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Unformatted text preview: Let ﬂ? = 21121533.; then .119 = 2 + 5 cmfoZnﬁJ9  (II)  2.4 cmfﬂonﬁJ9  4)) or .119 = 2 + 5 msﬂma t 4))  2.4 cmfymaf (I9 ..F.ourier series:
.119 =01: + a: [11$me 9 + a2 cmfzma 9 + . . .
+ in ﬂ'ﬂftﬂm + £12 ﬁﬂfEma9 + £13 sfﬂféma9 + . . . Here m? = 2 ; a2 = 4 ; 92 = 3 ; a9 = 4.4 ; 31 all others are D. Prob. 1.10: From prob. 1.9: XIHHIH a“ MU : xiii—1H} Fig. 1.34 a]: Prob. 1.22: .119 = 2 + sfan.4t)  4 castJ 1) Periodic: yes, since 1.4=2[D.T) & 2.1=3[D.T).
.So..fundamental angular frequency.r is on = 0;?"
and fundamental frequencyr is ﬁ = e. M211)
and fundamental period is To = (says. a Sines: 1.19 = 2 + sfan.4t)  4 sinfzJ t + m2)
= Zsfnfm) + 54111141) + 4 .5411er f m?) Frequencies: of; 1.44211); 114211;); Amplitude s: 2; I; 4; at,
Phases: m‘°2; 0; so”? Cosines: .119 = Zoosfﬂ) + cmﬂ.4f W) + 4 ﬁanJ t it) Phases: 4:3; 3; m2 Complex Farm: Mt) = :1. ﬁrm (amt?) ~ .1..4_m(%,t) . amplitusiez Phaae; .:i Memorylsss systems: R1
up} _._
R2 wt)
o +
5mm
Wt)
212 +
fun 0 +
wit} it ﬁt) Dne input, one output.
[linear]. Linear: 2 inputs, 3 outputs. anlinear Systems with memory: Linear system State: capacitor voltage; Hit} Zerosstate response: output yfﬂ corresponding to input aft} where the
initial capacitor voltage is zero. "Memoryless" component: operational ampliﬁer [opamp} Behavior: 1'. = ﬂ
II+ = ﬂ ' ' yﬂ} =Afv+fﬂ  “(0)
:‘L :L i where Areal and A is uerylarge. ..Ide.al.opamp: A. —r .90 .and so. ”+139 = up), for...linear operation. [Zipamp examples: Since mfg = “(9, v1 = ﬂ : and sum of currents into node [1] = D, so that (ergeym + @(yﬂ)ﬂr = ﬂ, and then y(9 = (Hfﬁﬁ1)ﬂ(9 C +
I _
' +
IIV
'iﬂjndﬂﬂ ifv'ti'ﬂf'="¥f'I/'fﬂ Cﬂﬂfﬁ ‘3?de = (L’(HC3‘)ﬂfl} ...
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 Spring '08
 Robertazzi,T

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