Let us consider the following block diagram of a feedback amplifier with input voltage feedback fraction,, be positive i.e. in phase.

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2 P a g e 2 Contents 1) Oscillators 3 Sinusoidal Oscillators Phase Shift Oscillators 4 Wien Bridge Oscillators 4 Square Wave Generator 5 Triangular Wave Generator Using Square Wave Generator 6 Using Comparator 7 Sawtooth Wave Generator 8 2) Wave Shaping Circuits Clippers 9 Using Diodes 9 Using Operational Amplifier 10 Clampers 11 Using Diodes 11 Using Operational Amplifier 12 3) Active Filters 12 Low Pass Filter First Order Low Pass Filter 13 Second Order Low Pass Filter 14 High Pass Filter First Order High Pass Filter 14 Second Order High Pass Filter 15 Band Pass Filter 16 4) Data Conversion Circuits 17 Digital to Analog Converter 17 Resistive Ladder or Weighted Resistor Ladder Method 18 R 2R Ladder or Binary Ladder Method 18 Analog to Digital Converter 20 Counter Type 20 Successive Approximation Type 20 5) Modulation techniques 21 Amplitude Modulation 22 Generation of AM Signal 24 Demodulator 24 Frequency Modulation 25 Characteristics of FM Signal 26

3 P a g e 3 The basic function of an oscillator is to generate alternating current or voltage waveforms of fixed amplitude and frequency without any external input signal. They are widely used in radio, televisions, computers and communications. An oscillator is basically a type of feedback amplifier in which part of the output is fed back to the input via a feedback circuit. When the signal fed back is of proper magnitude and phase, the oscillator circuit produces alternating current or voltages. Let us consider the following block diagram of a feedback amplifier with input voltage feedback fraction,, be positive i.e. in phase.. Let the Hence, the differential voltage, Let the gain of the amplifier be, is given as,. Hence, the output voltage is given as, Also, the feedback voltage is given as, Hence, the gain of the circuit is given as, Since, and, we get If expressed in polar form, the phase shift of the loop gain due to the circuit should be either or. Hence, the two basic requirements of an oscillator are, i) The magnitude of the loop gain should be at least. ii) The total phase shift of the loop gain should be either or.

4 P a g e 4 I. Phase Shift Oscillator The phase shift oscillator and its output waveform is as shown in figure, The circuit consists of an inverting Op Amp amplifier stage and three cascaded lead circuits as the feedback stage. As the Op Amp is used in the inverting amplifier mode, a phase difference of is introduced. The lead circuits produce a phase shift between and depending on the frequency. Hence, at some frequency, the total phase shift produced by the cascaded network is (approximately each). Hence, the total phase shift produced is. The frequency at which the total phase shift produced by the cascaded network is, is known as the frequency of oscillation of the oscillator. When the gain of the amplifier is sufficiently large, the circuit will oscillate at that frequency. The frequency of oscillation is given as, At this frequency, the gain of the amplifier must be at least. Hence, we get Hence, this circuit will produce a sinusoidal waveform of frequency and the total phase shift around the circuit is. if the gain of the amplifier is II. Wien Bridge Oscillator The Wien bridge oscillator is the standard oscillator circuit for low to moderate frequencies, in the range of to about. It is almost always used in commercial audio frequency generators and is usually preferred for other low frequency applications. The Wien bridge oscillator is as shown in the figure. The right hand figure depicts the oscillator in the bridge form. The circuit consists of an inverting Op Amp amplifier stage and the feedback stage is the Wien bridge which is basically a lead lag network. The lead lag network comprises of a series network in one arm and a parallel network in the other arm. This lead lag network provides a positive feedback from the output to the non inverting input. The inverting terminal receives a negative feedback from the output. Hence, the total phase shift around the circuit is. This condition occurs when the bridge is balanced or at resonance. The frequency of oscillation is exactly the resonant frequency of the balanced Wien bridge and is given as,

5 P a g e 5 Initially, there is more positive feedback than the negative feedback. This helps the oscillations to build up when the power is turned on. At power up, the input resistance (commercially a tungsten lamp) has low resistance and the negative feedback is small. Hence, the loop gain is greater than. This helps the oscillations to build up to the resonant frequency. As the oscillations build up, the tungsten lamp heats up slightly and its resistance increases. In most circuits the current is not enough to make the lamp glow but the change in resistance value is appreciable. At some high output level, the tungsten lamp has a resistance of value so that the closed loop gain is given as, The lead lag feedback circuit has a gain of. Hence the total gain is, The closed loop gain from the non inverting input to the output is greater than when the power is turned on. And hence the total gain is greater than. As the input resistance increases, the closed loop gain decreases and the total gain becomes equal to. At this point, the oscillations become stable and the output voltage has a constant peak to peak value. A square wave generator along with its output waveform is as shown in figure, Square wave waveforms are generated when the Op Amp is forced into saturation. That is, the output of the Op Amp is forced to swing repetitively between positive saturation and negative saturation, resulting in a square wave output. The square wave generator is also called as free running or astable multivibrator. Initially, the voltage across the capacitor is zero volts and hence the input to the inverting terminal of the Op Amp,. But there is a very small finite voltage at the non inverting terminal due to the output offset voltage. Thus the differential input voltage is given as,

6 P a g e 6 This input voltage is enough to drive the Op Amp to saturation. Let us say that the offset voltage is positive. Then the Op Amp is driven to positive saturation. With the output voltage of the Op Amp at, the capacitor starts charging towards through the resistor. The output still continues to stay at. As the voltage across the capacitor increases beyond the value, the output of the Op Amp is forced to switch to negative saturation,. The voltage across resistor is given as, Thus the differential voltage now becomes negative and holds the output of the Op Amp in negative saturation. The output remains in negative saturation until the capacitor discharges and then recharges to a negative voltage slightly higher than. As soon as the capacitor s voltage becomes more negative than, the differential voltage becomes positive and the Op Amp is again driven back to positive saturation,. The voltage is given by, In general, the voltage is given by, and the sign of the differential voltage decides the sign of the output waveform. The time period of the square waveform is given as, Hence the frequency of the square wave is given as, If, we get I. Using Square Wave Generator A triangular wave generator can be simply created using connecting an integrator to the output of a square wave generator as shown in figure, When the integrator is fed a square wave signal, the output produced by it is a triangular wave. Using this property of the integrator, we can create a triangular wave generator using a square wave generator

7 P a g e 7 and an integrator. The frequency of oscillation of the triangular wave generator is same as that of the square wave. Hence, For the output waveform to be a stable triangular wave, the product period,. should be equal to time II. Using Comparator A triangular wave generator can be created using a comparator and an integrator as shown in figure, The comparator compares the voltages and at the inverting and non inverting terminals respectively. As the voltage is fixed at, the comparator s output depends entirely on the voltage. When the voltage is less than, the Op Amp goes into negative saturation, and when above, the output is. Thus, the output is a square wave. This waveform is fed to the inverting integrator. An integrator produces triangular wave when the input is a square wave. For, the output is a negative going ramp and vice versa. One end of the voltage divider is connected to output of the comparator and the other end is connected to output of the integrator. Hence, when, the output of the integrator is a negative going ramp. When the negative going ramp attains a certain value,, the voltage dips below and the output becomes. And hence the output of the integrator becomes positive going and continues to do so until it reaches a maximum value,. At this point, the voltage rises above and the output becomes and the output of the integrator becomes negative going. These conditions are shown in the figure above. At the time of switching from to, the voltage at point is. This means that the voltage must be developed across and must be developed across. Hence we get, Similarly, when switches to, we get The peak to peak output amplitude of the triangular wave is, where,

8 P a g e 8 The time required for the output waveform to switch from to and vice versa is equal to half the time period,. The equation for the integrator s output voltage is given as, Here,,,, and. Hence, we get Hence, Since,, we get The frequency of oscillation is given as, A sawtooth wave generator along with its output waveform is as shown in figure, The basic difference between a triangular and sawtooth waveform is that in case of a sawtooth wave, rise and fall times are unequal. That is, it may rise positively many times faster than it falls or vice versa. The circuit for the sawtooth waveform generator is same as that of the triangular waveform generator with the difference that a voltage varying between and is applied to the non inverting input of the integrator. This introduces a dc voltage is inserted in the output of the integrator. Suppose the voltage is adjusted towards, then the dc level introduced will increase the rise time of the output voltage. Hence, the output obtained will be having unequal rise and fall times. Such type of a waveform is called as the sawtooth waveform.

9 P a g e 9 I. Clippers Clippers or limiters are circuits used to remove part of the input signal above or below a specified voltage level. Such wave shaping circuits are common in digital computers and communication devices. They not only are useful in signal shaping but also in protecting the circuits that receive the signal. A clipper which removes the positive part of an input signal is called a positive clipper and the one which removes the negative part of an input signal is called a negative clipper. Clipping circuits can be constructed using diodes and Op Amps. a. Using Diodes Let us consider that a sine wave as shown in the figure is fed to a positive clipper. During the positive half cycle of the input voltage, the diode turns on and the ideal output voltage across the load resistance is zero. But practically, the output is. During the negative half cycle, the diode is reverse biased and looks open to the input voltage and hence the negative half cycle drops across the load resistance,. Typically, the load resistance is at least 100 times greater than the series resistor,. The positive clipper along with its output waveforms is shown in figure. Positive Clipper Negative Clipper We can also introduce dc levels to shift the level of clipping of the input waveform. Let us suppose, we introduce a voltage,, in the circuit. Now, the circuit will clip the positive half cycle at. In a similar fashion, the waveform will be clipped at, when a negative voltage,, is introduced in the circuit. Care should be taken that the input voltage should be greater than the reference voltage i.e.. The clipping circuits along with the output waveforms are shown above. In a similar fashion, a negative clipper can be produced in which the diode will turn on during the negative half cycle and thus clipping the negative half cycle of the input waveform. Such a clipper along with its output waveforms is shown in the figure above.

10 P a g e 10 b. Using Operational Amplifier A positive clipper circuit using an operational amplifier and a diode is as shown in figure. In the circuit, the Op Amp is used as a voltage follower with a diode in the feedback path. The clipping level is determined by the reference voltage, which should be less than the input voltage range of the Op Amp. During the positive half cycle of the input voltage, the diode conducts until the input voltage is less than or equal to the reference voltage i.e.. When the input voltage is less than the reference voltage, the input to the inverting terminal of the Op Amp is greater than that at the non inverting terminal. As the reference voltage is positive, the output voltage of the Op Amp becomes sufficiently negative to drive diode into conduction. When the diode conducts, it closes the feedback loop and the Op Amp operates as a voltage follower i.e. the output voltage follows input till. When the input voltage becomes greater than the reference Input Voltage voltage i.e., the output voltage of the Op Amp becomes sufficiently positive to drive diode into cutoff. This opens the feedback loop and the Op Amp operates in open loop. It further drives the output of the Op Amp towards saturation. With diode reverse biased, the output voltage of the clipper is. Thus, when, we get. When the input voltage again becomes less than or equal to the reference voltage, the diode again starts conducting and the Op Amp acts as a voltage follower and the output. For the negative half cycle of the input voltage, input voltage is always less than the reference voltage i.e.. Hence, the diode conducts for the full half cycle and the output is. Output Voltage Thus, the diode is reverse biased when and forward biased when. If the reference voltage is derived from the negative supply, the reference voltage will be negative. The output waveform above is clipped off and the output follows the input only when. The waveforms are as shown in the figure above. In case of a negative follower, the negative part of the input signal is clipped off. Here, the diode conducts when and the output follows the input while for, the diode is reverse biased and the output is obtained with negative half cycle of the input waveform clipped at reference voltage,. The circuit along with the output waveform is as shown below,

11 P a g e 11 II. Clampers In clamper circuits, a predetermined dc level is added to the output voltage i.e. the output is clamped to a desired dc level. If the clamped dc level is positive, the clamper is called a positive clamper. On the other hand, if the clamped dc level is negative, the clamper is called a negative clamper. Clampers are also called dc inserter or resorter. Clamper circuits can be constructed using diodes and Op Amps. a. Using Diodes Let us consider a positive dc clamper with input and output waveforms, On the first negative half cycle of the input voltage, the diode turns on. At the negative peak, the capacitor charges to the peak value,. Slightly beyond the negative peak, the diode shuts off. The time constant is made greater than the time period of the input signal. Hence, the capacitor remains almost fully charged during the off time of the diode. The capacitor now acts like a battery of volts. Thus, a positively clamped signal is produced. A predetermined dc level can also be introduced by using a battery in the circuit. In this case, the signal is clamped at the positive dc level. Such a clamper along with the waveforms is shown below, For a negative clamper, the direction of the diode has to be changed. The polarity of the capacitor voltage reverses and the voltage is clamped to a negative dc level. A negative clamper with and along with the output waveforms is as shown in figure,

12 P a g e 12 b. Using Operational Amplifier A positive clamper using an operational amplifier and a diode is as shown in figure. The reference voltage is obtained from the positive supply of the Op Amp,. The output of the peak clamper is a net result of ac and dc input voltages applied to the inverting and non inverting terminals of the Op Amp. We have to consider each input separately to understand the circuit operation. Let us first consider the input voltage to the non inverting terminal. A positive reference voltage, is applied to this terminal. This voltage will make the output of the Op Amp, positive and hence the diode will be turned on. This closes the feedback loop and the Op Amp operates as a voltage follower. This is possible as the input capacitor,, is open for dc voltages. Hence, the output voltage of the circuit,. The input voltage,, is applied to the inverting terminal. During the negative half cycle of the input, the output voltage of Op Amp,, is positive and sufficient enough to forward bias the diode. As the diode conducts, it charges the capacitor to the negative peak value,, of the input signal. During the positive half cycle of the input, output voltage of Op Amp,, is negative and reverse biases the diode. Hence, the voltage,, acquired during the negative half cycle is retained. This retained voltage is in series with the positive peak voltage,. Hence, the output voltage is now. The net output voltage is now,. A negative clamper can be created by reversing the direction of the diode and using negative reference voltage by using the negative supply,. Such circuit along with its output waveform is as shown below, An electric filter is a frequency selective circuit that passes a specified band of frequencies and blocks or attenuates signals of frequencies outside this band. The filters can be classified as, i) Low Pass Filter Frequency Range: ( higher cutoff frequency) ii) High Pass Filter Frequency Range: ( lower cutoff frequency) iii) Band Pass Filter Frequency Range: iv) Band Reject Filter Frequency Range: and v) All Pass Filter

13 P a g e 13 There are many possible filter designs such as Butterworth, Chebyshev, Bessel and others. We will discuss Butterworth or maximally flat filters. I. Low Pass Filter a. First Order Low Pass Filter A first order or one pole low pass Butterworth filter using an Op Amp is as shown in figure. The Op Amp is used in non inverting mode. The resistors and determine the gain of the filter. According to the voltage divider rule, the voltage across the capacitor at the non inverting terminal is given by, where, Hence, we get and The output voltage of the non inverting operational amplifier is given as, The gain of the filter is given as, where, passband gain of the filter frequency of the input signal higher cutoff frequency of the filter The gain magnitude and the phase angle equations are given as, The operation of the filter can be understood in the following way, i) At very low frequencies,, ii) At,

14 P a g e 14 iii) At, All these conditions are as shown in the output waveform as shown in figure. The low pass filter has a constant gain from to higher cutoff frequency. At, the gain is and after that decreases at a constant rate with an increase in frequency. When the frequency is increased tenfold (one decade), the voltage gain is divided by. In other words, the gain decreases each time the frequency is increased by. Hence, gain decreases after. b. Second Order Low Pass Filter A second order or two pole low pass Butterworth filter using an Op Amp is as shown in figure. A first order low pass filter can be converted into a second order type by using an additional network. The gain of the amplifier is set by resistors and. The higher cutoff frequency is determined by the resistors, and capacitors,. It is given as, To simplify, let us have, and. Hence, we get The magnitude of voltage gain is given as, The second order low pass filter also has a constant gain from to higher cutoff frequency. At, the gain is and after that decreases at a constant rate with an increase in frequency. When the frequency is increased tenfold (one decade), the voltage gain is divided by. In other words, the gain decreases each time the frequency is increased by. Hence, gain decreases after. II. High Pass Filter a. First Order High Pass Filter A first order or one pole high pass Butterworth filter using an Op Amp is as shown in figure. The Op Amp is used in non inverting mode. The resistors and determine the gain of the filter. According to the voltage divider rule, the voltage across the capacitor at the non inverting terminal is given by, where, Hence, we get and

15 P a g e 15 The output voltage of the non inverting operational amplifier is given as, The gain of the filter is given as, where, passband gain of the filter frequency of the input signal lower cutoff frequency of the filter The gain magnitude and the phase angle equations are given as,, The operation of the filter can be understood in the following way, i) At very low frequencies,, ii) At, iii) At, All these conditions are as shown in the output waveform as shown in figure. The high pass filter has a constant gain from lower cutoff frequency. At, the gain is and before that increases at a constant rate with an increase in frequency. When the frequency is increased tenfold (one decade), the voltage gain is divided by. In other words, the gain increases each time the frequency is increased by. Hence, gain increases till. b. Second Order High Pass Filter A second order or two pole high pass Butterworth filter using an Op Amp is as shown in figure. A first order high pass filter can be converted into a second order type by using an additional network. The gain of the amplifier is set by resistors and. The lower cutoff frequency is determined by the resistors, and capacitors,. It is given as,

16 P a g e 16 To simplify, let us have, and. Hence, we get The magnitude of voltage gain is given as, The second order high pass filter also has a constant gain from lower cutoff frequency. At, the gain is and before that increases at a constant rate with an increase in frequency. When the frequency is increased tenfold (one decade), the voltage gain is divided by. In other words, the gain increases each time the frequency is increased by. Hence, gain increases till. III. Band Pass Filter A band pass filter is a filter that has a passband between two cutoff frequencies, and such that. All frequencies below and above are attenuated. A band pass filter can simply be constructed by cascading a first order high pass filter followed by a first order low pass filter. One such filter with its output waveform is shown below. The high pass filter helps in removing all the frequencies below the lower cutoff frequency,. A passband is formed according to the figure of merit or quality factor of the filter. The low pass filter removes all the frequencies above the higher cutoff frequency,. The quality factor of the filter is given as, where, centre frequency, bandwidth of the frequency For Quality factor,, the passband will be wide and the filter is called a wide band pass filter while for, the passband will be narrower and the filter is called a narrow band pass filter. In case of a narrow band pass filter, the output voltage peaks at the centre frequency. The magnitude of gain of the filter is given as, where, total passband gain of the filter passband gain of the high pass filter passband gain of the low pass filter

17 P a g e 17 Digital systems are being used in almost every application because of their increasingly efficient, reliable and economic operation. With the development of the microprocessors, data processing has become an integral part of various systems. Data processing involves transfer of data to and from the computers via input/output devices. Digital systems use a binary system of data while the input/output devices handle analog data. Hence there is a need of interface between these two types of data types. On the basis of conversion of data, the converters are of two types, i. Digital to Analog converters (D A converters) ii. Analog to Digital converters (A D converters) I. Digital to Analog Converter In case of a digital to analog converter, binary data is converted into analog voltages. The basic problem in converting a digital signal into an equivalent analog signal is to change the digital voltage levels into one equivalent analog voltage. This can be done by designing a resistive network that will change each digital level into an equivalent binary weighted voltage. Let us consider the following truth table of a 3 bit binary signal, Let us make the smallest number equal to and largest number equal to. Now we need to define seven discrete analog voltage levels between and. The smallest incremental change in the digital signal is represented by the least significant bit (LSB),. Thus, we would like to have this bit cause a change in the analog output that is one seventh of the full scale analog output voltage. In our case, full scale analog output voltage is and hence bit will cause a change of at the output. We know that, i.e. the second bit represents a number that is twice the size of the bit. Therefore a in the bit position must cause a change in the analog voltage that is twice the size of the LSB. Hence, bit will cause a change of. Similarly, i.e. the third bit Bit wise Analog represents a number that is four times the size of the contribution Output bit. Hence, bit will cause a change of. The total output voltage is due to the sum of the individual contribution of the bit wise voltages. The above truth table can be redrawn giving the analog output voltages. The process can be continued and for each successive bit, the analog voltage value must be twice that of the preceding bit. Hence, if there are bits in a binary system and the full scale output voltage is then the LSB is given by,. The subsequent bit position will have the output voltage in the following sequence,,,,, A digital to analog converter can be constructed using two methods, a. Resistive Ladder or Weighted Resistor Method b. or Binary Ladder Method

18 P a g e 18 a. Resistive Ladder or Weighted Resistor Method In the weighted resistor method, resistances are selected in such manner that the voltage drops across the resistors is in such fashion that as we go from the LSB towards the MSB, the voltage drop increases by a factor of at each step. One such resistive ladder is shown in the figure. It can be seen that for each successive bit, the resistance value decreases by a factor of. As is the requirement of a Digital to Analog converter, the voltage drop at each successive resistance increases by a factor of. Hence, at each successive step larger currents are needed to be handled by the resistors. A Digital to Analog converter can be constructed using a weighted resistor and an operational amplifier as shown in the figure. The output voltage, is given as, where, is the feedback resistance of the Op Amp, is the input voltage and,, and are the binary states or. This type of D A converter has two drawbacks, 1. Precision resistors of different values are required which increases the cost of the converter. 2. The MSB resistor has to handle much greater current than the LSB resistor. b. R R or Binary Ladder Method The binary ladder is a resistive network whose output voltage is a properly weighted sum of the digital inputs. It is constructed of resistors that have only two values and and thus overcomes the need of precision resistors of smaller values. The left end of the ladder is terminated in a resistance and the output is obtained at the right end. The ladder is as shown in figure. Let us assume that all the inputs are grounded. Beginning at node, the total resistance looking into the terminating resistance is. The total resistance looking outward towards input is also. These two equivalent resistors can be combined to form an equivalent resistor of value. Now, if we look from node, the total resistance looking towards the terminating resistance is and towards input is also. Hence, again the equivalent resistance is found to be. Same is the case for node and node. Now let us have the digital input data as i.e., and are grounded and is connected to volts. The situation is as shown in figure.

19 P a g e 19 With this input signal, the binary ladder can be redrawn as shown on the right side of the figure. From the equivalent circuit, the output can be found as, Thus for at MSB position, the output voltage is. Now let us have the digital input data as i.e., and are grounded and is connected to volts. The situation is as shown in figure. With this input signal, the binary ladder can be redrawn as shown in the middle of the figure. The left hand side of the circuit can be converted into a Thevenin equivalent circuit with a resistance in series with a voltage source, as shown in right side of the figure. From this equivalent circuit, the output can be found as, Thus for at position, the output voltage is. Proceeding further in the same fashion we can find that the voltages for bit and bit (LSB) are and respectively. This satisfies the primary condition of a D A converter to have voltages increasing by a factor of for each successive bit. It is seen that each digital input is transformed into a properly weighted binary output voltage. For bits the output voltages for each bit will go as,. Hence the net output voltage will be given as, A Digital to Analog converter can be constructed using a R 2R ladder and an operational amplifier as shown in the figure. The output voltage, is given as, where, is the feedback resistance of the Op Amp, is the input voltage and,, and are the binary states or. This type of digital to analog converter is widely used in electronic operations.

20 P a g e 20 II. Analog to Digital Converter The process of changing an analog signal to an equivalent digital signal is accomplished by the use of analog to digital converter. An A D converter is used to change the analog signals from transducers (measuring temperature, pressure, vibration, etc.) into equivalent digital signals. These signals would then be in a form suitable for entry into a digital system. There are various ways to construct an A D converter. We will discuss the following two methods, a. Counter type A D converter b. Successive Approximation type A D converter a. Counter type A D converter A high resolution A D converter can be constructed using an Op Amp comparator and a variable reference voltage. This reference voltage is created using a binary counter and a binary ladder. This reference voltage is fed to the comparator and when it becomes equal to the input analog voltage, the conversion is completed. Block diagram of the counter type A D converter is as shown in the figure. First the bit counter is reset to all s. When a convert signal appears on the line, the gate opens and clock pulses are allowed to pass through to the input of the binary counter. The counter advances through its normal binary count sequence. This binary count is amplified and fed to the binary ladder. The binary ladder acts as a simple D A converter and converts the binary counter output into an equivalent analog voltage. This voltage varies with the counter output and hence is the ideal voltage for the comparator operation. When the reference voltage equals (or exceeds) the input analog voltage, the gate is closed and the counter stops and the conversion is complete. The number stored in the counter is now the digital equivalent of the analog input voltage. The method is much simpler but the conversion time required is longer than in other methods. Since, the counter always begin at zero and counts through its normal binary sequence, as many as counts may be necessary before conversion is complete. The average conversion time is or counts. For a bit converter having clock of time period, full scale count requires. The average conversion time is. b. Successive Approximation type A D converter The main component of the successive approximation type A D converter is an bit successive approximation register (SAR) whose output is applied to an bit D A converter. The analog output of the D A converter is then compared by the Op Amp comparator to the input analog signal which is applied to the other terminal of the comparator. Block diagram of the successive approximation type A D converter is as shown in the figure. The SAR comprises of a control logic unit, a binary counter and a level amplifier. When a convert signal appears on the line of the SAR, the SAR is reset by holding the start signal high. On the first clock pulse, the most significant output bit (MSB), of the SAR is set. The D A converter then generates an analog equivalent to the bit which is compared with the analog input voltage. When D A converter output is less than the input voltage i.e., the comparator output is low and the SAR will clear its MSB,. On the other hand if, the comparator output is high and the SAR will keep its MSB,.

21 P a g e 21 On the next clock pulse, the SAR will set the next MSB. Depending on the output of the comparator, the SAR will either keep or reset the bit. This process is continued until the SAR tries all the bits. As soon as the LSB is tried, the SAR gives a HIGH signal at the Conversion Complete terminal. The signal enables the latch and the digital data appears at the output of the latch. For continuous converter action, the signal is also latched to the signal input. This type of converter has high speed and excellent resolution. For an bit converter counts are required. For a bit converter having clock of time period, full scale count requires. Block diagram of a communication system is as shown in figure, From a practical design point of view, the first and the last block i.e. Source and Destination are not important for the topic in hand. Anyways the electrical communication happens in the middle three blocks viz. Transmitter, Channel and Receiver. The objective of the transmitter block is to collect the incoming message signal and modify it in a suitable way (modulation) such that it can be transmitted via the chosen channel. Channel is a physical medium which connects the transmitter with the receiver. The channel can be a copper wire, coaxial cable, fibre optic cable, wave guide or atmosphere. The receiver block receives the incoming modulated signal and process to recreate the original message signal. This process is called demodulation. The term modulate means to regulate. Hence, the process of regulating is called as modulation. Thus for regulation, we need one physical quantity which is to be regulated and another physical quantity which controls the regulation. In electrical communication, the signal to be regulated is a high frequency signal called as carrier. The signal which controls the modulation process is called as the modulating signal. The message acts as the modulating signal in communication systems. The carrier signal is characterized by three parameters, amplitude, frequency and phase. The modulation process involves the message signal controlling the variation of one of the parameters. Depending on the variation of the parameter, we get the following three techniques, i. Amplitude Modulation ii. Frequency Modulation iii. Phase Modulation

22 P a g e 22 I. Amplitude Modulation (Double Sideband Full Carrier) (DSBFC) In amplitude modulation, the amplitude of a carrier signal is varied by the modulating voltage i.e. amplitude of the message. The amplitude and frequency of the message is invariably less than that of the carrier. The carrier signal is a high frequency signal while the message signal (modulating signal) is of audio frequency. For amplitude modulation, the amplitude of the carrier is made proportional to the instantaneous amplitude of the modulating signal. Let the voltages of the carrier and modulating signal be given as, where, maximum amplitude of carrier voltage maximum amplitude of modulating voltage angular velocity of carrier voltage represented in rad/sec angular velocity of modulating voltage represented in rad/sec When a carrier is amplitude modulated, the proportionality constant is made equal to unity and the instantaneous modulating voltage variations are superimposed onto the carrier amplitude. When there is no modulation temporarily, the amplitude of the carrier is equal to its unmodulated value. When modulation is present, the amplitude of the carrier is varied by the instantaneous value of the modulating voltage. Hence, the maximum value of the amplitude of the modulated voltage is made to vary with changes in the amplitude of the modulating voltage. The ratio is defined as the modulation index, and has a value between and. It is often expressed as a percentage and is called as the percentage modulation. i.e., Hence, the amplitude of the AM (amplitude modulated) signal can be written as, The instantaneous voltage of the resulting AM signal is,, we get The equation contains three terms. They are, a. The first component represents the unmodulated carrier. It is apparent that the process of amplitude modulation has the effect of adding to the unmodulated wave rather than changing it. b. The second component gives the lower sideband. The frequency of the lower sideband (LSB) is. c. The third component gives the upper sideband. The frequency of the upper sideband (USB) is.

23 P a g e 23 The bandwidth of the AM wave is given as, The frequency spectrum of an AM wave is shown in the figure. It contains three discrete frequencies. The central frequency i.e. carrier frequency has the highest amplitude. The other two disposed symmetrically about it have amplitudes which are equal to each other but never exceeds half the carrier amplitude. In AM broadcasting service, where several sine waves are modulated simultaneously, the bandwidth required is twice the highest modulating frequency. The AM wave is as shown in the figure. The maximum amplitude of the top envelope of the AM wave is given by,. Similarly, the maximum amplitude of the bottom envelope is given as,. The modulated wave extends between these two limiting envelopes and has a frequency equal to the unmodulated carrier frequency. From the figure, we get Hence, the modulation index is given as, The total power of the modulated wave is given as, All three voltages are root mean square (rms) values and can be expressed in terms of their peak values using the factor. is the resistance e.g. antenna resistance, in which the power is dissipated. The power of the carrier wave is given as, Similarly, Hence, the total power is given as,

24 P a g e 24 Generation of AM Signal A type of AM signal modulator using transformers and diodes is as shown in the figure. The modulating voltage and the carrier voltage are applied in series at the input of the diode. The output of the diode is collected via a tuned circuit tuned to the carrier frequency with bandwidth of twice the message bandwidth. The relationship between voltage and current in a linear resistance is given by, where is conductance. In case of non linear resistances such as diodes, transistors and FETs, the current voltage relationship is given as, We reject the higher powers and are left with the equation,, where represents the dc component, represents conductance and is the coefficient of non linearity. The diode in the above circuit is biased such that it exhibits the negative resistance property. Under this condition, the current is given by, Putting the values, and, we get Now we know, and Hence, we get cos + In the above equation, the first component is the dc component, second term is the message, third term is the carrier, fourth term contains the harmonics of message and the carrier, fifth term represents the lower sideband and sixth term represents the upper sideband. The requisite AM components can be selected using the tuning circuit tuned to the carrier frequency with bandwidth of twice the message bandwidth. At the output of the tuning circuit, we get If is the load resistance, the AM voltage is given as, Now,, and. Hence, we get This is the standard AM signal. Thus we can generate AM signal with the help of a device that exhibits non linear resistance property. Demodulator An AM demodulator is as shown in figure. Once the AM signal is received at the receiver, the work of the carrier is over. The demodulator separates the modulating signal from the carrier and sends to the destination. The circuit is basically a peak detector. Ideally, peaks of the input signal are detected so that the output is the upper envelope. During each carrier cycle, the diode turns on briefly and charges the capacitor to the

25 P a g e 25 peak voltage of the carrier. Between the peaks, the capacitor discharges through the resistor. If we make the time constant much greater than the period of the carrier, we get only a slight discharge between cycles. The output then looks like the upper envelope with a small ripple. A low pass filter is used on the output of the peak detector to remove the carrier ripple. The obtained signal is the message signal. II. Frequency Modulation In case of frequency modulation, the amplitude of the carrier wave is kept constant while its frequency is varied. Let the carrier signal and the modulating signal (message) be given as, where, maximum amplitude of carrier voltage maximum amplitude of modulating voltage angular velocity of carrier voltage represented in rad/sec angular velocity of modulating voltage represented in rad/sec phase angle of carrier voltage represented in radians phase angle of modulating voltage represented in radians In frequency modulation process, the amount by which the carrier frequency is varied from its unmodulated value is called as frequency deviation. Frequency deviation is made proportional to the instantaneous amplitude of the modulating voltage. The rate at which this frequency variation takes place is equal to the modulating frequency. In FM, all components of the modulating signal having the same amplitude will deviate the carrier frequency by the same amount. Similarly, all components of the modulating signal of the same frequency will deviate the carrier at the same rate. The situation is shown in the figure. The instantaneous frequency of the FM wave is given by, where, unmodulated carrier frequency proportionality constant expressed in The maximum deviation for this signal will occur when the term has its maximum value i.e.. Under these conditions, instantaneous frequency will be, The maximum deviation is given as, The instantaneous amplitude of the FM signal is given as, where, is the angle traced by the vector in time. It is a function of angular velocities and i.e.. The angular velocity of the FM wave is given as,

26 P a g e 26 Hence, Hence, instantaneous amplitude of the FM signal is now given as, The modulation index for FM is given as, Hence, Characteristics of FM Signal i. The amplitude of the FM signal is constant. It is thus independent of the modulation depth. Whereas in case of AM, modulation depth governs the transmitted power. ii. All transmitted power in FM is useful whereas in AM most of it is in the transmitted carrier, which contains no useful information. iii. FM receivers can be fitted with amplitude limiters to remove the amplitude variations caused by noise. This makes FM reception a good deal more immune to noise than AM reception. iv. Further reduction in noise in a FM signal is possible by increasing the deviation. This feature is not available for AM. Hence, AM signal cannot be produced without distortion. v. Standard frequency allocations provide a guard band between commercial FM stations, so that there is less adjacent channel interference than AM. vi. At the FM broadcast frequencies, the space wave is used for propagation. The radius of operation is limited to slightly more than line of sight. Hence, it is possible to operate several independent transmitters on the same frequency with considerably less interference than would be possible with AM. vii. FM requires a much wider bandwidth, about 10 times that of AM. viii. FM transmitting and receiving equipment tends to be more complex. ix. Since reception is limited to the line of sight, the area of reception for FM is much smaller than that of AM. 1) Op Amps and Linear Integrated Circuits Ramakant A. Gayakwad 2) Electronic Principles Albert P. Malvino 3) Digital Principles and Applications Albert P. Malvino, Donald P. Leach 4) Electronic Communication Systems George Kennedy, Bernard Davis, S R M Prasanna 5)