2. Phase
Phase is the same frequency, same cycle, same wavelength, but are 2 or more wave forms
not exactly aligned together.
The phase involves the relationship between the position of the amplitude crests and
troughs of two waveforms.
Inphase -If the peaks of two signals with the same frequency are in exact alignment at the same time.
Out of phase- If the peaks of two signals with the same frequency are not in exact alignment at the same time
Standard measure of Phase=
distance, time, or degrees
3. Mathematical Representation of an AM Wave
Carrier (High frequency) signal c t or 𝑣𝑐 = 𝑉
𝑐𝑐𝑜𝑠𝜔𝑐𝑡
Modulating (Low frequency/message/baseband/information) signal, m t or 𝑣𝑚 = 𝑉
𝑚𝑐𝑜𝑠𝜔𝑚𝑡
On amplitude modulation, 𝑣𝐴𝑀 = 𝑉𝑐+𝑣𝑚)𝑐𝑜𝑠𝜔𝑐𝑡
Time domain representation of AM wave, 𝒗𝑨𝑴 = 𝑽𝒄 𝟏 + 𝒎𝒄𝒐𝒔𝝎𝒎𝒕 𝒄𝒐𝒔𝝎𝒄𝒕
Frequency domain representation of AM wave, 𝑽𝑨𝑴 𝒕) = 𝑽𝒄𝒄𝒐𝒔𝝎𝒄𝒕 +
𝒎𝑽𝒄
𝟐
𝒄𝒐𝒔 𝝎𝒄 − 𝝎𝒎 +
𝒎𝑽𝒄
𝟐
𝒄𝒐𝒔 𝝎𝒄 + 𝝎𝒎 𝒕
𝑊ℎ𝑒𝑟𝑒, 𝑚 =
𝑉𝑚
𝑉𝑐
, modulation index of AM
The carrier is superfluous (beyond what is needed) and the other sideband is
redundant.
%𝜂 =
𝑃𝑜𝑤𝑒𝑟 𝑖𝑛 𝑠𝑖𝑑𝑒𝑏𝑎𝑛𝑑𝑠
𝑇𝑜𝑡𝑎𝑙 𝑃𝑜𝑤𝑒𝑟
× 100 =
𝑃𝐿𝑆𝐵+𝑃𝑈𝑆𝐵
𝑃𝑇
× 100 = 𝟑𝟑. 𝟑𝟑 %
RECAP- AM Wave
7. If the carrier and one sideband are suppressed, then the total power transmitted in SSB is
Power in SSB/SSBSC is 𝑃′′𝑇 = 𝑃𝑆𝑆𝐵=
𝑚2
4
𝑃
𝑐
Power savings in SSB =
𝑃𝑇−𝑃′′
𝑇
𝑃𝑇
=
4+𝑚2
4+2𝑚2 × 100
If the modulation index m=1, then power saving is 5/6 = 83.33%.
Bandwidth of SSB signal
The difference between upper and lower side frequencies will be fm and this is the bandwidth of SSB signal.
Power Distribution in SSB-SC Wave
9. Frequency-discrimination method (or) Filter Method
Two stages
The first stage is a product modulator which generates a DSBSC modulated wave
The second stage is a BPF, which is designed to pass one of the sidebands of the
modulated wave and suppress the other.
10. Filter method - The message signal should satisfies the following conditions :
The message signal should not have any low frequency content . The audio signal posses this
property, e.g. the telephone signal will have a frequency range extending from 300 Hz to 3.4 kHz .
The frequencies in the range 0-300 Hz are absent .
The highest frequency in the spectrum of the message signal i.e. W Hz should be much smaller than
carrier frequency fc .
This system is used for the suppression of Upper sideband
11. Three basic requirements in designing the BPF,
The desired sideband lies inside the bass band of the filter
The unwanted sideband lies in the stopband of the filter
The filter’s transition band, which separates the passband from the stopband is twice the
lowest frequency component of the message signal
𝑓𝑐 + 𝑓𝑎 − 𝑓𝑐 − 𝑓𝑎 = 2𝑓𝑎 = 𝑡𝑤𝑖𝑐𝑒 𝑡ℎ𝑒 𝑙𝑜𝑤𝑒𝑠𝑡 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑜𝑓 𝑚𝑒𝑠𝑠𝑎𝑔𝑒 𝑠𝑖𝑔𝑛𝑎𝑙
Highly selective filters –LC, ceramic or mechanical depending upon the carrier
frequency and other requirements.
Drawback of filter method
It requires sharp filtering, which requires filters with high Q.
Primary modulation cannot be done at the transmitting frequency.
12. Phase discrimination method - Phase Shift Method
This system is used for the suppression of lower sideband.
This system uses two balanced modulators M1 and M2 and two 90o phase shifting networks
16. Output of Modulators
Output of Adder
Note : the adder polarities for the in-phase is positive and for the quadrature paths is negative .
Suppression of the upper sideband
The modulating and the carrier signals are applied to the upper balanced modulator directly
(without any phase shift ) .
Whereas, both these signals are 90o phase shifted and then applied to the lower balanced
modulator .
17. Advantages of Phase Shift Method
It can generate the SSB signal at any frequency, so the frequency up converter stage is not
required .
It can use the low audio frequencies as modulating signal .(In filter method, this is not possible) .
It is easy to switch from one sideband to other .
Drawbacks of Phase Shift Method
The design of the 90o phase shifting network for the modulating signal is extremely critical .
This network has to provide a correct phase shift of 90o at all the modulating frequencies which is
practically difficult to achieve .
Advantages & Disadvantages
