EE104: Lecture 19 Outline Announcements: HW due today, new HW posted Review of Last Lecture Generation of AM Waves Square Law and Envelope Detection of AM Double Side Band Suppressed Carrier Product Modulators for DSBSC Coherent Detection for DSBSC: The Costas Loop

Review of Last Lecture White Noise Introduction to Modulation AM Modulation When |k a m(t)|<1, can recover m(t) from s(t) envelope a(t)=A c |1+k a m(t)|=A c [1+k a m(t)] m(t) X kaka X cos(2  f c t) + 1 s(t)=A c [1+k a m(t)]cos2  f c t

Generation of AM Waves Multipliers difficult to build in HW AM waves generated using nonlinear device m(t) + A c cos(2  f c t+  Squarer or Switch BPF s(t)

Detection of AM Waves Entails tradeoff between performance and complexity (cost) Square law detector squares signal and then passes it through a LPF Residual distortion proportional to m 2 (t) Noncoherent (carrier phase not needed in receiver) Envelope detector detects envelope of s(t) Simple circuit (resistors, capacitor, diode) Only works when |k a m(t)|<1 (poor SNR), no distortion. Noncoherent

Envelope Detector Only works when |k a m(t)|<1

Double Sideband Suppressed Carrier (DSBSC) Remove inefficient constant term Modulated signal is s(t)=A c cos(2  f c t)m(t) Generated by a product modulator Can also use ring modulator: diodes and inductors AM Modulator + AM Modulator -m(t) m(t) A c cos(2  f c t) s(t) + -

Coherent Detection of DSBSC Detector uses another product modulator Demodulated signal: m´(t)=.5A c cos(  2 -  1 )m(t) Phase offset: if  2 -  1 = , m´(t)=0 Coherent detection (  2  1 ) required m(t) A c cos(2  f c t+    Product Modulator s(t) Product Modulator LPF m´(t) A c cos(2  f c t+    Channel

Costas Loop Product Modulator Product Modulator A c cos(2  f c t+  )m(t) LPF Phase Discriminator VCO -90 o A c cos(2  f c t+  ´(V)) A c sin(2  f c t+  ´(V)) V=sin2  ´)  Goal: Maintain  0.5A c cos(  ´)m(t).5A c sin(  ´)m(t)  ´(V) V  0 DSBSC Demodulator

Main Points AM demodulated with nonlinear devices (some distortion) or envelope detectors (simple, no distortion, low SNR). DSBSC eliminates the power inefficiency of standard AM at the expense of significantly higher receiver complexity Coherent detection is needed for DSBSC: obtaining the carrier phase is one of biggest challenges in all demodulators. A Costas loop provides phase synchronization using a VCO and feedback control. SNR ratio in AM increases with signal power and decreases with noise spectral density and signal bandwidth