephone instrument has changed in its physical appearance and electrical characteristics since it was ﬁrst put into service. However, in broad terms, it remained basically the same until the introduction of electronics in the form of semiconductor devices. The availability of ampliﬁers at very low cost offered various options such as new microphones, electronic sidetone control, tone ringers and tone dialling. Some of these will now be discussed. 8.4 ELECTRONIC TELEPHONE By the late 1960s a number of electronics research and development organizations were working on the development of electronic telephone sets. Manufacturing cost reduction, improved performance and the possibility of offering the subscriber a
  13. 8.4 ELECTRONIC TELEPHONE 225 number of new uses for their telephones were incentives for this development. The ﬁrst truly electronic component to emerge was the tone dialler, more popularly known by its trade name TOUCH-TONETM. Telephone sets with other electronic components were not far behind so that by the early 1980s there were a number of telephones on the market with none of the well established components described above. 8.4.1 Microphones The features of the carbon microphone that made it indispensable in the telephone set for a very long time were low cost, acoustic-to-electrical power ampliﬁcation, suppression of low level background noise, and high level signal compression. Its drawbacks were distortion, high dc current requirements, and changes in its acoustic sensitivity due to dc current ﬂowing in it. All of its advantages can be obtained with none of the disadvantages by using other microphones in conjunction with a suitable ampliﬁer. The new microphones could be made considerably smaller than the carbon microphone. Examples of such microphones include the following: (1) Electret Microphone. This is a variation on the capacitance microphone. The incident sound causes the distance between two plates of a capacitance to change, resulting in a change of voltage. The output voltage and power are very low. The output impedance is very high (10 pF at audio frequency). The normal biassing of capacitor microphones is averted by a built-in charge that is placed on the capacitor during the manufacturing process. It has an excellent frequency response and is normally used in acoustical measuring instruments. [4] (2) Ribbon Microphone. A thin aluminum ‘‘ribbon’’ is suspended in the ﬁeld of a small powerful magnet. The incident sound causes the ribbon to vibrate in the ﬁeld, causing a voltage proportional to its velocity to be induced in it. It has a very good frequency response but a very low output power. (3) Crystal Microphone. A crystal of Rochelle salt (sodium potassium tartrate), quartz and other piezo-electric materials produce a voltage when subjected to mechanical deformation. The crystal is cut into a thin layer with suitable conductors connected to the faces. The incident sound pressure causes a voltage to appear across the conductors. The microphone is very often made up of several layers of crystals. 8.4.2 Receiver The receiver is one of the few components that has successfully resisted change since Alexander Graham Bell patented it in 1876. The materials used for making the magnet and diaphragm and the actual mechanical construction have changed but the basic principle of operation remains the same.
  14. 226 THE TELEPHONE NETWORK 8.4.3 Hybrid The function of the ideal hybrid is to direct the signal from the microphone on to the telephone line without loss and to direct the incoming signal on the line to the receiver with no loss. The operation of the hybrid is therefore similar to the operation of a circulator – a well known device in microwave engineering. The two devices are compared in Figure 8.14. There are two major differences: (1) There are two critical paths in the hybrid, (transmit and receive) but three critical paths in the circulator. In a normal circulator, the transmitter cannot have a path to the receiver. (2) Circulators are realizable in reasonable physical dimensions at microwave frequencies. A direct application of circulator theory at audio frequency predicts a device several kilometres in diameter. The problem of realizing a circulator at audio frequency can be solved by using a gyrator [5]. Gyrators are better known for their ability to invert impedances [6,7]. They were the subject of intense interest at a time when the micro-electronics industry was looking for a micro-miniaturized version of the inductor. Consider the two-port shown in Figure 8.15 with the port voltages and currents as indicated. Figure 8.14. The telephone hybrid (a) compared to the circulator (b). Figure 8.15. A two-port with its deﬁning voltages and currents.
  15. 8.4 ELECTRONIC TELEPHONE 227 Figure 8.16. The ideal voltage-controlled current source. The two-port is described by the matrix      I1 Y11 Y12 V1 ¼ : ð8:4:1Þ I2 Y21 Y22 V2 Applying this description to the ideal voltage-controlled current source shown in Figure 8.16 gives      I1 0 0 V1 ¼ ð8:4:2Þ I2 gm 0 V 2 where gm is the transconductance. Consider a second ideal voltage-controlled current source with a 180 phase shift. The matrix equation is      I1 0 0 V1 ¼ ð8:4:3Þ I2 Àgm 0 V2 when the two ideal voltage-controlled current sources are connected back-to-back as shown in Figure 8.17. The matrix equation is      I1 0 Àgm V1 ¼ : ð8:4:4Þ I2 gm 0 V2 Figure 8.17. Two ideal voltage-controlled current sources connected back-to-back to form a gyrator.
  16. 228 THE TELEPHONE NETWORK The two-port can be converted into a three-terminal element by lifting the ground. Its matrix equation is then 2 3 2 32 3 I1 0 gm Àgm V1 4 I2 5 ¼ 4 Àgm 0 gm 54 V2 5: ð8:4:5Þ I3 gm Àgm 0 V3 Figure 8.18 shows the three-terminal circuit in which the transconductance gm has been replaced by the more general transadmittance Y0 and port 1 has been terminated in an admittance Y1 , port 2 in Y2 and port 3 in Y3 . Consider that an ideal current source I1 is connected across port 1 so that a voltage V1 appears across it. This will induce voltages V2 and V3 across ports 2 and 3, respectively. The voltage ratio is V2 Y1 ðY3 À Y0 Þ ¼ 2 : ð8:4:6Þ V1 Y2 Y3 þ Y0 Similarly, V3 Y1 ðY2 þ Y0 Þ ¼ 2 : ð8:4:7Þ V1 Y3 Y2 þ Y0 When Y1 ¼ Y2 ¼ Y3 ¼ Y0 , Equation (8.4.6) gives V2 ¼0 ð8:4:8Þ V1 Figure 8.18. The gyrator when properly terminated behaves like a circulator.
  17. 8.4 ELECTRONIC TELEPHONE 229 and Equation (8.4.7) gives V3 ¼ 1: ð8:4:9Þ V1 This means that voltage across port 1 appears across port 2 but no voltage appears across port 3, that is, V2 ¼ V1 and V3 ¼ 0: ð8:4:10Þ When the process is repeated with the ideal current source connected across port 2, V3 ¼ V2 and V1 ¼ 0: ð8:4:11Þ Finally, with the ideal current source across port 3, V1 ¼ V3 and V2 ¼ 0: ð8:4:12Þ It is clear that the circuit is behaving like a circulator oriented in a clockwise direction. To get the desired effect, the transadmittance of the gyrator ampliﬁers have to be adjusted to ﬁt the line admittance. The admittances of the microphone and receiver circuits have to be tailored so that the gyrator sees an admittance equal to its own admittance connected to each port. In practice, less than a perfect match can be achieved and therefore some sidetone is obtained. This property can be exploited to adjust the level of the sidetone to a comfortable level. Several electronic telephones use the audio-frequency circulator concept and its various manifestations as hybrids. 8.4.4 Tone Ringer In most electronic telephone sets, the bell has been replaced by some kind of tone ringer which usually emits an attractive musical note or notes to signal an incoming call. Quite often amplitude and frequency modulation are used to enhance the tone. The tone ringer must satisfy the following conditions: (1) The input impedance must be high so as not to interfere with the signal on the line to which it is permanently connected. (2) It has to operate on the 20 Hz, 88 V ac ringing signal that was used with the electromagnetic bell. In terms of circuit design, what is required is one or two audio-frequency oscillators, a frequency and=or amplitude modulator, a power supply fed from the 20 Hz ring signal, an audio-frequency ampliﬁer and a loudspeaker. The design of all these items has been discussed earlier. Oscillators were discussed in Section 2.4, modulators in
  18. 230 THE TELEPHONE NETWORK Section 2.6, audio-frequency ampliﬁers in Section 2.7, and loudspeakers in Section 3.4.8. The power supply for the ringer would require a rectiﬁer and a capacitor to smooth the output of the rectiﬁer to form a suitable dc supply for the ringer. 8.4.5 Tone Dial Instead of producing current pulses to signal the number dialled to the central ofﬁce, the tone dial produces a pair of audio-frequency tones. The frequencies of these tones are carefully chosen so they are not harmonically related. This reduces the probability of other tones or signals being recognized as dialled numbers. The dial pad and the corresponding frequencies produced are shown in Figure 8.19. Touch-ToneTM – DigitoneTM Dial. This dial consists of two essen- tially identical oscillators, one of which produces the high-frequency and the other the low-frequency tones. The change in frequency is achieved by switching in resistors of appropriate values when the dial push button is depressed. Each button has a unique pair of tones associated with it. The central ofﬁce equipment recognizes the number dialled by the two frequencies present. Figure 8.19. The push-button dial and its corresponding frequencies.
  19. 8.4 ELECTRONIC TELEPHONE 231 The early versions of the TOUCH-TONETM dial used discrete bipolar transistors in conjunction with an inductor and capacitances in a Colpitts conﬁguration. Both the low- and high-frequency groups were produced by a single oscillator. One of the capacitances in each group was changed as the various buttons were depressed to produce the required frequencies. Later versions used an integrated-circuit ampliﬁer with an RC twin-tee feedback circuit to produce the tones. The basic conﬁguration of the circuit is shown in Figure 8.20. Two conditions have to be met for oscillations to occur, according to the Barkhausen criterion: (1) The closed loop gain must be equal to unity. In practice, the loop gain must be slightly larger than unity for sustained oscillation. (2) The change in phase around the loop must be an integer multiple of 2p radians: The classical RC twin-tee ﬁlter has values of Rs and Cs as shown in Figure 8.21(a) and the amplitude and phase responses in Figure 8.21(b). Its transfer function is given by V2 1 À o2 C 2 R2 ¼À : ð8:4:13Þ V1 1 À o2 C 2 R2 þ j4oCR Rationalizing and equating the imaginary part to zero gives the frequency at which the phase angle is zero or 180 1 o0 ¼ : ð8:4:14Þ RC Figure 8.20. The modiﬁed twin-tee feedback oscillator. The closing of one of the four switches connects a different R=a to produce the tones. Two such circuits are used in the dial, one for the low frequencies and the second for the high frequencies.
  20. 232 THE TELEPHONE NETWORK Figure 8.21. (a) The classical twin-tee notch ﬁlter showing its conﬁguration and circuit element ratios. (b) The gain and phase characteristics of (a). Under this condition the output voltage v2 ¼ 0; the circuit has a null in its frequency response with a very high Q factor. The high Q factor can be exploited for high stability of oscillating frequency if the oscillator is designed to operate at the frequency of the null. However, using the classical twin-tee values of Rs and Cs in oscillator design will be self-defeating since an ampliﬁer with inﬁnite gain will be required. Departure from the standard ratios of Rs and Cs produces lower values of Q factor. The amplitude–frequency responses of the modiﬁed twin-tee ﬁlter (Figure 8.20) with different values of a are shown in Figure 8.22(a). The frequencies at which the phase shift of the ﬁlter is zero or 180 coincides with the frequency at which the output voltage is a minimum (null). It can be seen that the notch frequency for the particular conﬁguration and circuit element ratios shown in Figure 8.20 changes with the parameter a. It can also be observed that the depth of the notch varies as a changes, with the ‘‘deepest’’ notch occurring when a is equal to approximately 2.25. For values of a less than 2.25, the modiﬁed twin-tee circuit has gain and phase characteristics as shown in Figure 8.22(b). When a is equal to or greater than 2.25, the gain and phase response is as shown in Figure 8.22(c). The
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