1. Modulation And De-modulation Radio Frequency Transmission Information signal are transported between a transmitter and a receiver over some form of transmission medium. The information signal typically a voice and a digital signal is very low frequency and not suitable for transmission. Therefore they must be transformed from their original form into a form that is more suitable for transmission. The process of impressing low frequency information signal onto a high-frequency carrier signal is called modulation. Demodulation is the reverse process where the received signals are transformed back to their original form.

2. Principles of Amplitude Modulation Amplitude modulation (AM) is the process of changing the amplitude of a relatively high frequency carrier signal in accordance with the amplitude of modulating information signal. AM modulators are nonlinear devices with two input signals: a single-frequency constant amplitude carrier signal and the information signal. The output from the modulator is the frequencies that are high enough to be efficiently radiated by an antenna and propagated through free space and are commonly called radio frequency or simply RF.

3. Principles of Amplitude Modulation Using trigonometric functions, the sine-wave carrier can be expressed as: A modulating sine-wave signal can be expressed as:

4. The instantaneous value of either the top and bottom voltage envelope, v 1 can be calculated as: The instantaneous value of the complete modulated wave is: By using the trigonometric function:

5. 3-1: AM Concepts Figure 3-3: Amplitude modulator showing input and output signals. V m sin2  f m t sin2  f c t is the characteristic of AM. The AM wave is the product of the carrier and modulating signals. The circuit used for producing AM is called a modulator.

6. The AM Envelope Although there are several types of amplitude modulation, AM double-sideband full carrier (DSBFC) is the most commonly used. This type of modulation is sometimes called conventional AM or simply AM. Figure 28 shows how an AM waveform is produced when a single-frequency modulating signal acts on a high-frequency carrier signal. The output waveform contains all the frequencies that make up the AM signal and it is used to transport the information through the system. The shape of the AM signal is called the AM envelope.

7. Figure 28: AM envelope.

8. Note that with no modulating signal, the output waveform is simply the carrier signal, however when the modulating signal is applied, the amplitude of the output wave varies in accordance with the modulating signal. The repetition rate of the envelope is equal to the frequency of the modulating signal and the shape of the envelope is identical to the shape of the modulating signal.

9. AM Frequency Spectrum And Bandwidth Figure 29 shows the frequency spectrum of an AM DSBFC. The spectrum extends from f c -f m(max) to f c +f m(max) where f c is the carrier frequency and f m(max) is the highest modulating signal frequency. The bands of frequencies between f c -f m(max) and the f c is called a lower sideband (LSB). The band of frequencies between f c and f c +f m(max) is called upper sideband (USB). Therefore the bandwidth (B) of an AM is equal to the difference between the highest upper side frequency and the lowest lower side frequency or two times the highest modulating signal frequency (B = 2 f m(max) ).

10. Figure 29: Frequency spectrum of AM DSBFC

11. Example: For an AM DSBFC modulator with a carrier frequency f c = 100 kHz and a maximum modulating frequency f m(max) = 5 kHz, determine: a) Frequency limits for the upper and the lower sidebands b) Bandwidth c) Upper side and lower side frequencies produced when the modulating signal is a single-frequency 3 kHz tone. d) Draw the output frequency spectrum.

12. Solution: a) LSB = [f c -f m(max) ] to f c = (100 – 5) kHz to 100 kHz = 95 kHz to 100 kHz. USB = f c to [f c – f m(max) ] = 100 to (100 + 5) kHz = 100 to 105 kHz b) Bandwidth, B = 2f m(max) = 2(5kHz) = 10 kHz. c) Upper side frequency: f USF = f c + f m = 100 kHz + 3 kHz = 103 kHz. Lower side frequency f LSF = f c - f m = 100 kHz - 3 kHz = 97 kHz

13. Solution: d) Output frequency spectrum

14. Modulation Index and Percentage of Modulation: Modulation index is a term that is used to describe the amount of amplitude change (modulation) present in an AM waveform. Percentage of modulation is a coefficient of modulation stated as percentage.  The amount, or depth, of AM is then expressed as the percentage of modulation (100 × m) rather than as a fraction.

15. Modulation index can also be read directly from the oscilloscope:

16. Example: Suppose that an AM signal, the V max(p-p) value read from the oscilloscope screen is 5.9 divisions and V min(p-p) is 1.2 divisions. (a) What is the modulation index? (b) Calculate V c, V m and m if the vertical scale is 2 V per division.

17. AM equation: The 1 st term is the carrier, the 2 nd term is the lower sideband and the 3 rd term is the upper sideband. V c and V m are peak values of the carrier and modulating sine waves, respectively. For power calculations, rms values must be used for the voltages. The power in the carrier and sidebands can be calculated by using the power formula P = V 2 /R, where P is the output power, V is the rms output voltage and R is the resistive part of the load impedance, which is usually an antenna. AM Power

18. Use just the coefficients on the sine and cosine terms in the power formula: V m = mV c, hence

19. is the rms carrier power P c. So, Ex: If the carrier of an AM transmitter is 1000 W and it is modulated 100% (m=1), the total AM power is :

20. Of the 1500 W, 1000 W is in the carrier. 500 W in both sidebands. Since the sidebands are equal in size, each sideband has 250 W. For a 100% modulated AM transmitter, the total sideband power is always one- half that of the carrier power. When the percentage of modulation is less than the optimum 100, there is much less power in the sidebands. Ex: For a 70% modulated 250 W carrier, the total power in the composite AM signal is 250 W is in the carrier, leaving 61.25 W in the sidebands. Hence, 30.625 W in each sideband.

21. AM Power distribution Power in unmodulated carrier can be defined as: The upper and lower sideband powers are: *

22. Rearranging yields ** Substituting * to **, we have: *** The total power in an AM wave is equal to the sum of the powers of the carrier, the USB and the LSB: #

23. Substituting *** in #, we have: Notice that the carrier power in the modulated wave is the same as the carrier power in the unmodulated wave. Thus, the power of the carrier is unaffected by the modulation process. In other words, if m increases, P t also increases.

24. AM Modulator Circuit The location in a transmitter where modulation occurs determines whether the circuit is a low or high-level transmitter. With low-level modulation, the modulation takes place prior to the output element of the final stage of the transmitter. An advantage of the low-level modulation is that less modulating signal power is required to achieve a high percentage of modulation. A small signal class A amplifier as shown in Figure 30 can be used to perform amplitude modulation. However, the amplifier must have two inputs: one for the carrier signal and the second for the modulating signal.

25. Figure 30: A single AM transistor modulator.

26. In this configuration, the carrier is applied to the base and the modulating signal to the emitter, therefore this circuit is called emitter modulation. With no modulating signal present, the circuit operates as a linear class A amplifier is simply the amplified carrier signal. However, when the modulating signal is applied, the amplifier operates nonlinearly and signal multiplication occurs. The disadvantages of emitter modulation is the amplifier operates class A, which is extremely inefficient and incapable of producing high-power output.

27. Medium-Power AM Modulator Figure 31 shows a single transistor medium power AM modulator. The modulating signal is applied to the collector while the carrier signal is applied to the base of the transistor. The circuit is called a collector modulator. The modulation takes place in the collector, which is the output element of the transistor. When the modulating signal is applied to the collector in series with the dc power supply voltage it adds to and subtracts from Vcc with a maximum peak modulating signal amplitude V m(max) = Vcc.

28. Figure 31: Medium power transistor AM DSBFC.

29. Figure 32: Output waveform.

30. High-Power AM Modulator Figure 33 shows a high power Am modulator that uses a combination of both emitter and collector modulations. The modulating signal is simultaneously fed into the collectors of the push-pull modulators and to the collector of the driver amplifier. Collector modulation occurs in Q1, thus the carrier signal on the base of Q2 and Q3 has already been partially modulated and the modulating signal power can be reduced.

31. Figure 33: High power AM transistor modulator

32. Amplitude Modulation Reception AM reception is the reverse process of AM modulation. Its simply to converts an amplitude-modulated wave back to the original source information. A typical AM receiver block diagram is shown below:

33. Peak Detector (Diode Detector) The AM signal will on and off the diode. RC low pass filter will filter out the high frequency signal (carrier +harmonic) and only the original information are recovered.

34. Single-Sideband Suppressed-Carrier Amplitude Modulation In conventional AM, a major drawback is, carrier power (contains no information) constitutes two-thirds or more of the total transmitted power. Uses twice the bandwidth (upper and lower side are identical). Thermal noise is doubled compared to SSB. Mathematically analysis Remove

35. DSBFC SSBFC SSBSC SSBRC ISBRC VSBFC

36. Angle Modulation Transmission Three properties of analog signal can be varied: amplitude, frequency and phase. Frequency and phase modulation are both form of angle modulation. The basic equation for an angle modulated sine wave is: Where: m(t) = angle-modulated wave V c = peak carrier amplitude  c = carrier radian frequency  (t) = instantaneous phase deviation (*#)

37. Frequency Modulation Frequency modulation (FM) is defined as varying the frequency of a constant-amplitude carrier directly proportional to the amplitude of the modulating signal at a rate equal to the frequency of the modulating signal. In FM, the carrier amplitude remains constant while the carrier frequency is changed by the modulating signal. As the modulating signal amplitude increases, the carrier frequency increases. If the amplitude of the modulating signal decreases, the carrier frequency decreases. Figure 36 shows the waveform for a sinusoidal carrier for which frequency modulation is occurred.

38. Figure 36: Frequency modulation of the sinusoidal signal.

39. PM/FM mathematical analysis Instantaneous frequency of the carrier is define as: Substituting 2  f C for  C : For a modulating signal v m (t),

40. Substituting V m (t) = V m cos(  m t) into, yields *#*#

41. Phase Modulation Phase modulation (PM) is defined as varying the phase of a constant-amplitude carrier directly proportional to the amplitude of the modulating signal at a rate equal to the frequency of the modulating signal. In PM, the carrier amplitude remains constant while the carrier phase is changed by the modulating signal. As the modulating signal amplitude increases, the carrier phase increases. If the amplitude of the modulating signal decreases, the carrier phase decreases. Figure 37 shows the waveform for a sinusoidal carrier for which angle modulation is occurred.

42. Figure 37: Angle modulation of a sine-wave carrier. Unmodulated carrier Modulating signal Frequency modulated wave Phase modulated wave

43. Phase Deviation, Modulation Index and Frequency deviation Equation *# that is being phase and frequency modulated by a single-frequency can be written in general form as: From equation , peak phase deviation or modulation index is: Where: V m = peak modulating signal (volts) KV m = peak phase deviation (radians) K = deviation sensitivity (radians/volt) For Frequency Modulation: Where: K 1 V m = frequency deviation (radians/second) K 1 = deviation sensitivity (radians/volt-second) Unitless

44. Frequency Deviation Frequency deviation is the change in frequency in the carrier when it is acted on by a modulating-signal frequency denoted as  f: Therefore the FM modulation index can be rewritten as:

45. Example a. Determine the peak frequency deviation (  f) and modulation index (m) for an FM modulator with a deviation sensitivity K1 = 5 kHz/V and a modulating signal V m (t) = 2cos(2  2000t). b. Determine the peak phase deviation (m) for a PM modulator with a deviation sensitivity K = 2.5 rad/V and a modulating signal V m (t) = 2cos(2  2000t). Solution: a. b.

46. Frequency Analysis Of The Angle Modulated Waves Modulation by a single frequency sinusoid: Recall back the general FM equation: To further analyse the equation, Bessel function identities can be applied: J n m is the Bessel function of the first kind of nth order with argument m. Equation  can be rewritten as:  

47. Expanding equation, yields :  

48. To solve for the amplitude of the sidebands, equation can be converted to: The next table is the Bessel function of the first kind for several values of modulation index. Modulation index of 0, produce no sidebands and the larger the modulation index, the more sets of frequencies produced. 

50. Example: For an FM modulator with modulation index m = 1, a modulating signal Vm(t) = Vmsin(2  1000t) and unmodulated carrier VC(t) = 10sin(2  5  10 5 t), determine a. Number of sets of significant side frequencies b. Their amplitudes c. Draw the frequency spectrum Solution: a. From the previous table, m = 1, there are three sets of significant side frequencies. b. The relative amplitude of the carrier and side frequencies are J 0 = 0.77(10) = 7.7V J 1 =0.44(10) = 4.4V J 2 =0.11(10) = 1.1V J 3 =0.02(10) = 0.2V c. Frequency spectrum

51. Bandwidth For low index modulation, the BW is: For high-index modulation, the BW is: By using Bessel table: Average Power Of An Angle-Modulated wave Unlike AM, the total power in an angle modulated wave is equal to the power of unmodulated carrier and independent of the modulating signal, modulation index and frequency deviation. Mathematically, average power in the unmodulated carrier is:

52. P c = carrier power (watts) V c = peak unmodulated carrier voltage (volts) R = load resistance (ohms) Total instantaneous power in an angle-modulated carrier is: Substituting m(t) gives: Expanding yields: }}

53. The second term of the equation }} consists of infinite number of sinusoidal frequencies and the average power is zero, therefore the average power of the modulated wave reduces to: The modulated carrier power is the sum of the powers of the carrier and the side frequency components, therefore the total modulated power is:

54. Example: a. Determine the unmodulated carrier power for the FM modulator and conditions given in the previous example (assume the load resistance is 50 ohm) b. Determine the total power in the angle-modulated wave: Solution: a. Unmodulated carrier power: b. Total power: The results shows that the power of the unmodulated wave and the modulated wave are equal.

55. Frequency Modulation Transmission Direct FM Modulators Direct FM is angle modulation in which the frequency of the carrier is varied directly by the modulating signal. Figure 38 shows a basic schematic diagram of the direct FM modulator. L and C m is the frequency-determining section for the LC oscillator. Figure 38: Simple direct FM modulator

56. The capacitor microphone is a transducer that converts acoustical energy to mechanical energy which is used to vary the distance between the plates of the microphone and consequently change its capacitor, C m. Because of the C m varied, the resonant frequency is varied, thus, the oscillator output frequency varies directly with the external sound source. This is direct FM because the oscillator frequency is changed directly by the modulating signal.

57. Varactor Diode Modulator Figure 39 shows the schematic diagram for a more practical direct FM generator that uses a varactor diode to deviate the frequency of a crystal oscillator. The varactor diode VD 1 is reverse biased by a potential divider R 1 and R 2 and determine the rest frequency of the oscillator. The external modulating signal voltage adds to and subtracts from the dc bias which changes the capacitance of the diode and subsequently the frequency of oscillation of the crystal oscillator. The alternating voltage across the varactor diode will cause the direct FM from the modulating signal. Varactor diode FM modulator is very popular because they are simple and reliable due to the stability of the crystal oscillator.

58. Figure 39: Varactor diode modulator.

59. However, because a crystal is used as a frequency stabilising element, the peak frequency deviation is limited to relatively small values. So that, they are used for narrowband modulation such as for voice modulation in walkie-talkies. Figure 40 shows the schematic diagram of the voltage- controlled oscillator (VCO) direct FM. Again, a varactor diode is used to translates the changes in the modulating signal amplitude to changes in frequency. The centre oscillation frequency for the oscillator is estimated as follows: (6)

60. Figure 40: Varactor diode VCO FM modulator.

61. With the modulating signal applied, the output frequency is: Where f is the new frequency of oscillation and  C is the change in varactor diode capacitance due to the excitation of the modulating signal. The change in frequency is: (7)

62. Reactance Modulator Figure 41 shows the schematic diagram for a reactance modulator using JFET as the active device. This circuit is called the reactance modulator because the JFET is a variable- reactance load to the LC tank circuit. Assuming an ideal JFET (gate current i g = 0), so that: where (8) (9)

63. Figure 41: Reactance FM modulator.

64. Therefore So that, JFET drain current is Where gm is the transconductance of the JFET, and the impedance between the drain and the ground is (10) (11) (12)

65. Substituting and rearranging gives us Assuming R<<<<X C, we have g m RC is equivalent to a variable capacitance and inversely proportional to resistance R, the angular velocity of the modulating signal (2  f m ) and the transconductance (g m ) of the JFET. (13) (14)

66. When a modulating signal is applied to the R 3, the gate-to- source voltage is varied accordingly, causing a proportional change in g m. As a result, the equivalent circuit impedance (Z d ) is a function of the modulating signal. Therefore the resonant frequency of the oscillator tank circuit is varied and the rate at which it changes is equal to f m. The output of the circuit is the FM.

67. Linear Integrated Circuit Direct FM Modulator Linear integrated circuit FM modulators can generate a direct FM output waveform that is relatively stable, accurate and directly proportional to the input modulating signal. The disadvantage of using LIC FM modulator is their low output power and the need for several additional external components for them to function such as the sinewave shaper because the output from the LIC FM modulator is a square or triangular wave rather than a sinewave. Figure 42 shows a basic block diagram for the LIC FM modulator. The VCO centre frequency is determined by external resistor and capacitor (R and C). The input modulating signal deviates the VCO frequency, which produces an FM output waveform.

68. Figure 42: A basic block diagram of the LIC FM modulator.

69. The analog multiplier will multiply the output frequency and the sinewave shaper converts the square to the sinewave output waveform. The unity gain amplifier provides a buffered output. The output frequency will be: Where  f is the peak deviation frequency. Figure 43 is the block diagram and the schematic diagram of the widely used LIC NE566 VCO FM modulator. External resistor R 1 at pin 6 sets the value of current produced by the internal current sources that is linearly charge and discharge external capacitor C 1 at pin 7. An external voltage, V c, applied at pin 5 is used to vary the amount of current produced by the current sources. (15)

70. Figure 43: A basic block diagram of the LIC FM modulator. (a) (b)

71. The Schmitt trigger is a level detector which controls the current source by switching between charging and discharging when the capacitor charges or discharges to a specific voltage level. A linear sawtooth of voltage is developed across the capacitor by the current source buffered by an amplifier and made available at pin 4. The Schmitt trigger output is a squarewave that is available at pin 3 and if the sinewave output is needed, the triangular wave is usually filtered with a tuned circuit resonant to the desired carrier frequency. A complete schematic diagram of the FM circuit using NE 566 is shown in Figure 43a. The current sources are biased with a voltage divider made up of R 2 and R 3. The modulating signal is applied through C2 to the voltage divider at pin 5. The 0.001  F capacitor between pin 5 and 6 is to prevent unwanted oscillations. The centre carrier frequency of the circuit is set by the values of R 1 and C 1.

72. The modulating signal can vary the carrier frequency over nearly a 10:1 range making very large deviations possible. Indirect FM Modulators Indirect FM is angle modulation in which the frequency of the carrier is deviated indirectly by the modulating signal. Figure 44 shows a schematic diagram for an indirect FM modulator. The modulator comprises of a varactor diode VD 1 in series with an inductive network L 1. The combined series-parallel network appears as a series resonant circuit to the output frequency from the crystal oscillator. A modulating signal is applied to VD 1, which changes its capacitance and consequently the phase angle of the impedance seen by the carrier varies, which result in phase shift in the carrier.

73. An advantage of indirect FM is that a buffered crystal oscillator is used for the source of the carrier signal, thus indirect FM are more frequency stable. A disadvantage of the indirect FM is that the capacitance- versus-voltage characteristic of a varactor diode are nonlinear so that the modulating signal must be kept quite small to minimise distortion, which limits the phase deviation to rather small values and its used for narrowband application. Figure 44: Indirect FM

74. FM Transmitter Direct FM Transmitter Figure 44 shows the schematic diagram for the Motorola MC1376 monolithic FM transmitter. The MC1376 is a complete FM modulator on a single 8-pin DIP (dual-inline-package) integrated-circuit chip. The MC1376 can operate with carrier frequencies between 1.4 MHz and 14 MHz and is intended to be used for producing direct FM waves for low-power applications such as cordless telephone. If the external transistor connected to the 12V supply voltage, output powers as high as 600 mW can be radiated.

75. Figure 44: MC1376 FM transmitter.

76. Crosby Direct FM Transmitter Direct FM transmitters produce an output waveform in which the frequency deviation is directly proportional to the modulating signal, consequently the carrier oscillator must be deviated directly. Therefore for medium and high-index FM systems, the oscillator cannot be a crystal because the frequency at which a crystal oscillates cannot be significantly varied. As a result the stability of the oscillators in direct FM transmitter often cannot meet Federal Communication Commission (FCC) specifications. To overcome this problem, automatic frequency control (AFC) is used. Figure 44 shows the block diagram for a commercial broadcast- band transmitter. This configuration is called a Crosby direct FM transmitter and includes an AFC loop.

77. Figure 45: Crosby FM transmitter.

78. The frequency modulator can be either a reactance modulator or a VCO. The carrier rest frequency is the unmodulated output frequency from the master oscillator (f c ) which is 5.1 MHz. This frequency is then multiplied by 18 in three steps to produce a final transmit carrier frequency f t at 91.8 MHz. Noted that the frequency deviation are multiplied as well, however the rate at which the carrier is deviated (the modulating signal frequency, f m ) is unaffected by the multiplication process. The purpose of the AFC loop is to achieve near-crystal stability of the transmit carrier frequency without using a crystal in the carrier oscillator. With AFC, the carrier signal is mixed with the output signal from a crystal reference oscillator and down- converted to 2 MHz and fed to the frequency discriminator.

79. A discriminator is the frequency-selective device whose output voltage is proportional to the difference between the input frequency and its resonant frequency. Therefore, the discriminator responds to the long-term, low frequency changes in the carrier centre frequency due to master oscillator frequency drift and because of low-pass filtering does not respond to the frequency deviation produced by the modulating frequency. If the discriminator respond to the frequency deviation, the feedback loop would cancel the deviation and remove the modulation from FM wave, this effect is called wipe-off.

80. Phase-locked-loop (PLL) FM Transmitter Figure 46 shows a wideband FM transmitter that uses a phase- locked-loop to achieve crystal stability from a VCO master oscillator and at the same time generate a wideband FM output signal. The VCO output frequency is divided by N and fed back to the PLL phase comparator where it is compared to a stable crystal reference frequency. The phase comparator generates a correction voltage that is proportional to the difference between the two frequencies. The correction voltage is added to the modulating signal and applied to the VCO input. The correction voltage adjust the VCO centre frequency to its proper value and the lowpass filter prevents changes in the VCO output frequency due to the modulating frequency to avoid wipe-out.

81. Figure 46: PLL FM transmitter.

82. Indirect FM Transmitter Indirect FM transmitters produce an output waveform in which the phase deviation is directly proportional to the modulating signal. Consequently, the carrier oscillator is not directly deviated. Therefore, the carrier oscillator can be a crystal because the oscillator itself is not the modulator. Therefore the stability with indirect FM transmitter can meet FCC specification without using the AFC. Figure 47 shows the wideband Armstrong indirect FM transmitter. With Armstrong transmitter, a relatively low- frequency subcarrier (f c ) is phase shifted 90º and fed to balanced modulator, where it is mixed with the input modulating signal (f m ). The output from the balanced modulator is double- sideband-suppress-carrier (DSBSC) wave that is combined with the original carrier in a combining network producing a low index phase-modulated waveform.

83. Figure 47: Armstrong indirect FM transmitter.

84. Because the suppressed-carrier voltage (V c ’) is 90º out of phase with V c, the upper and lower sidebands combine to produce a component (V m ) that is always in quadrature with V c. The output from the combining network is a signal whose phase is varied at a rate equal to f m and whose magnitude is directly proportional to the magnitude of V m. With Armstrong transmitter, the phase of the carrier is directly modulated in the combining network through summation, producing indirect frequency modulation.

85. FM Demodulator: Several circuit are used for demodulating FM signals. The most common are the slope detector, Foster-Seeley discriminator, ratio detector, PLL demodulator and quadrature detector. Tuned Circuit Frequency Discriminator Tuned circuit FM discriminator converts FM to AM and then demodulate the AM envelope with peak detector. Slope detector: A single-ended slope detector is the simplest form of tuned circuit frequency discriminator. The drawback is non-linear voltage versus frequency characteristic therefore seldom used.

86. Balanced Slope detector: Simply two single-ended slope detectors connected in parallel and fed 180  out of phase.