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chap4_lec3

# chap4_lec3 - Eeng 360 1 Chapter 4 Bandpass Circuits...

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Unformatted text preview: Eeng 360 1 Chapter 4 Bandpass Circuits Limiters Mixers, Upconverters and Downconverters Detectors, Envelope Detector, Product Detector Phase Locked Loops (PLL) Huseyin Bilgekul Eeng360 Communication Systems I Department of Electrical and Electronic Engineering Eastern Mediterranean University Eeng 360 2 Limiters Limiter is a nonlinear circuit with an output saturation characteristic. It rejects envelope variations but preserves the phase variations. ( ) ( )cos( ( )) ( ) cos( ( )) in c out L c v t R t t t v t KV t t ϖ θ ϖ θ = + = + Ideal limiter characteristic with illustrative input and unfiltered output waveforms. Eeng 360 3 Mixers Ideal mixer is a mathematical multiplier of two input signals. One of the signals is sinusoidal generated by a local oscillator. Mixing results in frequency translation. SSB mixer ( 29 ( 29 { } Bandpass Input Signal Re c j t in in v t g t e ϖ = Eeng 360 4 Mixers ( 29 ( 29 { } ( 29 ( 29 { } ( 29 1 Bandpass Input Signal Mixer Output Re Re cos 4 c c c j t in in j t in j t in in v t g t e v t A g t e t A g t e g ϖ ϖ ϖ ϖ = = = + ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 {} {} {} ( 29 ( 29 ( 29 { } ( 29 ( 29 { } * * * 1 * 4 1 1 R 2 2 e 2 2 Re Re c c c c c c c c c j t j t j t j t j t j t j t in in in in j t j t i u n in c t e e e A g t e g t e g t e g t e A A v t g t e g t f f e ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ-- +- +--- +- ⋅ = + = + + + + + ⋅ = = ⋅ UPCONVERSION DOWNC BANDPASS FILTER BASEBAND O ONVER R BAN DPASS FILTE SI N R O d c f f f f + = - Eeng 360 5 Choosing LO Frequency of Mixers ( 29 ( 29 ( 29 { } ( 29 ( 29 { } t j in t j c c e t g A e t g t v Re 2 Re 2 2 ϖ ϖ ϖ ϖ-- = = ( 29 ( 29 ( 29 { } ( 29 ( 29 { } t j in t j in c c e t g A e t g A t v ϖ ϖ ϖ ϖ- + + = * 1 Re 2 Re 2 ( 29 ( 29 ( 29 ( 29 ( 29 * * * *- Upper & lower sidebands are exchanged * Phase spectrum is inverted j t j t in in in in F g t g t e dt g t e dt f f G ϖ ϖ ∞ ∞----∞-∞ = = =- → → ∫ ∫ If ( f c- f ) = 0 Low Pass Filter gives baseband spectrum If ( f c- f )> 0 Bandpass filter Modulation is preserved Filter Output: If f c > f 0 modulation on the mixer input is preserved If f c < f ‘ ϖ ’ needs to be positive Complex envelope is conjugated...
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chap4_lec3 - Eeng 360 1 Chapter 4 Bandpass Circuits...

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