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Class22_InterconnectII

# Class22_InterconnectII - I nte rconne I I C 22 ct lass Pre...

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12/4/2002   Interconnect II – Class 22 Prerequisite Reading - Chapter 4

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12/4/2002 Interconnect II 2 Key Topics: Frequency Content of Digital Waveforms Frequency Envelope Incorporating frequency domain effects into time domain signals Effects of Frequency Domain Phenomena on Time Domain Digital Signals
12/4/2002 Interconnect II 3 Square wave: Y = 0 for - π < x < 0 and Y=1 for 0 < x < π Y = 1/2 + 2/pi( sinx + sin3x/3 + sin5x/5 + sin7x/7 … + sin(2m+1)x/(2m+1) + …) 1 2 3 4 5 May do with sum of cosines too. 1 0 - π π 2 π 3 π 1 1 + 2 1 + 2 + 3 1 + 2 + 3 + 4 1 + 2 + 3 + 4 + 5 Decomposing a Digital Signal into Frequency Components Digital signals are composed of an infinite number of sinusoidal functions – the Fourier series The Fourier series is shown in its progression to approximate a square wave:

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12/4/2002 Interconnect II 4 The amplitude of the the sinusoid components are used to construct the “frequency envelope” – Output of FT Frequency Content of Digital Signals 1 3 5 7 9 …... Harmonic Number 20dB/decade 40dB/decade r T 35 . 0 P w T T 1 T r
12/4/2002 Interconnect II 5 Estimating the Frequency Content Where does that famous equation come from? It can be derived from the response of a step function into a filter with time constant tau Tr F 35 . 0 = ) 1 ( / τ t input e V V - - = Setting V=0.1V input and V=0.9V allows the calculation of the 10-90% risetime in terms of the time constant 195 . 2 105 . 0 3 . 2 % 10 % 90 % 90 10 = - = - = - t t t The frequency response of a 1 pole network is dB dB F F 3 3 2 1 2 1 π πτ = = Substituting into the step response yields dB dB F F t 3 3 % 90 10 35 . 0 09 . 1 = = -

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12/4/2002 Interconnect II 6 Estimating the Frequency Content This equation says: The frequency response of the network with time constant tau will degrade a step function to a risetime of t 10-90% The frequency response of the network determines the resulting rise time ( or transition time) The majority of the spectral energy will be contained below F 3dB This is a good “back of the envelope” way to estimate the frequency response of a digital signal. Simple time constant estimate can take the form L/R, L/Z0, R*C or Z0*C. dB F t 3 % 90 10 35 . 0 = - Edge time  factor
12/4/2002 Interconnect II 7 The frequency dependent effects described earlier in this class can be applied to each sinusoidal function in the series Digital signal decomposed into its sinusoidal components Frequency domain transfer functions applied to each sinusoidal component Modified sinusoidal functions are then re-combined to construct the altered time digital signal

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Class22_InterconnectII - I nte rconne I I C 22 ct lass Pre...

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