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202 Lec 11

202 Lec 11 - Lecture 11 Switched Capacitor N...

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Unformatted text preview: Lecture 11: Switched Capacitor N etworks—Worksheet Approach EXAMPLE 1. Switch operation in the circuit below: (i) Position A at t = O and moves to B at t = 1. (ii) Moves to A at even integer time instants and back to B at odd integer time instants. OBJECTIVE: Assume all ICs are zero for t < 0. Compute vC 1(t) and v02(t) at several time instants. + lEiult) v62 Step 1. Draw and label S-domain equivalent for 0 s t < 1. Find Vcl(s), vc1(t), and vczm. Hag _ IBuC-e) vHIItII—ﬁ“ By Ohm's law in s—domain, V02(s) = 3 C03 8 Thus, 1202(2‘): l3x tilt“) 1<r<2 Step 3: Draw-label S-domain equiv. for 2 s t < 3. Find Vc1(S)a ch(s), 12610), and 12020). True-False: The voltage across each capacitor is the same. 1AM g 5 What is the combined current produced by the two sources, if for example the two sources were combined into a single source? 1+8 CQ 8 What is the impedance seen by t '3 combined current source? «'5 “ZS 6 Zé~ D By Ohm's law, V02(s) = g and 11020): / LL 3 l /3C05 EXAMPLE 2. Switched Op Amp Worksheet OBJECTIVE. Imitate an op amp integrator behavior by a switched capacitor circuit. Preliminaries: v. m i Q 2 F Vent _ _ L _ 23 Switched Op Amp Circuit. Find vou,(t) for O s t s 4 for the RELAXED circuit below. Switching Action: (i) position A at t = 0 and moves to position B att = 1. (ii) Returns to A at t = 2 (iii) Subsequently moves to B at all odd integer valued time instants and back to A at all even integer time instants. Step 1. Find vcl(t) for n s t < n+1, n = 0, 2, 4, 6, ...., i.e., when switch is in position A. The answer is obvious, says Mr. Obvious! mm: 2 fornst<n+1,n=0,2,4,6,.... Step 2. Find Vow“) for 0 s t < 1. Mr Obvious says: Vow“) = CD for 0 s t < 1. Step 3: Find Vom(s) and v0m(t) for l s t < 2. Label the s-domain equivalent circuit below. .3 H(S)—'—- _0___Vut(s)_ __Yn( C3 ]X( a ): -é \ang which implies that Vout(s)= [- QCS 3-3 £6515): "‘ch Therefore vout(t)- — for 1 s t < 2. Step 4: From step 1, Vow“) = —1 V for 2 _<_ t < 3. Step 5: Using the result of step 4, label the equivalent s—domain circuit below valid for 3 < t < 4. Strategy: superposition to obtain Vom(s). (a) Find the contribution to V 0mm) due to the source on the input branch of the circuit (b) F1nd the contribution to V out“) due to the source in the feedback branch of the circuit. A. «33 b 9 aye - 3 S (C) By superposition, Vow“) = Se __, L Therefore Vow“) : V for 3 s t < 4. Step 6: True-False: 0 OSt<1 voutm = —0.5(n+1) n St< n+2,n= 0dd# "Odd number" means positive odd integer. Plot Vout(t). Superimpose the line v = 0.5t on your plot. Does the switched cap amplifier approximate the preliminary continuous time integrator?? How well? ...
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