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RFIC_Lecture_Note_No6_p76-p92 (Bandwidth estimation)

# RFIC_Lecture_Note_No6_p76-p92 (Bandwidth estimation) -...

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ECE695F RFIC Prof. S. Mohammadi Bandwidth Estimation A lot of amplifiers that we design are wide bandwidth amplifiers Æ they show gain over a wide frequency range Æ a few octave sometimes a few decade gain at medium frequency voltage gain 0.707 BW f The 1st question is how to estimate the bandwidth 1. from measurement 2. from hand calculation frequency measurement time domain measurement of course we can do spice simulation (in our case spectre) and find the predicted performance but that does not give us insight into the design So we are looking into a better way of understanding limits of our design - 76 -

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ECE695F RFIC Prof. S. Mohammadi Measurement of bandwidth Take a network analyzer and measure S-parameters -3dB frequency frequency rt S plot ω 21 ) ( 21 dB S BW often network analyzer do not work at very low frequency so we may not see low-frequency roll-off regime from S-parm Æ calculate h-parm Æ calculate voltage gain frequency V A BW mid V A 707 . 0 Question: Can we measure bandwidth with an oscilloscope ? Æ time domain measurement The answer is yes you can but how? from tome domain, measure rise time to a step input input Amp 10% 90% t r : rise time Æ time it take for the signal to go from 10% to 90% of its final value of course this definition is completely arbitrary - 77 -
ECE695F RFIC Prof. S. Mohammadi Another rise time definition (Elmore rise time) Take a simple RC network R C in V ( ) RC t V out = exp 1 1 = final out V ( ) ( ) 9 . 0 ln 1 . 0 ln % 90 % 10 RC t RC t = = RC t RC RC t t t rise rise 2 . 2 2 . 2 1 . 0 9 . 0 ln % 90 % 10 % 10 % 90 % 90 % 10 = = = = % 90 % 10 rise t Apply impulse Amp t max impulse response 50% t D T T look at the impulse response time duration that impulse response is greater than 50% of its maximum value this is called Elmore time delay - 78 -

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ECE695F RFIC Prof. S. Mohammadi ( ) t V in δ = R C in V out V ( ) ( ) f H f jRC f V V in out = × + = π 2 1 1 now calculate Elmore rise time ( ) ( ) ( ) ( ) ( ) = = = 2 2 2 2 2 0 0 0 1 0 2 4 f f f H df d H f H df d H t rise π Elmore s rise time approximation ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) RC t RC RC RC t RC df H d RCf j RC df H d C R df dH RC j df dH RC j RC j df dH RCf j f H rise rise f f f 2 2 2 2 2 2 4 2 2 2 1 2 2 4 2 2 1 2 2 1 1 2 2 2 2 2 2 0 2 2 3 2 2 2 2 2 2 2 0 0 2 = = = = + = = = + = + = = = = π π π π π π π π π π π Elmore rise time * one more thing: Elmore rise time for cascaded system use approximation formula ( ) ( ) ( ) ( ) ( ) 2 2 2 1 2 2 0 2 1 2 1 0 2 1 2 2 2 1 2 2 0 0 1 0 0 2 4 rise rise rise f f rise t t t df H dH H H H H df d H H t total total + =
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RFIC_Lecture_Note_No6_p76-p92 (Bandwidth estimation) -...

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