Question 5 The circuit diagram below shows a low pass RC filter circuit, the function of which is to produce a potential difference at the output terminals (v) that resembles the potential difference at the input terminals (vin), but with any high frequency elements (e.g. noise) attenuated. R C 23 The value of v is governed by the ODE dv RC -+v= Vin dt Given that (in Sl units) R = 106, C = 10-7, vin = sin(t) and v(0) = 0, a) use Laplace transforms to solve the ODE to find v as a function of t, plot both v and vin on the same (fully labelled) graph in MATLAB so one can clearly see 4 cycles. (B) Delete this text and use this space to present your working out'. Make this row as deep as is necessary to contain your work. When vin = sin(t), v = Replace this text with your answer.
Question 5 The circuit diagram below shows a low pass RC filter circuit, the function of which is to produce a potential difference at the output terminals (v) that resembles the potential difference at the input terminals (vin), but with any high frequency elements (e.g. noise) attenuated. R C 23 The value of v is governed by the ODE dv RC -+v= Vin dt Given that (in Sl units) R = 106, C = 10-7, vin = sin(t) and v(0) = 0, a) use Laplace transforms to solve the ODE to find v as a function of t, plot both v and vin on the same (fully labelled) graph in MATLAB so one can clearly see 4 cycles. (B) Delete this text and use this space to present your working out'. Make this row as deep as is necessary to contain your work. When vin = sin(t), v = Replace this text with your answer.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Question 5
The circuit diagram below shows a low pass RC filter circuit, the function of which is to produce a potential
difference at the output terminals (v) that resembles the potential difference at the input terminals (Vin),
but with any high frequency elements (e.g. noise) attenuated.
R
Z3
The value of v is governed by the ODE
dv
RC
+v = Vin
dt
Given that (in Sl units) R = 10°, C = 10-7, vin
= sin(t) and v(0) = 0,
a)
use Laplace transforms to solve the ODE to find v as a function of t,
plot both v and vin on the same (fully labelled) graph in MATLAB so one can clearly see 4 cycles.
(B)
Delete this text and use this space to present your working out'. Make this row as deep as is necessary to contain your work.
When vin = sin(t), v =
Replace this text with your answer.
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