Chapter 25: Transmitters and Receivers

Chapter 25: Transmitters and Receivers This chapter describes the design o transmitters and receivers or radio transmission. The terms used shall have a deined meaning such that the components rom the modulator up to the transmitting antenna orm the transmitter, while the components rom the receiver antenna up to the demodulator orm the receiver. The demands placed on the transmitter and receiver are clearly distinct since the transmitter must process only the desired signal while the receiver must separate the desired signal rom the requency mixture received by the antenna. Furthermore, the transmitter handles signal levels which are constant or which vary very slightly, while the receiver copes with extremely large level dierences that depend on the distance to the transmitter. The main challenges or the transmitter include the task o converting the useul signal into a high-requency transmission signal with as little intererence as possible, to ampliy this signal with the highest possible eiciency and to minimize the transmission o undesirable intererence signals generated by the conversion or ampliication. The main challenges or the receiver are to ilter out the desired signal even rom very weak levels, while at the same time receiving very strong signals rom adjacent requency ranges, and producing a clear signal with a high signal-to-noise ratio and minimum intermodulation distortions. Thus, the main obstacle or concern in transmitters is eiciency, while receivers ace issues o selection, dynamics and noise. 25.1 Transmitters First we will look at the construction o transmitters with analog modulation, ollowed by a description o transmitters with digital modulation. These descriptions are supported by simpliied block diagrams showing only the essential components. 25.1.1 Transmitters with Analogue Modulation Transmitters with Direct Modulation The most simple transmitter is obtained when the carrier requency C o the analog modulator is identical to the transmission requency RF. In this case, the modulator output signal only needs to be ampliied and ed to the antenna. In practice, the transmission ampliier must be ollowed by an output ilter that reduces the distortion products originating in the ampliier to an acceptable level. Figure 25.1a shows the construction o a transmitter with direct modulation. The signal spectra are shown in Fig. 25.2.

1238 25 Transmitters and Receivers RF Output ilter Analog st () modulator s t RF () RF a With direct modulation st () Analog modulator IF M1 RF ilter RF Output ilter srf () t IF LO b With intermediate requency st () Analog modulator IF1 M1 IF ilter IF2 M2 RF ilter RF Output ilter srf () t IF1 LO1 LO2 c With two intermediate requencies Fig. 25.1. Transmitter with analog modulation st () S RF Analog modulator 0 S RF s t RF () RF Fig. 25.2. Signal spectra in transmitters with direct modulation

25.1 Transmitters 1239 Transmitters with One Intermediate Frequency With increasing requencies and growing demands, it becomes more and more diicult to obtain a modulator with the required accuracy. Thereore, a lower intermediate requency IF with which the modulator can be easily built is used as carrier requency C : C = IF RF Figure 25.1b shows the construction o a transmitter with one intermediate requency. Conversion to the transmission requency RF is done by mixer M1 which is provided with the requency LO = RF IF rom a local oscillator (LO). The mixing process generates the sum and dierence requencies LO + IF = RF, LO IF = RF 2 IF The portion at the transmission requency is iltered by an RF ilter and ed to the transmitter ampliier. Figure 25.3 shows the signal spectra. Owing to RF = LO + IF, the requency sequence is identical in the IF and RF signals, which means that a higher IF requency results in a higher RF requency; this is known as noninverted mode. It is also possible to choose RF = LO IF by iltering out the signal st () S IF Analog modulator 0 S IF sif () t LO M1 IF 0 IF sm1 () t S M1 LO IF LO RF = LO + IF RF ilter IF 2 RF ilter S RF s t RF () LO RF Fig. 25.3. Signal spectra in transmitters with one intermediate requency

1240 25 Transmitters and Receivers portion below the local oscillator requency in Fig. 25.3. Then the requency sequence in the transmission signal is inverted; this is known as inverted mode. The receiver must take the inverted requency operation into account in order to correctly receive the desired signal. For this purpose, the receiver uses a mixer operated in inverted mode. The mixer output signal contains a signal portion at the local oscillator requency LO (see Fig. 25.3). Consequently, the transition region o the RF ilter (transition rom the pass band to the cuto band) must not exceed the width IF /2 to ensure that the transmission signal lies ully within the pass band and the local oscillator signal is in the cuto band. Particularly suitable are surace acoustic wave (SAW) ilters with their very narrow transition region and constant group delay but whose high insertion loss (>20 d) is disadvantageous. Where no SAW ilters are available or the desired transmission requency, LC ilters or ilters with dielectric resonators must be used. As these ilters have unwanted group delay distortion at the borders o the transition region, it is necessary to select a clearly smaller transit region in order to prevent the transmission signal rom being aected. As an alternative, one may use the entire range between the portions above and below the local oscillator requency as the transition region and suppress the local oscillator requency by a separate serial or parallel resonant circuit (zero transmission at LO ). With rising transmission requencies, the ratio o the transmitter requency to the width o the transition region increases; hence, the quality o the RF ilter must also increase: Q RF RF IF /2 IF = C RF C This results in a higher ilter order and increased group delay distortions. In practice, the intermediate requency is made as high as possible so that the transition region becomes wider and the RF ilter quality becomes correspondingly low. Transmitters with Two Intermediate Frequencies In transmitters with one intermediate requency and high transmission requencies, the quality o the RF ilter becomes impermissibly high. A second intermediate requency is then required that ranges between the carrier requency o the modulator and the transmission requency: C = IF1 < IF2 < RF Figure 25.1c shows the construction o a transmitter with two intermediate requencies, while the signal spectra are presented in Fig. 25.4. Mixer M1 converts the modulator s output signal rom the irst to the second intermediate requency. This requires a local oscillator with the requency LO1 = IF2 IF1. Subsequently the portion above the local oscillator requency is iltered out by an IF ilter. The quality o the IF ilter is proportional to the ratio o the second intermediate requency and the width o the transition region: Q IF IF2 IF1 /2 IF1 = C IF2 C

25.1 Transmitters 1241 st () S IF1 Analog modulator 0 S IF1 s t IF1 () LO1 M1 IF1 0 IF1 sm1 () t S M1 LO1 IF1 LO1 IF2 = LO1 + IF1 IF ilter IF1 2 IF ilter S IF2 sif2 () t LO2 M2 LO1 IF2 sm2 () t S M2 LO2 IF2 LO2 RF = LO2 + IF2 RF ilter IF2 2 RF ilter S HF s t RF () LO2 RF Fig. 25.4. Signal spectra in transmitters with two intermediate requencies The conversion to the transmission requency is achieved with a mixer M2, which is ed by a second local oscillator with the requency LO 2 = RF IF2. An RF ilter o the quality Q RF RF IF2 /2 IF2 RF IF2 is required to ilter out the transmission signal.

1242 25 Transmitters and Receivers Obviously the overall quality is Q RF / C, which, in transmitters with one intermediate requency, has to be generated by the RF ilter and in transmitters with two intermediate requencies can be distributed to two ilters: Q = Q RF Q IF RF C The relative amounts can be controlled by the value o the second intermediate requency, more speciically, i it is relatively high then Q IF > Q RF, i it is relatively low then Q IF <Q RF. In practice, the values selected depend on the transmission requency and the available ilters. The planned number o units also has an important inluence since or high unit numbers customized dielectric or SAW ilters can be used, but or mass applications such as mobile communication even the design o new ilter technologies is warranted. For small batch production, on the other hand, standard ilters are used. The use o LC ilters with discrete components is avoided where possible or reasons o space and calibration. In transmitters with two intermediate requencies, one can also operate one or both mixers in inverted mode by iltering out the portions below the local oscillator requency. I both mixers are operated in inverted mode, then the transmission signal is in noninverted mode again. Transmitters with Variable Transmission Frequencies In transmitters with a variable transmission requency, the requency o the last local oscillator is variable, thus allowing the transmission requency to be altered without aecting the other components. Variations take place within the requency range assigned to the speciic application according to the channel spacing C. Figure 25.5 illustrates this taking a transmitter with ive channels as an example. The RF ilter is rated such that all channels are within the pass band and all local oscillator requencies are within the cuto band. Alternatively, a tuneable RF ilter may be used, but only in exceptional practical cases. For a lower number o channels and less channel spacing, the local oscillator and transmission requencies change very little. For such applications a transmitter with one intermediate requency can be used as long as the transition region between the highest local oscillator requency and the lowest limit o the channel pattern is suiciently wide. Although in most cases this requires a transmitter with two intermediate requencies where the second intermediate requency is selected relatively high so that the transition region becomes as wide as possible. S RF IF ( 2) C C C C RF ilter LO 2 ( ) RF = LO 2 + ( ) IF ( 2) Fig. 25.5. Transmitter with variable transmission requency

25.1 Transmitters 1243 25.1.2 Transmitters with Digital Modulation In principle, transmitters with digital modulation are o the same design as transmitters with analog modulation. The essential dierence is that digital modulators primarily generate the quadrature components i(t) and q(t) that are combined into a modulated carrier signal by an I/Q mixer. Figure 25.6a shows a digital transmitter with direct modulation. It corresponds to the analog transmitter with direct modulation in Fig. 25.1a i the combination o digital modulator, I/Q mixer (MI and MQ) and the subsequent ilter are regarded as being equivalent to the analog modulator. The same applies to the digital transmitter with one or two in- sn ( ) Digital modulator it () RF 0 o 90 o MI RF ilter RF Output ilter srf () t qt () MQ a With direct modulation sn ( ) Digital modulator it () IF 0 o 90 o MI IF ilter IF M1 RF ilter RF Output ilter srf () t qt () MQ LO b With one intermediate requency and an analog I/Q mixer sn ( ) Digital modulator in ( ) Digital I/Q mixer sif ( n ) D A IF ilter 1 IF1 M1 IF ilter 2 IF2 qn ( ) LO1 RF ilter RF Output ilter LO2 M2 srf () t c With two intermediate requencies and a digital I/Q mixer Fig. 25.6. Transmitter with digital modulation

1244 25 Transmitters and Receivers termediate requencies. A digital transmitter with one intermediate requency is shown in Fig. 25.6b. I particularly high demands are made in terms o the accuracy o the I/Q mixer, a digital I/Q mixer is used to prevent amplitude and phase errors between the two branches. The output o the digital I/Q mixer provides a digital IF signal that is converted into an analog IF signal by a D/A converter and subsequent IF ilter. As the requency o the IF signal must be comparatively low due to the limited sampling rate o the digital I/Q mixer and the D/A converter, a second intermediate requency is usually utilized. Figure 25.6c shows the resulting transmitter. 25.1.3 Generating Local Oscillator Frequencies The required local oscillator requencies are derived by phase-locked loops (PLL) rom a crystal oscillator with reerence requency REF. Figure 25.7 depicts this or a transmitter with one intermediate requency and variable transmission requency. The intermediate requency is ixed and is determined by the divider actors n 1 and n 2 : IF = n 2 n 1 REF The local oscillator requency is variable in steps according to the channel spacing C. For this purpose, the reerence requency is divided to the channel distance by the divider actor n 3 and multiplied by a PLL with the programmable divider actor n 4 : C = REF n 3, LO = n 4 C = n 4 n 3 REF Crystal oscillator Frequency divider Phase detector Loop ilter Controlled oscillator REF n 1 1 PD VCO IF = n 2 n 1 REF PLL or the intermediate requency (IF-PLL) n 2 1 Frequency divider Frequency divider Phase detector Loop ilter Controlled oscillator n 3 1 K PD VCO LO = n 4 n 3 REF PLL or the local oscillator requency (LO-PLL) n 4 1 Programmable requency divider Fig. 25.7. Generation o the local oscillator requencies

25.2 Receivers 1245 The local oscillator requency and thus the transmission requency is adjusted by changing the divider actor n 4. I the local oscillator requencies are not divisible by C, then the reerence requency must be divided by means o the divider actor n 3 to the largest common divisor o C and the local oscillator requencies and this common divisor must be multiplied by n 4. Example: In Fig. 24.81 on page 1225, a QPSK modulator with I/Q mixer is to be converted into a transmitter with one intermediate requency that is capable o a data rate o 200 kbit/s at a roll-o actor r = 1. A crystal oscillator with REF = 10 MHz is to be used as a reerence. The data rate D = 200 khz is obtained by division by a actor o 50. The carrier or intermediate requency is C = IF = 70 MHz since inexpensive SAW ilters are available or this requency. Since the I/Q mixer in Fig. 24.81 must be driven with the requency 2 C = 140 MHz, we select n 1 = 1 and n 2 = 14 or the IF PLL in Fig. 25.7. For QPSK, the symbol requency is equal to hal the data rate S = D /2, resulting in a bandwidth o = (1 + r) S = 200 khz. We assume that the transmitter can use 4 channels ranging rom 433 to 434 MHz with a channel spacing o C = 250 khz. From the transmission requencies RF = 433.125/433.375/433.625/433.875 MHz we obtain the local oscillator requencies LO = RF IF = 363.125/363.375/363.625/363.875 MHz. Since these are not multiples o C, we calculate the largest common divisor: lcd{k, LO }=125 khz. For the LO PLL this leads to n 3 = 10 MHz/125 khz = 80 and n 4 = LO /125 khz = 2905/2907/2909/2911. For all channels, the RF ilter must allow signal transmission without major group delay distortion and, at the same time, suiciently attenuate the highest local oscillator requency. The double-tuned-circuit bandpass ilter described in Sect. 26.2 can be set up or a center requency o 434.4 MHz and a bandwidth o 10 MHz. Thus the desired signal is attenuated by 6 d, while the local oscillator requency is reduced by more than 54 d and the portion below the local oscillator requency by more than 70 d. 25.2 Receivers The receiver has the task o iltering out the desired signal rom the antenna signal and ampliying it enough to eed it to the demodulator. In most instances, the receive requency is variable so that dierent channels, or example, various radio stations, can be received. As the signal level may vary widely depending on the distance between transmitter and receiver, the receiver must be provided with ampliiers o variable gain and gain control in order to compensate or the dierent levels o receive signals. Limiting ampliiers that convert the receive signal into a square wave signal and subsequent iltering can be used only or signals rom transmitters with pure angle modulation. First we shall describe receivers or analog modulation in which the receive signal is converted to an intermediate requency and then demodulated in an analog demodulator (or example, detector or AM and envelope discriminator or FM). Then we shall discuss the expansions to enable the reception o digital modulated signals.

1246 25 Transmitters and Receivers Preampliier Tuneable RF ilter Gain control VGA r Ant () t Demodulator r(t) RF a Direct-detection receiver rant () t RF IF Preampliier RF ilter IF ilter M1 Gain control VGA r IF () t Demodulator r(t) LO b Superheterodyne receiver (with one intermediate requency) Fig. 25.8. Types o receivers 25.2.1 Direct-Detection Receivers In the pioneer days o radio engineering, the direct-detector receiver shown in Fig. 25.8a was used. The receive signal was iltered by an RF ilter and ed directly to the demodulator ater a ixed or variable ampliication. The RF ilter needed tuning in order to receive the signals rom dierent radio stations. The only modulation technology that could be used was amplitude modulation since the envelope detector was the only demodulator that worked satisactorily with a variable carrier requency C = RF. All other demodulators must be set up or a ixed carrier requency or require requency-synchronous tuning according to the RF ilter. esides being limited to amplitude modulation, the direct-detection receiver has other signiicant draw-backs: The transmission requency must be no more than two orders o magnitude greater than the bandwidth o the signal to be received; otherwise, the quality o the RF ilter becomes too high. In the early days o broadcasting systems, there were only a ew stations with signiicantly diering transmission requencies. A simple resonant circuit was thereore suicient to ilter out the desired station. Tuneable ilters o high quality are expensive and can only be tuned to a very limited requency range i the bandwidth is to be maintained. On the other hand, the resonant circuits used in the early days allowed easy tuning by means o a variable capacitor. The entire ampliication must be done at the transmission requency, thus high-requency transistors with high quiescent currents and relatively low gains must be used.

25.2 Receivers 1247 With increasing requencies, the perormance o envelope detectors decreases due to the parasitic capacitance o the rectiier diode. With the growing density o transmitting stations and the use o higher requencies, the direct-detection receiver soon reached its limits. 25.2.2 Superheterodyne Receivers In the superhet(erodyne) receiver, the tuning o the RF ilter is replaced by the requency conversion rom a mixer with variable local oscillator requency LO. This converts the signal to be received to a ixed intermediate requency (IF requency): IF = RF LO RF An intermediate requency ilter (IF ilter) o a substantially lower quality Q IF IF IF RF RF Q RF is used to ilter out the signal. The variable ampliication and the demodulation are also done at the IF requency. Thus, all disadvantages o the direct-detection receiver are eliminated. Figure 25.8b shows the construction o a superhet receiver with one intermediate requency. RF Filters In the process o requency conversion, not only the desired receive requency RF = LO + IF but also the image requency RF,im = LO IF are converted to the IF requency (see Fig. 25.9). This causes a region located at the opposite side o the local oscillator requency to be converted to the pass band o the IF ilter. In order to prevent this, the RF ilter in ront o the mixer must be set up such that all desired receive requencies are within the pass band and the related image requencies in the cuto region (see Fig. 25.10). The RF ilter is thus also known as the image ilter. In practice, the RF ilter is designed such that the local oscillator requencies are also in the cuto region. This prevents the relatively strong signal o the local oscillator rom moving backwards into the pre-ampliier and to the receiving antenna. This characteristic is o high importance because the undesirable emission o local oscillator signals rom the Desired conversion IF Image requency conversion RF,im = LO IF RF ilter LO RF = LO + IF Fig. 25.9. Image requency in the superhet receiver

1248 25 Transmitters and Receivers R Ant IF IF C RF ilter RF,im = LO IF LO RF = LO + IF Fig. 25.10. RF ilter design in the superhet receiver receiving antenna is a major problem in the design o receivers which comply with EMC regulations. In practice, the local oscillator signals are not sinusoidal but present strong harmonic distortions. This results in additional image requencies o higher order on both sides o the harmonics o the local oscillator requency which are also converted to the pass band region o the IF ilter: RF,im(n) = n LO ± IF These image requencies and the corresponding harmonics o the local oscillator requency must also be suppressed by the RF ilter. The RF ilter must thereore provide a high stopband attenuation even above the range o reception. LC ilters or ilters with dielectric resonators are used in practical applications where two to our resonant circuits are typical. These ilters are called 2-, 3- or 4-pole ilters. The number o poles reers to the equivalent lowpass ilter and is thus equal to the number o resonant circuits 1. With an increasing receive requency and a constant IF requency, the relative dierence between the receive requency and the image requency becomes smaller and smaller; thus causing the quality Q RF RF IF o the RF ilter to increase. Where the separation o the receive and image requencies can no longer be achieved by reasonable means, it is necessary to either increase the IF requency in order to reduce the quality o the RF ilter or to use a superhet receiver with two intermediate requencies. It is also possible to conigure the RF ilter such that the requency LO IF below the local oscillator requency is used as the receive requency RF, while the corresponding image requency RF,im = LO + IF is suppressed. In this case, the mixer M1 operates in the inverted mode as the requency sequence is inverted due to the relation IF = LO RF ; but, with IF = RF LO, the mixer operates in the noninverted mode and the requency sequence remains the same. In noninverted mode, the image requency is below the receive requency, while in inverted mode, it is above. Thereore, the inverted mode is always used in cases where the requency range above the receive requency has clearly weaker signals than the requency 1 A simple resonant circuit has two poles: s =±jω 0. A ilter with our resonant circuits thereore has eight poles, but is still called a 4-pole ilter in practice since bandpass ilters with a lowpass/bandpass transormation are calculated on the basis o an equivalent lowpass ilter with hal the number o poles.

25.2 Receivers 1249 range below the receive requency; in this way it is easier to suppress the image requency. The inverted mode must be compensated or in the modulator or by an inverted mode in the transmitter. Pre-Ampliiers A low-noise ampliier (LNA) is used in ront o the RF ilter to keep the noise igure o the receiver low (see Fig. 25.8b). Without a pre-ampliier, the noise igure is according to (4.201): F r = F RFF + F M1 1 G A,RFF F RFF =D RFF G A,RFF =1/D RFF = D RFF F M1 Here, F RFF is the noise igure and G A,RFF is the available power gain o the RF ilter and F M1 is the noise igure at the input o mixer M1. The latter is calculated with (4.201) rom the noise igure o the mixer and the noise igures o the subsequent components.an overall impedance matching is assumed so that the noise igure o the ilter corresponds to the power attenuation D RFF in the pass band region, and the available power gain corresponds to the reciprocal value o the power attenuation. With the typical values D RFF 1.6 (2 d) and F M1 10 (10 d), the noise igure becomes unacceptably high: F r 16 (12 d). Using a pre-ampliier with noise igure F LNA and available power gain G A,LNA the noise igure is: F r = F LNA + F r 1 = F LNA + D RFFF M1 1 G A,LNA G A,LNA With a suiciently high gain this value is much smaller than the noise igure without a pre-ampliier and in the limiting case o a very high gain it approaches the noise igure o the pre-ampliier. In practice, the gain o the pre-ampliier cannot be increased without limits since at this point it is still the entire receive signal o the antenna that is ampliied. This means that both the signal to be received and, under good receiving conditions, the signals o neighboring channels can reach relatively high levels which may overdrive a pre-ampliier with too high a gain. In addition, a high gain in the RF range is achievable with great eort only.thereore, the gain is selected at a level which is high enough to reduce the noise igure o the receiver to an acceptable level. Typical values are F LNA 2 (3 d) and G A,LNA 10...100 (10...20 d). In the above example, these values lead to F r 2.15...3.5(3.3...5.4 d) compared to F r 16 (12 d) without pre-ampliication. IF Filters Due to the mixer, the entire pass band region o the RF ilter is shited to the intermediate requency range (see Fig. 25.11). Here, the channel with the desired receive requency is iltered out by the IF ilter. For this reason the IF ilter is also known as the channel ilter.it must have very steep edges since the transition region between the pass band and the cuto band must not be wider than the region between adjacent channels. Particularly well suited are surace acoustic wave (SAW) ilters which, despite extremely steep edges, have almost no group delay distortions. In contrast, the group delay distortions o LC or dielectric ilters increase with rising edge steepness. Filters with ceramic resonators (ceramic ilters) are used in applications that are relatively insensitive to group delay distortions, such is the

1250 25 Transmitters and Receivers IF IF rant () t R Ant RF ilter RF,im = LO IF LO RF = LO + IF R RFF IF RF ilter r t RFF () LO M1 LO RF = LO + IF r M1 () t R M1 IF IF ilter R IF IF ilter r IF () t IF Fig. 25.11. Signal spectra in a superhet receiver with one intermediate requency case in AM broadcasting or example. In digital modulation modes, on the other hand, group delay distortions have to be kept as low as possible and thus the use o SAW ilters is usually mandatory. Superhet Receiver with Two Intermediate Frequencies In the superhet receiver with two intermediate requencies as shown in Fig. 25.12, the receive requency is converted into a relatively high irst intermediate requency IF1, which is selected such that the separation o receive and image requencies can occur with an RF ilter o acceptable quality: Q RF RF IF1 Fig. 25.13 shows the signal spectra. IF ilter 1 ilters out a portion that contains the desired channel. It is not possible to ilter out the desired channel alone at this point because o the necessary high quality. IF ilter 1 serves as the image requency ilter or the second mixer, this means that the image requency IF1,im = IF1 2 IF2

25.2 Receivers 1251 r Ant (t) Preampliier RF ilter RF M1 IF ilter 1 IF1 M2 IF ilter 2 IF2 VGA r IF (t) LO1 LO2 Gain switchover Demodulator r (t) Fig. 25.12. Superhet receiver with two intermediate requencies must be within the cuto band o the ilter. To prevent a backwards transmission o the second local oscillator requency LO 2 = IF1 IF2 this requency must also be within the cuto band; consequently, the quality o the ilter is: Q IF1 IF1 IF2 Ater conversion to the second intermediate requency with the mixer M2, the desired channel is iltered out by means o IF ilter 2 which acts as the channel ilter. It is possible to operate one or both mixers in inverted mode by regarding the requencies LO 1 IF1 or LO 2 IF2 below the local oscillator requencies as the receive requencies. In this case, the RF ilter suppresses the image requency RF,im = LO 1 + IF1 while IF ilter 1 suppresses the image requency IF1,im = LO 2 + IF2. I only one o the mixers is operated in inverted mode, then the requency sequence is inverted, due to IF1 = LO 1 RF or IF2 = LO 2 IF1. This must be taken into account in the demodulator or must be compensated via an inverted mode in the transmitter. I both mixers are operated in inverted mode, the overall receiver operates in noninverted mode. The advantage o the superhet receiver with two intermediate requencies is that the quality or iltering out the desired channel can be distributed to two IF ilters Q IF IF1 = IF1 IF2 IF2 Q IF1 Q IF2 which is in contrast to the superhet receiver with one intermediate requency where the task must be perormed by one IF ilter. This is required whenever the receive requency RF is very high, meaning that a high (irst) intermediate requency IF1 is required in order to limit the quality o the RF ilter or i the bandwidth o the receive signal is very low. Generating the Local Oscillator Frequencies The local oscillator requencies required are derived rom a crystal oscillator by means o a phase-locked loop (PLL) which has already been explained in the description o transmitters (see page 1244 and Fig. 25.7). In receivers with a variable receive requency,

1252 25 Transmitters and Receivers r Ant () t R Ant IF1 IF1 RF ilter RF,im = LO1 IF1 LO1 RF = LO1 + IF1 R RFF IF1 RF ilter r RFF () t LO1 M1 LO1 RF = LO1 + IF1 IF2 IF2 r M1 () t R M1 IF ilter 1 IF1,im = LO2 IF2 LO2 IF1 = LO2 + IF2 R IF1 IF2 IF ilter 1 r IF1 () t LO2 M2 LO2 IF1 = LO2 + IF2 r M2 () t R M2 IF ilter 2 IF2 IF ilter 2 r t IF2 () R IF2 IF2 Fig. 25.13. Signal spectra in a superhet receiver with two intermediate requencies the requency o the irst local oscillator is varied by adapting the divider actors o the corresponding PLL.

25.2 Receivers 1253 VGA v i (t) v o (t) a Simpliied diagram VGA v = v ^ i (t) i cos t ^ v o (t) = vo cos t AV ( R ) Peak value measurement ^ v o V R ʃ ^ v setpoint b Equivalent circuit Fig. 25.14. Gain control 25.2.3 Gain Control A variable gain ampliier (VGA) and an amplitude detector are used or gain control as shown by a simpliied diagram in Fig. 25.14a. The VGA generates the voltage v o (t) = A(V R )v i (t) ˆv o = A(V R ) ˆv i (25.1) with the variable gain A(V R ) and the control voltage V R. A peak value rectiier is usually used to determine the amplitude. y comparing the rectiier output with the setpoint value an integrator generates the control voltage V R rom the dierence. Figure 25.14b shows the equivalent circuit or the gain control. Control Characteristic In steady state (operating point A) we have ˆv o =ˆv setpoint and V R = V R,A with: A(V R,A ) = ˆv setpoint ˆv i For examination o the dynamic response we linearize (25.1) at the operating point: ( ) d A A d ˆv o = ˆv i dv R + A(V R ) d ˆv i dv R A d A = ˆv i,a dv dv R + A(V R,A ) d ˆv i (25.2) R A }{{}}{{} k F k R

1254 25 Transmitters and Receivers VGA V i (s) k F V o (s) k R V R (s) 1 st I Fig. 25.15. Linear model o the gain control H R d k F 3d 20d/Dek. 3d [log] Fig. 25.16. Frequency response o the gain control Using actors k R and k F and the Laplace transorms V i (s) = L{d ˆv i }, V o (s) = L{d ˆv o }, V R (s) = L{dV R } we obtain the linear gain control model as shown in Fig. 25.15 eaturing the transer unction: H R (s) = V o(s) V i (s) = k F st I /k R 1 + st I /k R T R =T I /k R = k F st R 1 + st R Here, T I is the time constant o the integrator and T R the resulting time constant o the control circuit. This results in a highpass ilter with gain k F and a 3 d cuto requency o: 1-3d = = k R = ˆv i,a d A 2πT R 2πT I 2πT I dv (25.3) R A Figure 25.16 shows the requency response. Changes to the input amplitude with a requency, that is below the cuto requency, are better suppressed with decreasing requency; while changes with requencies above the cuto requency are ampliied with k F = A(V R,A ). The cuto requency must be less than the lower cuto requency o the amplitude modulation contained in the desired signal to prevent the desired signal rom being invalidated. According to (25.3) the cuto requency is proportional to the input amplitude ˆv i and to the derivative o the gain characteristic A(V R ). In order to prevent the cuto requency rom being dependent on the operating point, the condition d A k R = ˆv i = ˆv setpoint d A = const. dv R A(V R ) dv R must be met; it ollows: d A dv R = k R k R V R A(V R ) A(V R ) = A 0 e ˆv setpoint (25.4) ˆv setpoint

25.2 Receivers 1255 Thereore, the VGA must have an exponential gain characteristic. In practice, the gain is quoted in decibel, i.e. logarithmically, thus producing a linear relationship: A(V R ) [d] = A 0 [d]+ k RV R ˆv setpoint 8.68 d Variable Gain Ampliier (VGA) There are several circuit designs or constructing a variable gain ampliier (VGA). In integrated circuits, the VGA with dierential ampliiers or current distribution as shown in Fig. 25.17 is used almost exclusively. It oers a control range o approximately 60 d with the required exponential characteristic. The VGA cell consists o a common-emitter circuit with current eedback (T 1,R 1 ) and a dierential ampliier (T 2,T 3 ). The quiescent current is adjusted with resistances R 2 and R 3, while R 7 serves as the load resistance. The output current g m1 I C1 (t) = I C1,A + i C1 (t) = I C1,A + v i (t) 1 + g m1 R 1 o the common-emitter circuit is distributed by the dierential ampliier to the load resistance and the supply voltage; according to (4.61) 2 this is: I C3 = I ( C1 1 + tanh V ) R I C1 = 2 2V T 1 + e V R V T Taking the subsequent ampliier with gain A V into account, the small-signal output voltage is: v o (t) = A V i C3 (t)r 7 = A V i C1 (t)r 7 1 + e V R V T = A V g m1 R 7 v i (t) 1 + g m1 R 1 1 + e V R V T V b = 3V V b V b V b V b V b R 3 R 7 R 6 32 kω 8kΩ 32 k Ω I R7 1.4 V Ampliier V R 1.3 V 1.3 V I C2 I C3 I C5 I C6 T 2 T 3 T 5 T 6 1 1 1 1 A V =60d V o C 1 100 pf 0.7 V 0.75 V 0.75 V I C1,A = 200μA T 1 T 4 2 2 I C4,A = 200μA 0.7 V V i R 2 10 kω R 1 R 4 R 5 200Ω 200Ω 10 kω Fig. 25.17. VGA with dierential ampliiers or current distribution 2 Current I C1 corresponds to the quiescent current 2I 0 o the dierential ampliier.

1256 25 Transmitters and Receivers A d 90 80 70 60 50 40 30 20 10 0 180mV 0.33d/mV 60d 300 200 100 0 100 V R mv Fig. 25.18. Characteristic o the VGA o Fig. 25.17 ( = 3 MHz) A 90 d 80 70 60 50 40 30 20 10 0 10 20 V R =0V 50mV 100mV 150mV 200mV 250mV 300mV 2M 5M 100k 1M 10M 100M Hz Fig. 25.19. Frequency response o the VGA o Fig. 25.17 The control range is V R < 2V T. Here, the constant value o one is negligible with respect to the exponential unction, and the desired exponential gain characteristic is: v o (t) A V V g m1 R R 7 e V T v i (t) A(V R ) A V V g m1 R R 7 e V T (25.5) 1 + g m1 R 1 1 + g m1 R 1 Figure 25.18 shows the characteristic o thevga in Fig. 25.17 or a signal requency o 3 MHz. The control range covers 60 d with a slope o 0.33 d/mv. It is limited upward by the deviation rom the exponential shape and downward by the reverse attenuation o the VGA cell. The latter depends on the parasitic capacitances and becomes worse with a requency increase. Figure 25.19 shows the requency response or dierent control voltages. Above 10 MHz the gain drops at a rate o 20 d/decade; thus, the control range narrows accordingly. In this region, the minimum gain increases to 25 d due to the declining reverse attenuation o the VGA cell. The change in the current distribution also changes the DC voltage at the output o the VGA cell making the galvanic coupling with the subsequent ampliier diicult. The change can be compensated by connecting a second VGA cell with the same quiescent current (T 4...T 6, R 4...R 6 ) in parallel and inversely controlling the dierential ampliier. Then we have I R7,A = I C3,A + I C6,A = I C1,A = I C4,A

25.2 Receivers 1257 and the DC voltage remains constant. Dimensioning the control circuit according to (25.3) requires actor k R to be determined. A comparison between (25.4) and (25.5) yields: k R = ˆv setpoint V T (25.6) Here, ˆv setpoint is the desired amplitude at the VGA output (see Fig. 25.14b). The time constant T I o the integrator can be calculated rom ˆv setpoint and the cuto requency 3d : T I = k R 2π-3d = ˆv setpoint 2π-3dV T (25.7) Localization o Gain Control in the Receiver In the direct-detection receiver o Fig. 25.8a, the gain control must be located in the RF section. This is inconvenient because the control range decreases with rising requencies and the RF requency is variable. In the superhet receiver with one intermediate requency shown in Fig. 25.8b, the gain control is located in the IF section behind the IF ilter. This arrangement is compulsory since, beore the IF ilter, the signal contains not only the desired channel but also all the adjacent channels with requencies in the pass band region o the RF ilter. In systems with received levels that vary extremely, the high levels require an additional gain reduction o the pre-ampliier in order to prevent the subsequent components rom being overloaded. The gain switchover o Fig. 25.12 serves this purpose. However, it only works well under the presumption that the high level is caused solely by the desirable channel. Thus, overdriving o the pre-ampliier by a neighboring channel can not be prevented. From these considerations, it ollows that an optimum operating range or all components is only possible i all ampliiers are made controllable by the level at their own output. This provides maximum sensitivity or the desired channel independent o the levels o adjacent channels. Such an elaborate design or the gain control is used in exceptional cases only. For most applications, a control system based on the level o the desired signal, as described here, is suicient. Level Detection In addition to the amplitude-controlled useul signal, many systems require a measure or the received level o the useul signal. Typical examples include the VHF broadcasting system with automatic stereo/mono switchover controlled by the received level, and mobile communication in which several base stations receive a signal transmitted rom a mobile unit and then the base station with the highest received level takes over the communication. Level detection can be based on the control voltage o the gain control. I the controllable ampliier has an exponential characteristic, the control voltage V R is a logarithmic measure or the received level. In steady state, (25.4) provides: ˆv setpoint = A(V R ) ˆv i = A 0 ˆv i e k R V R ˆv setpoint V R = ˆv setpoint k R ln ( ˆvsetpoint A 0 ˆv i )

1258 25 Transmitters and Receivers Using (25.6), it ollows or the VGA o Fig. 25.17: ( ) ( ) ˆvsetpoint ˆvi V R = V T ln V T ln A 0 1V 1V I ˆv i increases by a actor o 10 (20 d), V R decreases by V T ln 10 60 mv. Thereore, the slope o the level detection is 3mV/d. This simple level detection is conined to the exponential portion o the characteristic and depends on the temperature. Integrated receiver circuits usually provide a temperature compensated level signal positive with a slope which is called the received signal strength indicator (RSSI). Digital Gain Control With respect to the cuto requency o the gain control there are contradicting demands. On one hand, it should be as low as possible so that an amplitude modulation contained in the useul signal is not invalidated; whereas, on the other hand, it should be as high as possible so that ollowing a channel switchover, the steady state is reached in the shortest time possible. One method o optimization is to switch over the time constant o the integrator. In normal operation a large time constant with a correspondingly low cuto requency is used, but in the case o large deviations, or example ollowing a switchover to another channel, the system changes to a smaller time constant. A more lexible and suitable solution is to use a digital gain control according to Fig. 25.20. Here, a microcontroller evaluates the received signal strength indicator (RSSI) o the last IF ampliier and perorms a gain adaptation o the RF and IF ampliiers. Here, too, the majority o the control range has to be covered by the last IF ampliier because all other ampliiers also boost the neighboring channels. I, in addition to the desired channel, the neighboring channels have comparably high levels, then the risk o overdriving exists. Switching the three ampliiers on the input side o Fig. 25.20 is optional. In practice, usually only one ampliier is switched over. Very oten the digital gain control is perormed in steps o 2...4 d resolution in accordance with the gain graduation o the last IF ampliier. The gain is adjusted by a binary command (n VGA it in Fig. 25.20). The change in gain is done either by a gain switchover in the individual ampliier stages or by using programmable attenuators between the stages. RF ilter LO IF ilter VGA r Ant (t) r IF (t) RSSI Optional Optional Optional n VGA Microcontroller A D Fig. 25.20. Digital gain control

25.2 Receivers 1259 The microcontroller can evaluate the received level by averaging relatively quickly the RSSI signal, while at the same time taking into account the current ampliier setting. The microcontroller can thus programme all controllable ampliiers in one step with high accuracy, thus signiicantly reducing the transient time. Following this pre-setting, the duration o averaging is increased so that only amplitude variations with requencies below the lower limit o the desired signal amplitude modulation are adjusted. In practice, the gain is set by a central microcontroller that controls the overall system. Thereore, it is particularly easy to adapt the perormance to the given mode o operation (normal reception, channel switching, search mode, etc.). 25.2.4 Dynamic Range o a Receiver The dynamic range o a receiver corresponds to the dierence between the maximum and minimum received level. The maximum received level is determined by the maximum permissible intermodulation distortions and depends on the intercept point o the receiver. The minimum received level ollows rom the minimum signal-to-noise ratio at the input o the demodulator and depends on the noise igure o the receiver. In turn, the intercept point and noise igure o the receiver are dependent on the intercept points, the noise igures and the gain actors o the individual components. Thereore, the main task in designing a receiver is the selection o components with suitable characteristics. On one hand, the perormance o the signal processing chain is limited by its weakest member, while on the other hand, components with unnecessarily high characteristics are either expensive or have a high power consumption. Thus, the selection o components must be balanced between the two extremes in order to achieve an optimum result. In the example below, the dynamic range o the receiver shown in Fig. 25.21 is calculated. It is assumed that the receiver picks up channels in the range o 434 MHz with a bandwidth o = 200 khz and a channel spacing o C = 250 khz. We use a receiver with one intermediate requency IF = 70 MHz. Two identical RF ampliiers with gain A = 12 d are used in the RF stage where RF ampliier 1 corresponds to the pre-ampliier in Fig. 25.8a. The RF ilter or suppressing the image requency RF,im = RF 2 IF = 434 MHz 2 70 MHz = 294 MHz is arranged between the two RF ampliiers and is designed as a two-circuit bandpass ilter with an attenuation o 6 d (A = 6d). A programmable attenuator perorms the gain switching to adapt the received level. The attenuator perormance can be switched between 1 d and 25 d (A 1 = 1 d, A 2 = 25 d). It should be noted in this respect that the noise igures o a passive reactive ilter and an attenuator correspond to the respective attenuation.a diode mixer with a conversion loss o 7 d (A = 7d) and a noise igure o 7 d is used as the mixer. Two identical IF ampliiers with gain A = 25 d, and the IF ilter arranged between them, ollow in the IF stage.the IF ilter is a surace acoustic wave (SAW) ilter with a center requency o 70 MHz and a bandwidth o 200 khz. The attenuation is 24 d (A = 24 d). This is ollowed by a variable gain IF ampliier that provides the

1260 25 Transmitters and Receivers variable gain IF ampliier IF ampliier 2 RF ilter IF ilter IF ampliier 1 LO RF ampliier 2 RF attenuator RF ampliier 1 vi () t vo () t A =12d A = 6 d A 1 = 1d A =12d A = 7d A =25d A = 24d A =25d A 1 =67d F =3d F =6d F 1 =1d F =3d F =7d F =4d F =24d F =4d F 1 =20d IP3 =8dm A 2 = 25d IP3 =8 dm IP3=8dm IP3=18dm A 2 =13d IP3 = 7dm 91 dm 97 dm 98 dm 86 dm 93 dm 68 dm 92 dm 67 dm 0 dm 13 dm 19 dm 44 dm 32 dm 39 dm 14 dm 38 dm 13 dm 0 dm 103 dm 25 dm 3.2 μ V 2.8 μ V 11.2 μ V 5μ V 89 μ V 5.6 μ V 100 μ V 224 mv 1.6 μ V 6.3 μ V 25 mv 1.4 mv 5.6 mv 2.5 mv 45 mv 2.8 mv 50 mv 224 mv 12.6 mv 50 mv 6d 5d 17d 10 d 35 d 11 d 36 d 103 d 6d 19 d 7d 14 d 11 d 13 d 12 d 25 d 0d 12 d 0d 12 d 141000 1 4 2 1.8 7.1 3.2 56 3.5 63 18 1 4 2 0.11 0.45 0.2 3.5 0.22 4 250 1.5 99 3200 12.6 4000 1.5 10 4 50 1 3.2 3 0.26 16 4 1 1 F Z Π A 2 1 0.19 0.07 0.31 0.08 0.15 0.08 0.12 0.025 (i) F Z F Z,r = 2.025 F r 3 (4.8 d) 0.1 V 0.56 V 0.07 V 1.78 V 0.11 0.45 0.2 3.5 0.56 V 4 2 v o,ip3 Π A v i,ip3 = 0.124 V ( 5.1 dm) 0.5 V 0.35 V 1.24 V 0.91 V 0.14 V Signal level min [dm] max Signal level [V] min max (i) v o,ip3 Gain min [d] max Gain min max Calculation o noise actor Calculation o intercept point IP3 Fig. 25.21. Example or calculating the dynamic range o a receiver

25.2 Receivers 1261 subsequent demodulator with a constant output level o 0 dm (v e = 224 mv) 3.Itis based on the VGA o Fig. 25.17 and has a high noise igure o 20 d which is typical or VGA cells. Noise Figure o the Receiver To calculate the noise igure F r o the receiver, we assume that all components are matched to the characteristic impedance and the quoted gain actors in decibel correspond to the available power gain G A ; it thus ollows: G A [d] = A [d] G A = A 2 The noise igure can be calculated with (4.201): F r = F 1 + F 2 1 + F 3 1 + (4.199) = 1 + F Z1 + F Z2 G A1 G A1 G A2 A 1 2 + F Z3 A 1 A 2 2 + Here, F Z = F 1 is the supplementary noise igure o the respective component. In Fig. 25.21 the noise igures o the components are quoted in decibel, and with F [d] F Z = 10 10 1 we obtain the supplementary noise igures stated in the upper portion o the table. eneath the supplementary noise igures, the power gains at the input o the receiver, up to the input o the given component, are stated ( A 2 ). This allows us to convert the supplementary noise igures to the input o the receiver: F (i) Z = F Z A 2 The supplementary noise igure and the noise igure o the receiver are obtained by arithmetic addition: F Z,r = F (i) Z F r = F Z,r + 1 For the receiver in Fig. 25.21, F Z,r 2 and F r 3 (4.8d). Ater conversion to the input, the supplementary noise igures o the components indicate their individual contribution to the supplementary noise igure o the receiver. This shows which o the components must be o low-noise design to ensure that the noise igure o the receiver is markedly reduced and which o the components may have a higher noise igure without causing a noticeable increase in the noise igure o the receiver. In the receiver o Fig. 25.21, the contribution o the irst RF ampliier dominates, ollowed by the contributions o the second RF ampliier and the RF ilter. Under practical considerations the receiver appears to be well balanced since the noise igures o the RF ampliiers may only be decreased with a great eort. The irst RF ampliier oten requires a compromise between a low noise igure and a high intercept point. A high intercept point necessitates eedback and this causes an increase in the noise igure. 3 The 0 dm level corresponds to a power o 1 mw at 50 : P = v2 e 50 = 1mW v e = 223.6mV v e [dm] = 20 log v e [V] 0.2236 V

1262 25 Transmitters and Receivers Minimum Received Level The minimum received level P i,min is determined by the eective noise power P n,i at the receiver input and the minimum required signal-to-noise ratio SNR i,min or an error-ree demodulation o the received signal: SNR i,min = P i,min P i,min = SNR i,min P n,i (25.8) P n,i The minimum received level is also called the sensitivity, where a lower minimum received level is the same as an increased sensitivity. The eective noise power results rom the thermal noise power density N 0, the bandwidth and the noise igure F r o the receiver: T =300 K P n,i = N 0 F r = kt F r = 4.14 10 21 W Hz F r (25.9) Consequently: P n,i [dm] = 174 dm + 10 d log Hz + F r [d] (25.10) Insertion into (25.8) yields the minimum received level: P i,min [dm] = 174 dm + 10 d log Hz + F r [d]+snr i,min [d] (25.11) The minimum received level essentially depends on the bandwidth. Thereore, the minimum received level o a system with a high data rate and a resulting high bandwidth is greater than that o systems with a low data rate, provided the systems use the same modulation mode (same as SNR i,min ) and receivers with the same noise igure. An increase in the data rate by a actor o 10 increases the minimum received level by 10 d. We assume that the receiver in Fig. 25.21 receives a QPSK-modulated signal with a maximum symbol ailure rate o 10 6. According to [25.2] this requires a power eiciency o E b /N 0 = 13 d. With the required power eiciency, the assumed data requency D = 200 khz, and the bandwidth = 200 khz 4, equation (24.83) provides the required signal-to-noise ratio: ( ) Eb D SNR i,min [d] = [d] = 13 d N 0 Insertion into (25.11) with = 200 khz and F r 5 d leads to the minimum received level: P i,min [dm] = 174 dm + 53 d + 5d + 13 d = 103 dm This corresponds to an rms voltage o 1.6 mv. Maximum Received Level The maximum received level depends on the permissible intermodulation distortions. The dominating intermodulation o 3rd order (IM3) is as described by the intermodulation ratio 4 We presume a QPSK system with a data rate r D = 200 kbit/s and a roll-o actor r = 1. This results in a data requency o D = 200 khz, the symbol requency S = D /2 = 100 khz (two bits per symbol) and the bandwidth = (1 + r) S = 200 khz (see (24.84)).