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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