AMPLITUDE MODULATION

Amplitude Modulation and Demodulation circuit of AM signal Introduction : Signals are transported between a transmitter and receiver over some form of transmission medium. However, original signals are selected in a form that is suitable for transmission. Therefore, they must be transformed into a form that is more suitable for transmission. The process of impressing low-frequency information signals onto a highfrequency carrier signal is called modulation. Demodulation is the reverse process where the received signals are transformed back to their original form.Alternatively, a process that causes a shift in the range of frequency of a signal is called Modulation. Amplitude modulation is defined as varying the amplitude of the carrier wave according to the message or information signal. AM generation involves mixing of a carrier and an information signal.

Theory: Amplitude Modulation is defined as a process in which the amplitude of the carrier wave c (t) is varied linearly with the instantaneous amplitude of the message signal m(t). The standard form of amplitude modulated wave is defined by

Where Ka is a constant called the amplitude sensitivity of the modulator, Ac is the amplitude of carrier signal, m(t) is the massege signal, fc is the carrier frequency. The demodulation circuit is used to recover the message signal from the incoming AM wave at the receiver. An envelope detector is a simple and yet highly effective device that is well suited for the demodulation of AM wave, for which the percentage modulation is less then 100%. Ideally, an envelope detector produces

an output signal that follows the envelop of the input signal wave form exactly; hence, the name. Same version of this circuit is used in almost all commercial AM radio receivers.

Methods to Generate AM :  Low level modulation and  High level modulation  In low level modulation, the message signal and carrier signal are modulated at low power levels and then amplified. The advantage of this technique is that a small audio amplifier is sufficient to amplify the message signal. The disadvantage is that the linear amplifiers are necessary to amplify the modulated signal to transmitter levels. Nonlinear amplifiers cause distortion of the modulated wave.  In high level modulation, the carrier and message signals are sufficiently

amplified to the transmitting levels and modulation is done at high power levels. The advantage of this technique is that nonlinear high-efficiency amplifiers can be used to amplify the signals. The disadvantage is that large audio amplifier needs to be used to amplify the message signal.

In AM the amplitude, A, of the carrier 𝑐(𝑡) = 𝐴𝑐𝑜𝑠(ωc 𝑡 + 𝜃𝑐) is varied in proportion with the baseband signal m(t), the modulating signal , 𝜔𝑐and 𝜃𝑐 are constants ( we assume 𝜃𝑐=0) without loss of generality. The carrier itself carries no information at all. Assume that we have a message signal m(t) with bandwidth (BW) 2πB rad/s (or B Hz) that has a Fourier Trasform. m(t) ⇔ M(ω). such that the frequency of the carrier ωc is much larger than the highest frequency in the information signal (we set the amplitude of the carrier to be 1, but it can be any value).

Different types of AM: 1. Double Sideband with carrier (we will call it AM): This is the most widely used type of AM modulation. In fact, all radio channels in the AM band use this type of modulation. 2. Double Sideband Suppressed Carrier (DSBSC): This is the same as the AM modulation above but without the carrier. 3. Single Sideband (SSB): In this modulation, only half of the signal of the DSBSC is used. 4. Vestigial Sideband (VSB): This is a modification of the SSB to ease the generation andreception of the signal.

Double Sideband Suppressed Carrier (DSBSC) DSBSC Modulation: The DSBSC signal is simply obtained by multiplying the information signal with the carrier signal as shown in the modulator (or transmitter) block diagram shown below: DSBSC(t) = m(t)⋅cos(ωc t ) ⇔ (1/2) [M(ω – ωc) + M(ω + ωc)]. Bandwidth B Hz → 2B Hz

On the frequency domain Figure below, explain: USB: Upper Sideband (above ωc) LSB: Lower sideband (below ωc) No discrete component of ωc → DSB-SC (Double sideband suppressed carrier) Modulation:

This signal DSBSC(t) is a modulated signal that has its spectrum centered around ωc and – ωc .Therefore, this signal becomes a passband signal with frequency that is much larger than the maximum frequency in m(t). To avoid overlap of the frequency spectrum, and m(t) can be recovered,𝜔c ≥ 2𝜋𝐵 DSBSC Demodulation The demodulation process of a DSBSC signal involves obtaining the original information signal or scaled version of it from the modulated signal. This can be done by multiplying the modulated signal with another carrier signal that has EXACTLY the same frequency and phase as the carrier signal in the modulator block as seen in the demodulator block diagram shown below. The amplitude of the two carrier signals in the modulator and demodulator are not important since they just affect the magnitude of the different intermediate signals and final output signal of the demodulator.

The signal labeled e(t) in the demodulator becomes e (t) = gDSBSC(t)⋅cos( ωct) = m(t)⋅cos2( ωct) = (1/2) m(t) [1 + cos(2ωct)] = (1/2) m(t) + (1/2) m(t) cos(2 ωct) ⇔ (1/2) M(ω) + (1/4) [M(ω – 2 ωc) + M(ω+ 2 ωc)]. However, as seen in the FT of e(t), the original message signal (scaled by 1/2) is present but also other components with frequencies centered around 2 ωc and –2 ωc. These components are undesired and must be removed to get the message signal. This can be done using a LPF (a filter centered around zero frequency that permits low frequencies to pass and rejects high frequencies). The BW of the filter must be 2πB rad/s (or B Hz) or possibly slightly higher (but not much higher that it will allow the high-frequency components around 2 ωc and -2ωc to partially or completely pass). Therefore, the output signal f(t) of the LPF will be e (t) = (1/2) m(t) ⇔ (1/2) M(ω).

This is simply a scaled version of the original transmitted signal that can be easily amplified to obtain the original signal exactly. We can get rid of the half by demodulating with 2cos(ωct). We need to generate a local signal with the same frequency and same phase as the carrier.

SSB modulation: Depending on which half of DSB-SC signal is transmitted, there are two types of SSB modulation: 1. Lower Side Band (LSB) Modulation 2. Upper Side Band (USB) Modulation

SSB signals from orignal signal

From Hilbert transform :

Similarly,

Generation of SSB signals

Coherent Demodulation of SSB signals : SSB signal is multipliedwith cos(ωct) and passed through low pass filter to get back theorignal signal.

Demodulated SSB signal The demodulated signal is passed through an LPF to remove unwanted SSB terms.

Vestigial Side Band (VSB) Modulation: The following are the drawbacks of SSB signal generation: 1. Generation of an SSB signal is difficult. 2. Selective filtering is to be done to get the original signal back. 3. Phase shifter should be exactly tuned to 90o.

To overcome these drawbacks, VSB modulation is used. It can viewed as a compromise between SSB and DSB-SC.

VSB Modulation In VSB 1. One sideband is not rejected fully. 2. One sideband is transmitted fully and a small part (vestige) of the other sideband is transmitted. The transmission BW is BWv = B + v. where, v is the vestigial frequency band. The generation of VSB signal is shown below:

Block Diagram - Generation of VSB signal Here, Hi(ω)is a filter which shapes the other sideband. V SB(ω) = [M(ω-ωc) +M(ω+ ωc)].Hi(ω) To recover the original signal from the VSB signal, the VSB signal is multiplied with cos(ωct) and passed through an LPF such that original signal is recovered.

Block Diagram - Demodulation of VSB signal

Circuit Diagrams: For Modulation:

For Demodulation:

Procedure: 1. The circuit is connected as per the circuit diagram shown in Fig.1. 2. Switch on =12V Vcc supply 3. Apply sinusoidal signal of 1KHz frequency and amplitude 2 Vp-p as modulating signal, and carrier signal of frequency 11 KHz and amplitude 15 Vp-p. 4. Now slowly increase the amplitude of the modulating signal up to 7V and note down values of Emax and E min. 5. Calculate modulation index using equation 6. Repeat step 5 by varying frequency of the modulating signal. 7. Plot the graphs: Modulation index vs Amplitude & Frequency 8. Find the value of R from taking C=0.01μF 9. Connect the circuit diagram as shown in Fig.2. 10. Feed the AM wave to the demodulator circuit and observe the output. 11. Note down frequency and amplitude of the demodulated output waveform. 12. Draw the demodulated wave form. m=1.

Example: Dual Tone Modulation: A modulating signal m(t) is given by 𝑚(𝑡) = 2 cos 20𝑡 + cos 30𝑡 i. Sketch the spectrum of m(t) ii. Sketch the spectrum of the DSB-SC signal 2𝑚(𝑡) cos 100𝑡

Advantages: AM: 1.Corverage area of AM Reciever is wider because of atmospheric propagation 2.AM is long distance propagation because λ 3. AM Circuit is cheapter and non complex. 4.AM have limited bandwidth. 5.Envelope detection is possible. DSB-SC: 1.Lower power consumption . 2.The modulation system is simple. SSB-SC: 1. Better management of the frequency spectrum . 2.Low power consumption . VSB-SC: It is a compromise between DSB and SSB. Therefore it is easier to generate than SSB-SC

Disadvantages: AM: 1.The only one way to withance to noise happen is increasing power transmit. 2.Signal of AM is not stronger than FM when it propagate to obstacle. 3.Only one sideband of AM transmites Information Signal, So it loss power on other sideband and Carrier. 4. Noise mixes AM Signal in amplitude when it propagates in free space that it make difficulty to recover Original Signal at reciever. 5.Low power efficiency

DSB-SC: 1.Complex detection . 2.More power transmission. SSB-SC: 1. The generation of exact SSB is difficult. 2.Complex detection VSB-SC: 1.Demodulation system is still complex. 2.Its bandwidth is about 25% greater than SSB

Applications: AM: Wireless broadcasting systems DSB-SC: Analog TV systems: to transmit color information SSB-SC: Two way radio Frequency division multiplexing VSB-SC: Analog TV broadcast systems