(a) Consider the circuit shown in Figure Q2-1, derive an expression for Vout in terms of vin Rf ww R₁ Vin +0 Vout I Figure Q2-1 (b) Describe the usage of negative-feedback and positive-feedback amplifier circuits in real world applications.

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Table 1: Laplace Transform Properties
Linearity L {af(t)} = aF(s)
Superposition
Modulation L {e-at f(t)} = F(s + a)
Time-Shifting L{f(t-7)u(t-7)} = e-TF(s)
Scaling L{f(at)} = F(2)
| L { $(10)} = 8
= 8F(s)-f(0)
L{f(t)} = F(s)
L {fi(t) + f₂(t)} = F₁(s) + F₂(s)
Real Differentiation L
Real Integration
Complex Differentiation
L {tf(t)}
-F(s)
ds
Complex Integration {f} = f* F(®)
L
Convolution L {f(t) *g(t)} = F(s). G(s)
Table 2: Common Laplace Transform Pairs
f(t)
F(s)
8(t)
u(t)
tu(t)
e-atu(t)
te-atu(t)
cos(wt)u(t)
sin(wt)u(t)
1
1
s+a
1
(s + a)²
8
8² +w²
8² +w²
Transcribed Image Text:Table 1: Laplace Transform Properties Linearity L {af(t)} = aF(s) Superposition Modulation L {e-at f(t)} = F(s + a) Time-Shifting L{f(t-7)u(t-7)} = e-TF(s) Scaling L{f(at)} = F(2) | L { $(10)} = 8 = 8F(s)-f(0) L{f(t)} = F(s) L {fi(t) + f₂(t)} = F₁(s) + F₂(s) Real Differentiation L Real Integration Complex Differentiation L {tf(t)} -F(s) ds Complex Integration {f} = f* F(®) L Convolution L {f(t) *g(t)} = F(s). G(s) Table 2: Common Laplace Transform Pairs f(t) F(s) 8(t) u(t) tu(t) e-atu(t) te-atu(t) cos(wt)u(t) sin(wt)u(t) 1 1 s+a 1 (s + a)² 8 8² +w² 8² +w²
(a) Consider the circuit shown in Figure Q2-1, derive an expression for vout in terms of vin.
Rf
R₁
W
Vin
o+
Vout
Figure Q2-1
(b) Describe the usage of negative-feedback and positive-feedback amplifier circuits in real
world applications.
Transcribed Image Text:(a) Consider the circuit shown in Figure Q2-1, derive an expression for vout in terms of vin. Rf R₁ W Vin o+ Vout Figure Q2-1 (b) Describe the usage of negative-feedback and positive-feedback amplifier circuits in real world applications.
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