This document discusses amplitude modulation using a balanced FET modulator. It begins by providing the mathematical representation of an AM-DSB-SC waveform. It then describes how a balanced FET modulator can be used to generate an AM-DSB-SC signal. Specifically, it explains that a balanced FET modulator uses two matched FETs in a differential amplifier configuration. The carrier signal is applied in phase to the gates, while the message signal is applied out of phase. This results in an output signal that is amplitude modulated by the message signal. The document concludes by noting that while a balanced FET modulator can heavily suppress the carrier, it cannot achieve 100% carrier suppression due to imperfect matching of the F

1. EC8491-Communication Theory
Dr.Arun Chokkalingam
Professor
 Mathematical Representation of AM –DSB-SC Wave
 Generation of AM-DSB-SC using Balanced FET Modulator
Amplitude Modulation(AM)

2. Mathematical Representation of an AM –DSB-SC Wave
AM –DSB-FC waveform

3. Cont.
Product Modulation
𝑴𝒆𝒔𝒔𝒂𝒈𝒆 𝒔𝒊𝒈𝒏𝒂𝒍 𝒗𝒎 𝒕 = 𝑽𝒎𝒄𝒐𝒔 𝝎𝒎𝒕
Carrier signal 𝒗𝒄 𝒕 = 𝑽𝒄𝒄𝒐𝒔 𝝎𝒄𝒕
DSB-SC- 𝒔 𝒕 = 𝒗𝒎 𝒕 𝒗𝒄𝒕 𝒕
𝒔 𝒕 = 𝑽𝒎𝒄𝒐𝒔 𝝎𝒎𝒕 𝑽𝒄𝒄𝒐𝒔 𝝎𝒄𝒕
𝒔 𝒕 =
𝑽𝒄𝑽𝒎
𝟐
𝒄𝒐𝒔 𝝎𝒄 + 𝝎𝒎𝒕 + 𝒄𝒐𝒔 𝝎𝒄 − 𝝎𝒎𝒕
USB LSB

4. Generation of AM-DSB-SC
1. Balanced FET Modulator Method
2. Diode Ring Modulator Method
▪ A nonlinear device used to produce amplitude modulation.
▪ Nonlinear devices are diode , transistor etc…

5. Balanced Modulator Method
▪ Balanced modulators are the building blocks from which a wide variety of
frequency mixers, modulators, and demodulators are built.
▪ two matched FETs connected in a differential amplifier, which acts a balanced
modulator
𝑣𝑐 + 𝑣𝑚
𝑣𝑐 − 𝑣𝑚

6. Operation
▪ Carrier voltage is applied in phase to the two gates of FET
▪ Modulating signal appears 1800out of phase at the gate.This is because of input transformerT1 is
a center tapped transformer.
▪ Mode -1 (only carrier signal applied and message signal =0)
▪ Both FETs conduct simultaneously due to the in phase carrier voltage applied to their gates
▪ Their drain currents are equal in magnitude but opposite in direction and cancel each other .The
net output is Zero.
▪ Mode =2 (both carrier and message signal both present)
▪ The drain currents of the two FETs flow due to the combined effect of carrier and message
signal.
▪ The current due to message are equal but not opposite so they do not cancel out.

7. Cont .
▪ 𝒗𝒈𝒔𝟏 = 𝒗𝒄 + 𝒗𝒎 (1.36)
▪ 𝒗𝒈𝒔𝟐 = 𝒗𝒄 − 𝒗𝒎 (1.37)
▪ 𝒊𝒅𝟏 = 𝑰𝟎 + 𝒂𝒗𝒈𝒔𝟏 + 𝒃𝒗𝒈𝒔𝟏
𝟐
(1.38)
▪ 𝒊𝒅𝟐 = 𝑰𝟎 + 𝒂𝒗𝒈𝒔𝟐 + 𝒃𝒗𝒈𝒔𝟐
𝟐
(1.39)
▪ 𝒊𝒑 = 𝒊𝒅𝟏 − 𝒊𝒅𝟐 (1.40)
▪ Use (1.38) and (1.39) in (1.40), we get,
▪ 𝒊𝒑 = 𝟐𝒂 𝒗𝒎 + 𝟒𝒃 𝒗𝒄 𝒗𝒎 (1.41)
▪ Substitute 𝒗𝒎 = 𝑽𝒎𝒄𝒐𝒔 𝝎𝒎𝒕 and 𝒗𝒄 = 𝑽𝒄𝒄𝒐𝒔 𝝎𝒄𝒕 in equation (1.41) we get,
▪ 𝒊𝒑 = 𝟐𝒂𝑽𝒎𝒄𝒐𝒔 𝝎𝒎𝒕 + 𝟐𝒃𝑽𝒎𝑽𝒄 𝒄𝒐𝒔 𝝎𝒄 − 𝝎𝒎 𝒕 + 𝒄𝒐𝒔 𝝎𝒄 + 𝝎𝒎 𝒕 (1.42)
▪ 𝒗𝟎 ∝ 𝒊𝒑 (1.43)

8. Disadvantages of FET balanced modulator
▪ 100% of carrier suppression is not possible .
▪ Because both FETs must have the identical characteristics and the
transformer center taps must be exactly at the center of the
windings.
▪ Carrier will be heavily suppressed but not completely removed.