1. Amplitude/Phase Modulation

2. Baseband and carrier communications
The term baseband refers to a band of frequencies of signal generated by a information source.
In telephony, baseband signal is 0Hz-3.4kHz
In TV, it is 0Hz to 4.3 MHz

3. Baseband and carrier communications
In baseband communication, baseband signal is transmitted without modulation. It cannot be transmitted through radio link.
In carrier communication, one of the basic parameters (amplitude, frequency and phase)of a sinusoidal carrier of high frequency wc is varied in proportion to the baseband signal m(t)

4. AM: Double side band DSB
In AM, the amplitude ( ) of the carrier is varied according to the message signal m(t). If the carrier amplitude is made proportional to the carrier signal,
The modulated signal is
is the shifted to left by
is the shifted to right by

6. is the BW of , the BW of the modulated signal is
We observe that the modulated signal spectrum centered at is composed of two part: the portion that lies above is called USB and the portion that lies below is called LSB.
For the reason it is called double sideband suppressed carrier (DSB-SC)
In order to avoid the overlap in the spectrum

7. Demodulation DSB-SC
The process of recovering the baseband signal from the modulated signal is called demodulation. In time domain,

8. Demodulation DSB-SC In time domain, In frequency domain,
At the output of the LPF

9. Problem 4.1
If , Find DSB-SC signal and Sketch its spectrum. Identify USB and LSB.
Find that can be find at the receiver from the modulated signal.

11. AM with carrier Limitation of SC scheme
Frequency and phase synchronism is required
Sophisticated receiver must be required.
The alternative is to transmit a carrier
In this scheme, the transmitter needs to transmit much larger power
The Tx signal can be given by

13. Amplitude Modulation
The condition for envelope detection of the AM signal for all t
If and A=0 also satisfy the above condition
Let be the peak amplitude of
This condition is equivalent to
The min. carrier amplitude required for envelope detection is

14. Modulation index
The modulation index

15. Problem
Sketch for modulation indices of 0.5 and 1, when

16. Sideband and carrier power
Carrier term does not carry information, and hence the carrier power is wasted
The carrier power is the mean sq. value of
which is
The sideband power is the mean sq. value of which is

17. The power efficiency
For the special case of tone modulation
Hence

18. Problem
Find the power efficiency for and

19. The voltage across the terminal bb is
Other terms are suppressed by BPF

20. If an AM signal is applied to a diode and a resistor circuit, the –ve part of the AM wave will be suppressed. The output across the resistor is a ½ wave rectified version of AM signal the AM signal is multiplied by w(t). Hence the rectified o/p is
The o/p of LPF is The first term can be blocked by a capacitor

22. Single-sideband suppressed-carrier transmission
The information represented by the modulating signal is contained in both the upper and the lower sidebands. Since each modulating frequency fc produces corresponding upper and lower side-frequencies
fc + fi and fc − fi it is not necessary to transmit both side-bands. Either one can be suppressed at the transmitter without any loss of information.
Advantages
Less transmitter power.
Less bandwidth, one-half that of Double-Sideband (DSB).
Less noise at the receiver.
Size, weight and peak antenna voltage of a single-sideband (SSB) transmitters is significantly less than that of a standard AM transmitter.

23. Vestigial sideband (VSB)
A vestigial sideband (in radio communication) is a sideband that has been only partly cut off or suppressed. Television broadcasts (in analog video formats) use this method if the video is transmitted in AM, due to the large bandwidth used. It may also be used in digital transmission, such as the ATSC standardized 8-VSB. The Milgo 4400/48 modem (circa 1967) used vestigial sideband and phase-shift keying to provide 4800-bit/s transmission over a 1600 Hz channel.
The video baseband signal used in TV in countries that use NTSC or ATSC has a bandwidth of 6 MHz. To conserve bandwidth, SSB would be desirable, but the video signal has significant low frequency content (average brightness) and has rectangular synchronizing pulses. The engineering compromise is vestigial sideband modulation. In vestigial sideband the full upper sideband of bandwidth W2 = 4 MHz is transmitted, but only W1 = 1.25 MHz of the lower sideband is transmitted, along with a carrier. This effectively makes the system AM at low modulation frequencies and SSB at high modulation frequencies. The absence of the lower sideband components at high frequencies must be compensated for, and this is done by the RF and IF filters.

25. Advantages/disadvantages
Advantages of Amplitude Modulation, AM
There are several advantages of amplitude modulation, and some of these reasons have meant that it is still in widespread use today:
It is simple to implement
it can be demodulated using a circuit consisting of very few components
AM receivers are very cheap as no specialized components are needed.
Disadvantages of amplitude modulation
Amplitude modulation is a very basic form of modulation, and although its simplicity is one of its major advantages, other more sophisticated systems provide a number of advantages. Accordingly it is worth looking at some of the disadvantages of amplitude modulation.
It is not efficient in terms of its power usage
It is not efficient in terms of its use of bandwidth, requiring a bandwidth equal to twice that of the highest audio frequency
It is prone to high levels of noise because most noise is amplitude based and obviously AM detectors are sensitive to it.

26. Noise power is proportional to the modulated signal bandwidth (sideband).
Finding the modulation scheme that will reduce the BW.
In FM carrier freq is varied proportional to the baseband signal.
The carrier freq is varied with time

27. Where k is an arbitrary constant
Where k is an arbitrary constant. If is the peak amplitude, then the max and min values of the carrier freq will be
Hence the spectral components would remain within this band with a BW
The FM BW was found to be always greater than or equal to AM BW.

28. A sine wave is
is the generalized angle and it is function of t.
The generalized angle of conventional sine wave is
For small angle

29. The instantaneous frequency at any instant
The technique in which the angle of carrier wave is varied with modulating signal is called angle modulation or exponential modulation

30. In PM the angle is varied linearly with information signal
When
The resulting PM wave
The instantaneous frequency is given by

31. If is varied linearly with the modulating signal, the modulation is called FM.
The angle
The FM wave is

33. In PM it is directly proportional to
In FM it is directly proportional to integral of
We have an infinite no of possible ways of generating measure of information signal. If we restrict the choice to a linear operator, the generalized angle modulated carrier can be written as