代写代考 ECE 2020 Fall 2022 HW 8

ECE 2020 Fall 2022 HW 8

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1. Consider the circuit below, where the output voltage is measured across the resistor.

a. Find the transfer function for the filter circuit above (

) as a function of jω. (Leave R and C as
variables)

b. Transpose the transfer function to a Magnitude and Phase , that is |𝐻(𝑗𝜔)|𝑒𝑗𝜃 form.

c. Approximate the magnitude and phase of H(jω) as ω approaches 0; and as ω approaches infinity.

d. If R = 4000 ohms, C = 2.5uF what is the corner frequency ω0 in rad/s.

e. What is the corner frequency, f0 in Hz?

f. Is this a high pass or low pass filter?

g. What is the passband gain of the circuit in [dB].

h. Assuming C does not change, choose R for a cut off frequency of 50Hz.

2. For the circuit below:

a. Leaving R and C as variables, find the current transfer function, HI =

b. Find the – 3dB frequency (Hz).
c. Is this a low pass or high pass filter?
d. If R = 1000 ohms, what value capacitor would make the cutoff frequency 2000 Hz?

M : a 品ti—
— phase : 逾 |tam

magnitude : = 0 piase:aovsmagsitude : 1 Phase : 00

点 = 计 (☆ ( u— =⇒ω= c≈ 3 ω
= 4000* 2 .

6 : 100 rad / s

器 =器 ≈ 15 . 92 HZ

High pass filter

O UB HoidB } = 20 log 。 H 。

50 = π R ( 2 – 5 × 10 – 6 ) ( w

品̂ = 襄 : 痴i

( a ) simcIi cz 了 H

: 计 5… (c 3 w = O = ) Hi =

cd ) c = Iatiz

及 t juwc W E ω = ∞ =⇒ ( Hi

2π fc = 及 C

u = 号 =iwacy fc = 之πO low Rassfiltet

7 . 96 × 30-

zol 0g ( 1 t ( ☆ 。

—, = – 2010 g [ 1+ ] = – { ds ≈ 0 . 7010^~ O
-3 ds fe 4 . = Cat – ott teq . = corner

fle 9 . = wc = 79 . 6 nF

3.) For the circuit below, R = 2000Ω, L = 2mH and the output is the voltage across the inductor:

a. Find the transfer function for the filter.
b. Find the cutoff frequency of the filter.
c. Is this a high or low pass filter?
d. What is the maximum value of the transfer function in V/V?

ca ” 品tzn = jul+ )☆πmu

sok = 品 1 =π zmH 元 159154

= ⼁ H 0 cjw 3 l

w = 0 = 3 – H =
=☆ =☆ Hi ∞

ligh pass filter

^= 1000000

≈ 0 – 7071Uπ ⼀

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