M E 345 Professor John M. Cimbala Lecture 22
Today, we will:
•
Do some example problems – Filters
•
Review the pdf module: Digital Filters
Example: Low-pass filter circuit
Given: The following components are available:
•
two resistors, 10.0 kΩ and 87.0 kΩ
•
a capacitance decade box
The input voltage contains a signal frequency of 50 Hz, and some unwanted noise at 1000
Hz. We want to amplify the signal, with G
amplifier
≈ 8.5, and we decide to use a first-order
low-pass filter with a cutoff frequency of 200 Hz to attenuate the noise.
(a) To do: Draw the filter circuit and calculate the required capacitance.
Solution:
(b) To do: Calculate the overall gain of both the signal and the noise, and calculate how
well we have improved the signal-to-noise ratio (SNR). Note: SNR is the ratio of signal
power to noise power. Since electrical power is proportional to voltage
2
, we define SNR as
2
signal
signal
noise noise
Power
SNR=
Power
V
V
⎛⎞
⎜⎟
=
⎜⎟
⎝⎠
, or in terms of decibels,
signal
dB 10
noise
SNR =20log
V
V
⎛⎞
⎜⎟
⎜⎟
⎝⎠
.
Solution: