Vestigial Sideband Modulation KEEE343 Communication Theory Lecture #11, April 7, 2011 Prof.Young-Chai Ko [email protected] Summary ·•Vestigial sideband modulation ·•Baseband representation of modulated wave ·•Baseband representation of pass-band filter ·•Frequency division multiplexing ·•Introduction to Angle Modulation Generation of LSB SSB Using Wideband Low-Pass Filter DSB Spectrum fc SSB Spectrum fc fc HL (f ) sgn(f + fc ) HL (f ) fc sgn(f fc ) Generation of USB SSB Using High-Pass (or Passband) Filter DSB Spectrum HHP (f ) fc SSB Spectrum fc fc fc HHP (f ) = sgn(f + fc ) + sgn(f + fc ) sgn(f + fc ) sgn(f fc ) SSB Modulated Wave • Lower Sideband SSB sLSB (t) = • 1 1 m(t) cos(2 fc t) + m̂(t) sin(2 fc t) 2 2 Upper sideband SSB 1 sU SB (t) = m(t) cos(2 fc t) 2 1 m̂(t) sin(2 fc t) 2 Applications of SSB and Difficulties in Implementing SSB • Two difficulties of SSB modulations • Designing and implementing the sharp Low-pass (or High-pass/pass-band) filter is not easy for circuit designer. • Hence, the message signal which does not contain the significant energy in the DC area is often modulated by the SSB such as the speech signal. Spectrum of Speech Signal (Example) 0 • [Hz] However, the SSB cannot be applicable for the message signal which contains the significant energy around zero frequency such as video signal, computer data, and etc. Vestigial Sideband (VSB) Modulation • VSB Modulation • • Modulation to overcome the two difficulties of the SSB modulations. Allow a small amount, or vestige, of the unwanted sideband to appear at the output of an SSB modulator • The design of the sideband filter is simplified since the need for sharp cutoff at the carrier frequency is eliminated. • In addition, a VSB system has improved low-frequency response and can even have dc response. Idea of VSB Modulator • Pass-band (or High-pass) filter for USB-SSB modulation 1 |HU (f )| fc • fc The filter below is much easier to design and implement 1 1 ✏ ✏ fc f1 fc fc + f1 • Consider the two-tone message signal given as m(t) = A cos(2 f1 t) + B cos(2 f2 t) • Message signal multiplied by the carrier wave, that is, DSB signal eDSB (t) = = (A cos(2 f1 t) + B cos(2 f2 t)) · cos(2 fc t) 1 1 A cos(2 (fc + f1 )t) + A cos(2 (fc f1 )t) 2 2 1 1 + B sin(2 (fc + f1 )t) + B sin(2 (fc f1 )t) 2 2 • • Spectrum of DSB signal fc f2 1 1 A 2B 2 1 A 2 1 B 2 fc f1 Frequency response of the VSB filter 1 fc fc + f1 fc + f2 1 ✏ ✏ • s(t) = fc f2 fc f1 Output response 1 A cos(2⇥(fc f1 )t) 2 1 + A(1 ) cos(2⇥(fc + f1 )t) 2 1 + B cos(2⇥(fc + f2 )t) 2 1 A 2 fc f1 fc 1 [A(1 2 fc + f1 fc + f2 )] 1 B 2 fc + f1 fc + f2 Demodulation of VSB Signal (Coherent method) • Downconvert (by Multiplying 4 cos(2 fc t) ) and low pass filtering • Downconvert s(t) · 4 cos(2⇥fc t) 1 = A cos(2⇥(fc f1 )t) · 4 cos(2⇥fc t) 2 1 + A(1 ) cos(2⇥(fc + f1 )t) · 4 cos(2⇥fc t) 2 1 + B cos(2⇥(fc + f2 )t) · 4 cos(2⇥fc t) 2 1 cos(2 (fc + f1 )t) · cos(2 fc t) = cos(2 (2fc + f1 )t) + cos(2 f1 t) 2 d(t) = Low-Pass Filtering 1 cos(2 f1 t) 2 • Signal after Low-pass filtering ⇥(t) = A cos(2⇤f1 t) + A(1 ) cos(2⇤f1 t) + B cos(2⇤f2 t) = A cos(2⇤f1 t) + B cos(2⇤f2 t) Television Signals [Ref: Haykin & Moher, Textbook] Baseband Representation of Modulated Waves • DSB modulated wave signal sDSB (t) = Am(t) cos(2 fc t) • SSB modulated wave signal sSSB (t) = • 1 1 Am(t) cos(2 fc t) ± Am̂(t) sin(2 fc t) 2 2 In general, we can write the “linear modulated wave” as s(t) = sI (t) cos(2 fc t) Carrier wave with frequencyfc sQ (t) sin(2 fc t) quadrature-phase version of the carrier c(t) = cos(2 fc t) Orthogonal each other ĉ(t) = sin(2 fc t) • We can rewrite the modulated wave as s(t) = sI (t)c(t) in-phase component of s(t) • sQ (t)ĉ(t) quadrature(-phase) component of s(t) Introduce the complex envelop of the modulated wave s(t) s̃(t) = sI (t) + jsQ (t) • Define the complex carrier wave c̃(t) = cI (t) jcQ (t) • Consider the following s̃(t) · exp(j2 fc t) = • sI (t) + jsQ (t) · cos(2 fc t) + j sin(2 fc t) Real term ⇥ s̃(t) · exp(j2 fc t) • = sI (t) · cos(2 fc t) sQ (t) · sin(2 fc t) Imaginary term s̃(t) · exp(j2 fc t) s̃(t) = sI (t) sin(2 fc t) + sQ (t) cos(2 fc t) X exp(j2 fc t) · s(t) • Now consider s̃(t) = sI (t) + jsQ (t) = a(t)ej (t) where a(t) = • q s2I (t) + js2Q (t), (t) = tan 1 sQ (t) sI (t) Then we can represent the modulated wave as s(t) = = = < s̃(t)ej2⇥fc t = < a(t)ej < a(t)ej[2⇥fc t+ (t)] a(t) cos[2⇥fc t + (t)] (t) j2⇥fc t e • Three different representation of modulated wave using its equivalent baseband signal s(t) = sI (t) cos(2⇥fc t) = < s̃(t)ej2 fc t sQ (t) sin(2⇥fc t) = a(t) cos[2⇥fc t + (t)] Superheterodyne Receiver [Ref: Haykin & Moher, Textbook] Communication Chipset Architecture Receiver PLL LNA ÷2 ABB Section 90 0 PLL ÷2 antenna switch 90 ABB 0 Power Amplifier Transmitter Switchplexer module PA Ctrl LDO’s 26MHz Osc. Digital Baseband IC Frequency-Division Multiplexing • To transmit a number of communication signals over the same channel, the signals must be kept apart so that they do not interfere with each other, and thus they can be separated at the receiving end. • • • • FDM (Frequency division multiplexing) TDM (Time division multiplexing) SDM (Space division multiplexing) CDM (Code division multiplexing) Block Diagram of FDM Angle Modulation • Basic Definition of Angle Modulation s(t) = Ac cos[ i (t)] = Ac cos[2⇥fc t + ⇤c ] • Phase modulation (PM) if i (t) • = 2⇥fc t + kp m(t) Frequency modulation (FM) if i (t) = 2⇥fc t + 2⇥kf Z t m(⇤ ) d⇤ 0
© Copyright 2024 Paperzz