RFIC_Lecture_Note_No4_p44-p63 _Resonant circuit, Distribuà

RFIC_Lecture_Note_No4_p44-p63 _Resonant circuit, Distribuà

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ECE695F RFIC Prof. S. Mohammadi - 44 - RLC Networks Parallel RLC Tank y 0 ω R 1 C L in I in I + = + + = L C j R L j C j R y 1 1 1 1 R Resonance Æ when capacitive and inductive admittances cancel 0 1 0 0 = L C LC 1 0 = r e s o n a c t R I V in = 0 at resonance: R CI j L j R I Z V I R CI j C j R I Z V I in in ind ind in in cap cap 0 0 0 0 1 = = = = = = currents in inductor/capacitor branches can be very high but they cancel each other how high ? That depends on quality factor Q ?! Q I C L R I C j R I L j R I I I in in in in ind Cap = = = = = 0 0 LC 1 0 = C L R Q = dissipated power stored power factor quality Q = = This is a general definition and applies to both distributed and lumped circuits
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ECE695F RFIC Prof. S. Mohammadi - 45 - Power stored: for parallel RLC it is easy to find the stored energy in the capacitor at resonance! inpeak RI V at = 0 ω inpeak I () 2 2 1 2 1 2 0 2 0 2 2 inpeak cap cap inpeak peak cap I C R E P RI C CV E = = = = Maximum energy in capacitor Resonance energy C L R L R RC Q RI I C R P P Q RI P inpeak inpeak diss cap inpeak diss = = = = = = = 0 0 0 2 2 0 2 2 2 1 2 1 2 1 remember Æ This definition of Q is only valid at resonance! away from resonance we still use this formula but it is not accurate!
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ECE695F RFIC Prof. S. Mohammadi - 46 - Relation between bandwidth and Q Q=20 Q=10 Q=5 y ω 0 + = 0 assume 0 2 2 0 2 2 ωω + + = 2 0 1 = LC 0 2 0 2 2 1 +  ∆ + = LC () 1 1 1 1 2 + = + + = LC L j R L j C j R y + = + +  ∆ + = jC R L j R L j R y 2 1 2 1 2 1 0 0 2 0 LC 1 0 = 0 y R 2 R 1 RC 2 1 = Q RC BW RC BW 1 1 1 0 0 = = = or -3 dB bandwidth Æ So high Q Æ sharper peak
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ECE695F RFIC Prof. S. Mohammadi - 47 - Series RLC L R C R Z Z resonance = = min L & C cancel R C L RC R L Q resonance = = = 0 0 1 ω C S R S L to analyze transform series to parallel P P S S L R R L Q 0 0 = = C P R P L ( ) 2 2 0 2 2 0 2 0 0 0 0 0 P P P P P P P P P P P P S S L R R L j R L R L j R L j R L j R L j + + = + = = + valid at ~ resonance ( ) () + = + = + = + = 1 1 1 1 2 2 2 2 2 2 Q Q C C Q R R Q Q L L Q R R S P S P S P S P S R S L S R S C P R P L P C P L similarly
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ECE695F RFIC Prof. S. Mohammadi - 48 - P R P jX S R S jX ( ) + = + = 2 2 2 1 1 Q Q X X Q R R S P S P S P S P X X R Q R Q = = ⟩⟩ 2 1 only valid for frequencies around resonance * at high frequency Power Gain is important because active devices have limited gain so maximum power transform is an important issue S V S S S jX R Z + = L L L jX R Z + = source impedance is often fixed load impedance?
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This note was uploaded on 02/19/2012 for the course ECE 695f taught by Professor Mohammadi during the Fall '09 term at Purdue.

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RFIC_Lecture_Note_No4_p44-p63 _Resonant circuit, Distribuà

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