Learning Objectives:

1. Compare analog filters with digital filters.
2. Operating characteristics of simple analog filters, such as RC, LC, RL, RLC, Chebychev filters

In order to eliminate the unwanted interference that accompanies a signal, a filter is needed.

A filter is an electrical circuit that can be designed to modify, reshape or reject all unwanted frequencies of an electrical signal and accept or pass only those signals wanted by the circuit designer.

Classification of filters based on frequencies allowed:

• Low pass filters: Allows signal with low frequencies while rejecting higher frequencies. Can be a combination of capacitance, inductance or resistance intended to produce high attenuation above a specified frequency and little or no attenuation below that frequency.
• High pass filters
• Band-pass filters
• Band-reject filters

Classification of filters based on Type of signal handled:

• Continuous time
• Discrete time

Classification of filters:

• Passive filters
• Active filters

Low Pass Filter

Vadmium, Public domain, via Wikimedia Commons

High Pass Filter

No machine-readable author provided. Vadmium assumed (based on copyright claims)., Public domain, via Wikimedia Commons

Active band pass filter

SeeOnKasutaja, CC BY-SA 4.0, via Wikimedia Commons

Passive Band Pass Filter

SeeOnKasutaja, CC BY-SA 4.0, via Wikimedia Commons

Solved Example: 9940-01

Find the cut-off frequency for an RC low pass filter of R = 8.2 $\Omega$ and C = 0.0033 $\mu$F.

A. 6 kHz

B. 5.88 MHz

C. 4.26 kHz

D. 170 MHz

\begin{align*} f_c &= \dfrac{1}{2\pi RC}\\ &= \dfrac{1}{2 \pi \times 8.2 \times 0.0033 \times 10^{-6}}\\ &=5.88\ MHz \end{align*}

Correct Answer: B

Solved Example: 9940-02

A simple low pass RC filter having a cut-off frequency of 1 kHz is connected to a constant ac source of 10 V. Calculate C if R = 10 k$\Omega$

A. 15.9 nF

B. 15.9 F

C. 1 nF

D. 1 F

\begin{align*} f_c &= \dfrac{1}{2 \pi RC}\\ 1000 &= \dfrac{1}{2 \pi \times 10 \times 10^3 \times C}\\ C &= \dfrac{1}{2 \pi \times 10 \times 10^3 \times 1000}\\ C &= 15.9\ nF \end{align*}

Correct Answer: A

Solved Example: 9940-03

$G(s) = \dfrac{1}{(1 + sRC)}$ in a RC network represents _______:

A. Low pass

B. High pass

C. Band pass

D. Band stop

Correct Answer: A

Solved Example: 9940-04

For attenuation of high frequencies, we should use:

A. Shunt capacitance

B. Series capacitance

C. Inductance

D. Resistance

Correct Answer: A

Solved Example: 9940-05

Consider a low-pass filter module with a pass-band ripple of $\delta$ in the gain magnitude. If M such identical modules are cascaded, ignoring the loading effects, the pass-band ripple of the cascade is:

A. $1 - (1-\delta)^M$

B. $\delta^M$

C. $(1- \delta^M)$

D. $(1-\delta)^M$

Correct Answer: A

Solved Example: 9940-06

An apparatus to capture ECG signals has a filter followed by a data acquisition system. The filter best suited for this application is:

A. Low pass with cutoff frequency 200 Hz

B. High pass with cutoff frequency 200 Hz

C. Band pass with lower and upper cutoff frequencies 100 Hz and 200 Hz for its pass band

D. Band reject with lower and upper cutoff frequencies 1 Hz and 200 Hz for its stop band

Correct Answer: A