Consider the system shown below in block form. The first filter block, designated generically asH,(s) is a linear system characterized by a differential equation given by,V) + 100 V,) + 10ʻV,1) = 100 V,C)(1)where V,(t) and V,(1) are the input and output to that block, respectively. The second filter block,designated generically as H,(s) is a linear system characterized by a differential equation given by,Vot) + 100 Vt) = 100 V,()(2)where V,(t) and V(t) are the input and output to that block, respectively. The various other inputsare steady state and given in the block diagram. Note that the summer produces the signal, V,, byadding Vsj and Vs2. The multiplier produces the signal, V, by multiplying V, and VL0-V5 = cos(2000t) -+)H,(s)H,(s)- V.outVs2 = cos(10001)V10 = cos(1000t)a) What frequencies will appear in the output? For example, frequencies of 1000 and 2000appear as inputs in this system.b) What is the DC average of Vout?c) Find the impulse responses, hi(t) and h2(t), of the linear systems.

Answered: What frequencies will appear in the…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

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Consider the system shown below in block form. The first filter block, designated generically as
H,(s) is a linear system characterized by a differential equation given by,
V) + 100 V,) + 10ʻV,1) = 100 V,C)
(1)
where V,(t) and V,(1) are the input and output to that block, respectively. The second filter block,
designated generically as H,(s) is a linear system characterized by a differential equation given by,
Vot) + 100 Vt) = 100 V,()
(2)
where V,(t) and V(t) are the input and output to that block, respectively. The various other inputs
are steady state and given in the block diagram. Note that the summer produces the signal, V,, by
adding Vsj and Vs2. The multiplier produces the signal, V, by multiplying V, and VL0-
V5 = cos(2000t) -
+)
H,(s)
H,(s)
- V.
out
Vs2 = cos(10001)
V10 = cos(1000t)
a) What frequencies will appear in the output? For example, frequencies of 1000 and 2000
appear as inputs in this system.
b) What is the DC average of Vout?
c) Find the impulse responses, hi(t) and h2(t), of the linear systems.

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Writing the equations in Laplace domain

$\overset{. .}{V_{2}} (t) + 100 \dot{V_{2}} (t) + 10^{6} V_{2} (t) = 100 \dot{V_{1}} (t) = S^{2} V_{2} (S) + 100 S V_{2} (S) + 10^{6} V_{2} (S) = 100 S V 1 (S) . . . . . . (1) {\dot{V}}_{o u t} (t) + 100 \overset{}{V_{o u t}} (t) = 100 \overset{}{V_{3}} (t) = S V_{o u t} (S) + 100 V_{o u t} (S) = 100 V_{3} (S) . . . . . . . . . . . . . . (2)$

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