Notes8-1

Notes8-1 - Notes#8, ECE594I, Fall 2009, E.R. Brown...

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Notes#8, ECE594I, Fall 2009, E.R. Brown 121 Heterodyne and Homodyne Conversion Background The heterodyne technique goes back to the early days of radio (World War I) when amplifiers were in their infancy and all made from vacuum tubes, meaning that it was difficult to boost the amplitude of incoming signals, even at the ~1 MHz or lower carrier frequencies that were being used at that time. 1 Taken from two Greek roots, “hetero” “different”, and “dyne” “force”, the basic idea is to couple the incoming signal to a nonlinear “mixer” that is simultaneously driven by a “local oscillator” (LO), thereby creating a beat note at an intermediate frequency (IF) between the incoming signal and baseband. In the early days, baseband was often just the human audible range since the information being transmitted was imposed by a human voice. So the IF band was usually in the “supersonic” region between ~20 KHz (approximate upper end of audible range) and 1000 KHz, leading to the descriptor “supersonic heterodyne” or super heterodyne for short. Today, superheterodyne continues to be the descriptor, even when the incoming radiation is in the THz region, and the IF band is in the UHF or microwave regions, typically between 0.1 and 10 GHz. Arguably, super heterodyne has been one of the most valuable, if not the most valuable, developments in the history of communications, RF sensors, and more recently THz systems. Operational Principles The heterodyne technique generally utilizes a three-port nonlinear device called a mixer. The incoming signal X IN is coupled to one port, and the local oscillator X LO to a second port. The output X OUT is taken from the third (intermediate frequency) port. in out Lo X X X →→ The mixer design and the amplitude of the LO are chosen to impart on X OUT a beat note at the intermediate frequency through product terms of the form 0 out in L X XX = A quadratic or “square law” term in the mixer transfer function is an effective way to do this: X out = AX in 2 1 for a fascinating story behind the roots of the heterodyne technique, see Wikipedia entry http://en.wikipedia.org/wiki/Superheterodyne. This is in large part the personal story of the creative genius, Edwin Armstrong, who later invented and developed FM radio in the 1930s.
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Notes#8, ECE594I, Fall 2009, E.R. Brown 122 To see how the beat note is created, we assume coherent input and LO waveforms with a arbitrary phase difference, φ : 2 2 ) ( ) ( LO in out X X A t X + = ) cos( φ ω + = t B X in in ( ) cos LO LO X Ct = ( 1 ) () ( ) ( ) + + + + + + + + = ] ) cos[( ] ) cos[( ) 2 cos( 1 2 ) 2 2 cos( 1 2 ) ( 2 2 t BC t BC t C t B A t X in LO in LO LO in out The first two terms (with prefactors B 2 /2 and C 2 /2, respectively) represent the “self-mixing” of the LO and input waveforms, respectively, with a dc term and second harmonic for each.
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Notes8-1 - Notes#8, ECE594I, Fall 2009, E.R. Brown...

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