Q1. (a) Show an opamp circuit that can perform 1st order derivative of a time function, f(t). f' df (t) dt Specify the resistor and capacitor values so that the coefficient of the 1st order derivative is 1. (Note: Polarity of the implemented function is not important)

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Q1.
(a) Show an opamp circuit that can perform 1st order derivative of a time function, f(t).
df (t)
dt
Specify the resistor and capacitor values so that the coefficient of the 1st order
derivative is 1. (Note: Polarity of the implemented function is not important)
f' =
(b) The temperature at a place can be described by the following time function, f(t):
f(t) = a3t³ + a₂t² + a₁ +ao,
which exhibits the following characteristic as shown in Fig. Q1:
Temperature (°C)
T₁
T₂
Time (hour)
Fig. Q1
(i) Determine the 1st order derivative of f(t), and estimate T and T₂ in terms of a3, a2,
ai, ao.
(ii) An engine will be turned on between the interval of T, and T₂. Devise a circuit that
will generate an EN signal that will be high during the interval between T₁ and T₂.
Transcribed Image Text:Q1. (a) Show an opamp circuit that can perform 1st order derivative of a time function, f(t). df (t) dt Specify the resistor and capacitor values so that the coefficient of the 1st order derivative is 1. (Note: Polarity of the implemented function is not important) f' = (b) The temperature at a place can be described by the following time function, f(t): f(t) = a3t³ + a₂t² + a₁ +ao, which exhibits the following characteristic as shown in Fig. Q1: Temperature (°C) T₁ T₂ Time (hour) Fig. Q1 (i) Determine the 1st order derivative of f(t), and estimate T and T₂ in terms of a3, a2, ai, ao. (ii) An engine will be turned on between the interval of T, and T₂. Devise a circuit that will generate an EN signal that will be high during the interval between T₁ and T₂.
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