This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 Sdomain equivalent for 0 s t < 1. Find Vcl(s), vc1(t), and vczm. Hag _ IBuCe)
vHIItII—ﬁ“ By Ohm's law in s—domain, V02(s) = 3 C03 8 Thus, 1202(2‘): l3x tilt“) 1<r<2 Step 3: Drawlabel Sdomain equiv. for 2 s t < 3. Find Vc1(S)a ch(s), 12610), and 12020). TrueFalse: 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 sdomain equivalent circuit below. .3
H(S)—'— _0___Vut(s)_ __Yn( C3 ]X( a ): é \ang which implies that Vout(s)= [ QCS 33
£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: TrueFalse:
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? ...
View
Full Document
 Spring '06

Click to edit the document details