Table of Contents

**Modem Concepts and Methods**

**FSK | PSK | DPSK** **:** Binary signals are switched dc pulses, so how do such signals get transmitted over telephone lines, cable TV, coaxial cables, twisted-pair cables, or wireless links? Binary pulses can be transported over short cables even at very high data rates. The transformers, capacitors, and other ac circuitry in the data path virtually ensure that no dc signals get through in a recognizable form. Furthermore, high-speed data is fi ltered out by the limited-bandwidth media.

The question is, then: How does digital data get transmitted over cables and wireless links? The answer is by using broadband communication techniques involving modulation, which are implemented by a modem, a device containing both a modulator and a demodulator. Modems convert binary signals to analog signals capable of being transmitted over telephone and cable TV lines and by radio and then demodulate such analog signals, reconstructing the equivalent binary output. Fig. 11-12 shows two ways that modems are commonly used in digital data transmission. In Fig. 11-12(a), two computers exchange data by speaking through modems. While one modem is transmitting, the other is receiving. Full duplex operation is also possible. In Fig. 11-12(b), a remote video terminal or personal computer is using a modem to communicate with a large server computer. Modems are also the interface between the millions of personal computers and servers that make up the Internet.

There are four basic modem types: low-speed analog modems, digital subscriber line (DSL) modems, cable TV modems, and wireless modems. The first three are discussed in the following sections. Analog modems of the dial-up type are no longer widely used, but there are many low data rate applications that use these techniques in both wired and wireless equipment.

**Modulation for Data Communication**

Four main types of modulation are used in modern modems: frequency-shift keying (FSK), phase-shift keying (PSK), quadrature amplitude modulation (QAM), and orthogonal frequency-division multiplexing (OFDM). FSK is used primarily in lower speed (,500 kbps) modems in a noisy environment. PSK operates in narrower bandwidths over a wide range of speeds. QAM is a combination of both amplitude modulation and PSK. It can produce very high data rates in narrow bandwidths. OFDM operates over a very wide bandwidth and can achieve very high rates in a noisy environment.

**FSK frequency-shift keying**

The oldest and simplest form of modulation used in modems is frequency-shift keying (FSK). In FSK, two sine wave frequencies are used to represent binary 0s and 1s. For example, a binary 0, usually called a space in data communication jargon, has a frequency of 1070 Hz. A binary 1, referred to as a mark, is 1270 Hz. These two frequencies are alternately transmitted to create the serial binary data. The resulting signal looks something like that shown in Fig. 11-13. Both of the frequencies are well within the 300- to 3000-Hz bandwidth normally associated with the telephone system, as illustrated in Fig. 11-14.

The simultaneous transmit and receive operations that are carried out by a modem, known as full duplex operation, require that another set of frequencies be defined. These are also indicated in Fig. 11-14. A binary 0 or space is 2025 Hz; a binary 1 or mark is 2225 Hz. These tones are also within the telephone bandwidth but are spaced far enough from the other frequencies so that selective fi lters can be used to distinguish between the two. The 1070- and 1270-Hz tones are used for transmitting (originate), and the 2025- and 2225-Hz tones are used for receiving (answer).

Fig. 11-15 is a block diagram of the modulator and demodulator sections of an FSK modem. Each modem contains an FSK modulator and an FSK demodulator so that both send and receive operations can be achieved. Bandpass filters at the inputs to each modem separate the two tones. For example, in the upper modem, a bandpass filter allows frequencies between 1950 and 2300 Hz to pass. This means that 2025- and 2225-Hz tones will be passed, but the 1070- and 1270-Hz tones generated by the internal modulator will be rejected. The lower modem has a bandpass filter that accepts the lower- frequency tones while rejecting the upper-frequency tones generated internally.

A wide variety of modulator and demodulator circuits are used to produce and recover FSK. Virtually all the circuits described in Chap. 6 have been or could be used. A typical FSK modulator is simply an oscillator whose frequency can be switched between two frequencies. A typical demodulator is a PLL. Most modems now use digital techniques because they are simpler and more adaptable to IC implementations. A large portion of modem operations if not all operations are now implemented with DSP.

FSK signals typically occupy a wide bandwidth because of the multiple sidebands produced by the FM process. Higher orders of sidebands are also generated by the harmonics contained in the fast binary modulating signal. Any abrupt signal changes further aggravate the problem. Several techniques have been developed to improve the spectral effi ciency of FSK. The term spectral efficiency refers to how well a specific modulation technique produces a maximum data rate in a minimal bandwidth.

When the mark and space frequencies are arbitrarily chosen, they will not be phasecoherent. That is, there will be abrupt signal changes during 0-to-1 or 1-to-0 transitions. This is illustrated in Fig. 11-16(a). The “glitches” or phase discontinuities produce even more harmonics and wider bandwidth. In addition, such discontinuities make demodulation more diffi cult and produce more bit errors.

To overcome this problem, the mark and space frequencies can be chosen so that the periods of the sine waves both cross zero at the mark-to-space and space-to-mark transitions. This is illustrated in Fig. 11-16(b). No phase discontinuities exist, so the resulting bandwidth is less. This type of modulation is called continuous-phase frequency-shift keying (CPFSK).

Another term for signals that start and stop at the zero crossing points is coherent. You could call this form of modulation coherent FSK. You can also have coherent ASK or OOK. Coherent versions use less bandwidth and perform better in the presence of noise. An improved variation of CPFSK is minimum shift keying (MSK). As in CPFSK, the mark and space frequencies are some integer multiple of the bit clock frequency. This ensures that the signals are fully synchronized with one another and that no phase discontinuities occur.

MSK further improves spectral efficiency by using a low modulation index. Recall that the number of pairs of sidebands produced (and therefore the wider the bandwidth) is proportional to the modulation index. With analog FM, the modulation index is

m_{f} = f_{d}/f_{m}

where f_{d} is the frequency deviation and f_{m} is the modulating signal frequency. With FSK, the modulation index m is

m = Δf (T)

where Δf is the deviation or frequency shift between the mark frequency f_{M} and the space frequency f_{S}.

Δf = f_{S} – f_{m}

Also T is the bit time or the reciprocal of the data rate.

T =1/bps

MSK generally specifies that m must be 0.5. However, other values (0.3) are used. For example, assume a MSK modem with f_{M} = 1200 and f_{S} = 1800 Hz. The bit rate is 1200 bps. The modulation index is

Δf = f_{S} – f_{m} = 1800 – 1200 = 600 Hz

T = 1/bps = 1/1200 = 0.0008333 s

m = Δf (T) = 600(0.0008333) = 0.5

MSK is a very spectrally efficient form of FSK. But the MSK signal bandwidth can be further reduced by prefiltering the binary modulating signal. This filter removes some of the higher-level harmonics that are responsible for the added sidebands and wider bandwidth. One of the best prefilters is called a Gaussian low-pass filter. It rounds the edges and somewhat lengthens the rise and fall times. This in turn reduces harmonic content. And that decreases the overall signal bandwidth. Gaussian filtered MSK is referred to as GMSK. It is widely used in data communication and is the basis of the popular GSM digital cell phones.

**PSK**

In phase-shift keying (PSK), the binary signal to be transmitted changes the phase shift of a sine wave character depending upon whether a binary 0 or binary 1 is to be transmitted. (Recall that phase shift is a time difference between two sine waves of the same frequency.) Fig. 11-17 illustrates several examples of phase shift. A phase shift of 180°, the maximum phase difference that can occur, is known as a phase reversal, or phase inversion.

11-18 illustrates the simplest form of PSK, binary phase-shift keying (BPSK). During the time that a binary 0 occurs, the carrier signal is transmitted with one phase; when a binary 1 occurs, the carrier is transmitted with a 180° phase shift.

Fig. 11-19 shows one kind of circuit used for generating BPSK, a standard lattice ring modulator or balanced modulator used for generating DSB signals. The carrier sine wave is applied to the input transformer T1 while the binary signal is applied to the transformer center taps. The binary signal provides a switching signal for the diodes. When a binary 0 appears at the input, A is + and B is – , so diodes D1 and D4 conduct.

They act as closed switches, connecting the secondary of T1 to the primary of T2. The windings are phased so that the BPSK output is in phase with the carrier input. When a binary 1 appears at the input, A is – and B is +, so diodes D1 and D4 are cut off while diodes D2 and D3 conduct. This causes the secondary of T1 to be connected to the primary of T2 but with the interconnections reversed. This introduces a 180° phaseshift carrier at the output.

Demodulation of a BPSK signal is also done with a balanced modulator. A version of the diode ring or lattice modulator can be used, as shown in Fig. 11-20. This is actually the same circuit as that in Fig. 11-19, but the output is taken from the center taps. The BPSK and carrier signals are applied to the transformers. IC balanced modulators can also be used at the lower frequencies. The modulator and demodulator circuits are identical to the doubly balanced modulators used for mixers. They are available as fully wired and tested components for frequencies up to about 1 GHz.

The key to demodulating BPSK is that a carrier with the correct frequency and phase relationship must be applied to the balanced modulator along with the BPSK signal. Typically the carrier is derived from the BPSK signal itself, using a carrier recovery circuit like that shown in Fig. 11-21. A bandpass filter ensures that only the desired BPSK signal is passed. The signal is then squared or multiplied by itself by a balanced modulator or analog multiplier by applying the same signal to both inputs. Squaring removes all the 180° phase shifts, resulting in an output that is twice the input signal frequency (2f ). A bandpass filter set at twice the carrier frequency passes this signal only. The resulting signal is applied to the phase detector of a PLL. Note that a x2 frequency

The key to demodulating BPSK is that a carrier with the correct frequency and phase relationship must be applied to the balanced modulator along with the BPSK signal. Typically the carrier is derived from the BPSK signal itself, using a carrier recovery circuit like that shown in Fig. 11-21. A bandpass filter ensures that only the desired BPSK signal is passed. The signal is then squared or multiplied by itself by a balanced modulator or analog multiplier by applying the same signal to both inputs. Squaring removes all the 180° phase shifts, resulting in an output that is twice the input signal frequency (2f ). A bandpass filter set at twice the carrier frequency passes this signal only. The resulting signal is applied to the phase detector of a PLL. Note that a x2 frequency multiplier is used between the VCO and phase detector, ensuring that the VCO frequency is at the carrier frequency. Use of the PLL means that the VCO will track any carrier frequency shifts. The result is a signal with the correct frequency and phase relationship for proper demodulation. The carrier is applied to the balanced modulator-demodulator along with the BPSK signal. The output is the recovered binary data stream.

**DPSK**

to simplify the demodulation process, a version of binary PSK called differential phase-shift keying (DPSK) can be used. In DPSK, there is no absolute carrier phase reference. Instead, the transmitted signal itself becomes the phase reference. In demodulating DPSK, the phase of the received bit is compared with the phase of the previously received bit.

For DPSK to work, the original binary bit stream must undergo a process known as differential phase coding, in which the serial bit stream passes through an inverted exclusive-NOR circuit (XNOR), as shown in Fig. 11-22(a). Note that the XNOR output is applied to a 1-bit delay circuit before being applied back to the input. The delay can simply be a clocked flip-flop or a delay line. The resulting bit pattern permits the signal to be recovered because the current bit phase can be compared with the previously received bit phase.

In Fig. 11-22(b), the input binary word to be transmitted is shown along with the output of the XNOR. An XNOR circuit is a 1-bit comparator that produces a binary 1 output when both inputs are alike and a binary 0 output when the two bits are different. The output of the circuit is delayed at a 1-bit interval by being stored in a flip-flop. Therefore, the XNOR inputs are the current bit plus the previous bit. The XNOR signal is then applied to the balanced modulator along with the carrier to produce a BPSK signal.

Demodulation is accomplished with the circuit shown in Fig. 11-23. The DPSK signal is applied to one input of the balanced modulator and a 1-bit delay circuit, either a flip-flop or a delay line. The output of the delay circuit is used as the carrier. The resulting output is fi ltered by a low-pass filter to recover the binary data. Typically the low-pass filter output is shaped with a Schmitt trigger or comparator to produce clean, high-speed binary levels.

**QPSK**

The main problem with BPSK and DPSK is that the speed of data transmission in a given bandwidth is limited. One way to increase the binary data rate while not increasing the bandwidth required for the signal transmission is to encode more than 1 bit per phase change. There is a symbol change for each bit change with BPSK and DPSK, so the baud (symbol) rate is the same as the bit rate. In BPSK and DPSK, each binary bit produces a specifi c phase change. An alternative approach is to use combinations of two or more bits to specify a particular phase shift, so that a symbol change (phase shift) represents multiple bits. Because more bits per baud are encoded, the bit rate of data transfer can be higher than the baud rate, yet the signal will not take up additional bandwidth.

One commonly used system for doing this is known as quadrature, quarternary, or quadra phase PSK (QPSK or 4-PSK). In QPSK, each pair of successive digital bits in the transmitted word is assigned a particular phase, as indicated in Fig. 11-24(a). Each pair of serial bits, called a dibit, is represented by a specifi c phase. A 90° phase shift exists between each pair of bits. Other phase angles can also be used as long as they have a 90° separation. For example, it is common to use phase shifts of 45°, 135°, 225°, and 315°, as shown in Fig. 11-24(b).

The diagram in Fig. 11-24(b) is called a constellation diagram. It shows the modulation signal in the form of phasors. The length of the arrow or phasor indicates the peak voltage level of the signal while its angle to the axis is the phase shift. Sometimes the constellation diagram is simplified by just showing dots on the axis indicating the location of the phasor arrowhead, as in Fig. 11-24(c). This simplifies the diagram, but you should always imagine a phasor drawn from the origin of the axis to each dot. Constellation diagrams are widely used to show phase-amplitude modulation schemes.

You will often hear the term M-ary used in discussing higher coding levels of PSK It is derived from the word binary where in binary M = 2, so 2-ary indicates two phase shifts. QPSK is the same as 4-PSK or 4-ary PSK; 8-PSK would be called 8-ary PSK with eight phase positions.

A circuit for producing QPSK is shown in Fig. 11-25. It consists of a 2-bit shift register implemented with flip-flops, commonly known as a bit splitter. The serial binary data train is shifted through this register, and the bits from the two flip-flops are applied to balanced modulators. The carrier oscillator is applied to balanced modulator 1 and through a 90° phase shifter to balanced modulator 2. The outputs of the balanced modulators are linearly mixed to produce the QPSK signal.

The output from each balanced modulator is a BPSK signal. With a binary 0 input, the balanced modulator produces one phase of the carrier. With a binary 1 input, the carrier phase is shifted 180°. The output of balanced modulator 2 also has two-phase states, 180° out of phase with each other. The 90° carrier phase shift at the input causes the outputs from balanced modulator 2 to be shifted 90° from those of balanced modulator 1. The result is four different carrier phases, which are combined two at a time in the linear mixer. The result is four unique output phase states.

Fig. 11-26 shows the outputs of one possible set of phase shifts. Note that the carrier outputs from the two balanced modulators are shifted 90°. When the two carriers are algebraically summed in the mixer, the result is an output sine wave that has a phase shift of 225°, which is halfway between the phase shifts of the two balanced modulator signals.

A demodulator for QPSK is illustrated in Fig. 11-27. The carrier recovery circuit is similar to the one described previously. The carrier is applied to balanced modulator 1 and is shifted 90° before being applied to balanced modulator 2. The outputs of the two balanced modulators are filtered and shaped into bits. The 2 bits are combined in a shift register and shifted out to produce the originally transmitted binary signal.

Encoding still more bits per phase change produces higher data rates. In 8-PSK, for example, 3 serial bits are used to produce a total of eight different phase changes. In 16-PSK, 4 serial input bits produce 16 different phase changes, for an even higher data rate.

Fig. 11-28 shows the constellation diagram of a 16-PSK signal. The phase increment is 22.58. Each phasor or dot on the diagram represents a 4-bit number. Note that since all the dots fall on a circle, the amplitude of the 16-PSK signal remains constant while only the phase changes. The radius of the circle is the peak amplitude of the signal. It is said that the signal has a constant “envelope,” where the envelope is simply the line or curve connecting the peaks of the carrier sine waves. It is flat or constant, as is an FM signal.

**QAM**

One of the most popular modulation techniques used in modems for increasing the number of bits per baud is quadrature amplitude modulation (QAM). QAM uses both amplitude and phase modulation of a carrier; not only are different phase shifts produced, but also the amplitude of the carrier is varied.

In 8-QAM, there are four possible phase shifts, as in QPSK, and two different carrier amplitudes, so that eight different states can be transmitted. With eight states, 3 bits can be encoded for each baud or symbol transmitted. Each 3-bit binary word transmitted uses a different phase-amplitude combination.

Fig. 11-29 is a constellation diagram of an 8-QAM signal showing all possible phase and amplitude combinations. The points in the diagram indicate the eight possible phaseamplitude combinations. Note that there are two amplitude levels for each phase position. Point A shows a low carrier amplitude with a phase shift of 1358. It represents 100. Point B shows a higher amplitude and a phase shift of 315°. This sine wave represents 011.

A block diagram of an 8-QAM modulator is shown in Fig. 11-30. The binary data to be transmitted is shifted serially into the 3-bit shift register. These bits are applied in pairs to two 2-to-4 level converters. A 2-to-4 level converter circuit, basically a simple D/A converter, translates a pair of binary inputs into one of four possible dc output voltage levels. The idea is to produce four voltage levels corresponding to the different combinations of 2 input bits, i.e., four equally spaced voltage levels. These are applied to the two balanced modulators fed by the carrier oscillator and a 90° phase shifter, as in a QPSK modulator. Each balanced modulator produces four different output phase- amplitude combinations. When these are combined in the linear mixer, eight different phase-amplitude combinations are produced. The most critical part of the circuit is the 2-to-4 level converters; these must have very precise output amplitudes so that when they are combined in the linear summer, the correct output and phase combinations are produced.

A 16-QAM signal can also be generated by encoding 4 input bits at a time. The result is 12 different phase shifts and 3 amplitude levels, producing a total of 16 different phase-amplitude combinations. Even higher data rates can be achieved with 64-QAM and 256-QAM. Multilevel modulation schemes using 1024-QAM to 4096-QAM are also used. These signals are used in cable TV modems, wireless local area networks (WLANs), satellites, and high-speed fi xed broadband wireless applications.

**Spectral Efficiency and Noise**

As indicated earlier in this section, spectral efficiency is a measure of how fast data can be transmitted in a given bandwidth. The measure is bits per second per Hertz (bps/Hz). As you have seen, different modulation methods give different efficiencies. The table shows the common efficiencies for several common types of modulation.

With a modulation method like BPSK where the efficiency is 1 bps/Hz, you can actually

transmit data at a rate equal to the bandwidth or

BW = f_{b} = 1/t_{b}

where f_{b} is the data rate in bits per second and t_{b} is the bit time.

Another factor that clearly influences the spectral efficiency is the noise in the channel or the signal-to-noise (S/N) ratio. Obviously the greater the noise, the greater the number of bit errors. The number of errors that occur in a given time is called the bit error rate (BER). The BER is simply the ratio of the number of errors that occur in 1 s of a 1-s interval of data transmission. For example, if five errors occur in 1 s in a 10 Mbps transmission, the BER is

BER = 5/10 x10^{6} = 0.5 x 10^{-6} or 5 x 10^{-7}

Some modulation schemes are more immune to the noise than others.

The S/N covered in previous chapters was the ratio of signal rms voltage to noise rms voltage. You can also use the ratio of the average signal power of the carrier plus the sidebands to the noise power, usually the thermal noise. This is called the carrier to-noise (C/N) ratio. Generally, C/N is expressed in decibels.

Fig. 11-31 shows the relationship between the C/N and BER for different modulation methods. What this graph shows is that for a given BER, the modulation methods with the fewest symbol changes or the smaller bits per hertz give the best performance at the lower C/N ratios. For a BER of 10^{-6} , BPSK needs only a C/N of 11 dB, while for 16-QAM a C/N of 20 dB is needed. Amplitude-modulated signals are always more susceptible to noise than are constant-envelope forms of modulation such as PSK and FSK, so you need more signal power to overcome the noise to get the desired BER. Such a graph lets you compare and evaluate different modulation schemes. Just keep in mind that bandwidth does not enter the picture here. When comparing methods, you must remember that noise increases with bandwidth.

A better measure of signal-to-noise ratio for digital data is the ratio of energy per bit transmitted to the noise power density or Eb/N0, usually pronounced “E sub b over N sub-zero.” Remember that energy is expressed in joules (J), where one joule per second (J/s) is equal to one watt (1 W), or 1 W = 1 J/s. Therefore, Eb is the power in 1 bit P multiplied by the bit time tb, or E_{b }= Pt_{b.}

The noise power density in watts per hertz (W/Hz), which we call N0, is the thermal noise power N divided by the bandwidth of the channel B. Recall that thermal noise power is N = kTB, where k is Boltzmann’s constant 1.38 x 10^{-23}, T is the temperature in kelvins, and B is the bandwidth in hertz. Room temperature is about 290 K.

N_{0} = kTB/B = kT

The overall result is

E_{b}/N_{0}= Pt_{b}/kT

This relationship can be further manipulated to show Eb/N0 in terms of C/N. This relationship is

Eb/N0=(C/N)(B/fb)

Here B is the bandwidth in hertz and fb is the bit rate or bit frequency (fb) where fb =1/tb. Given C/N and the other factors, you can calculate Eb /N0. What Eb /N0 does is to take bandwidth out of the comparison. It normalizes all the different multiphase/ amplitude schemes to a noise bandwidth of 1 Hz, giving you a better way to compare and contrast the various modulation methods for a given BER. You will often see curves like that in Fig. 11-31 plotted with BER on the vertical axis and Eb /N0 rather than C/N on the horizontal axis. Fig. 11-32 is an example. Note the role that coherency plays (carrier sine waves start and stop on the zero-crossing). Coherent OOK needs a lower signal-to-noise ratio than incoherent OOK for a given BER.

**Watch Video** Modem Concepts | FSK | PSK | DPSK | QPSK | QAM | Spectral Efficiency

PCM ( Pulse Code Modulation ) | T-Carrier Systems| Duplexing ( FSK | PSK | DPSK | QPSK | QAM | Spectral Efficiency | Modem Concepts)

Receiver and Transceiver | AM | FM | SW Radio | SDR | Wi-Fi ( FSK | PSK | DPSK | QPSK | QAM | Spectral Efficiency | Modem Concepts)

IF Amplifiers | RF Input Amplifiers | Squelch Circuits | Controlling Gain ( FSK | PSK | DPSK | QPSK | QAM | Spectral Efficiency | Modem Concepts)

Digital to Analog Converters | Analog to Digital Converters ( FSK | PSK | DPSK | QPSK | QAM | Spectral Efficiency | Modem Concepts)

Noise Level & Types | Conversion Receivers | Signal-to-Noise Ratio (SNR) ( FSK | PSK | DPSK | QPSK | QAM | Spectral Efficiency | Modem Concepts)

Signal Reproduction | Super heterodyne | RF Amplifiers | Mixing ( FSK | PSK | DPSK | QPSK | QAM | Spectral Efficiency | Modem Concepts)

Impedance Matching Networks | T and π | Transformers and Baluns ( FSK | PSK | DPSK | QPSK | QAM | Spectral Efficiency | Modem Concepts)

Click here to Learn more ( FSK | PSK | DPSK | QPSK | QAM | Spectral Efficiency | Modem Concepts)

Learn More ( FSK | PSK | DPSK | QPSK | QAM | Spectral Efficiency | Modem Concepts)