Electronic Devices and Circuits Engineering Sciences 154

Why do we need filters?

One one thing, they are indispensible in communication:

As example, consider a DSB-AM communication protocol:

DSB-AM signal

Suppose we have a single component information signal

Corresponding and manipulated DSB-AM signal

Temporal representation

Spectrum representation

 
FDMA Channel Allocations

Multiplex Paradigm-1: This figure shows a schematic of multiple voice channels aggregated into a channel or message group by using frequency multiplexing.

Multiplex Paradigm-1: This figure shows multiple channel groups aggregated into a higher-order supergroup, again, by using frequency multiplexing.
 

Op Amps are invaluable in the design of filters

Op Amp Unity Gain Configuration Eliminates "Loading" Problems

Our analysis of simple RLC filters can only valid work if the load draws negligible current!  However, an op amp buffer solves the problem. And, thus, buffered filter sections can be cascaded to obtain sharper characteristics - e.g.

Negative Impedance Converter (NIC) (source)

Negative Resiatance Oscillator

Gyrator (source) "Fake L" C Circuit (source)

Combined Notch/Bandpass Filter Responses (reference)

Nodal equations:

Since  the nodal equations become

After much algebra, we find

When   it is a bandpass filter

 

When   it is a notch filter

Nomenclature of Filter:

All of these response characteristics roll off 3 dB at the corner frequency (in this case 10 kHz).  After that, they all differ:

Butterworth is the most popular response. It has no ripple in the pass or stop. There is a single set of component ratios that produces a Butterworth response.

 

Chebyshev response has more roll off than Butterworth, and it has ripple in the pass band.

 

Inverse Chebyshev response has ripple in the stop band, and therefore has a lot of rejection near the corner frequency, but the rejection bounces back, and there is some passage in the stop band.

 

Elliptical response combines the characteristics of Chebyshev and inverse Chebyshev, having ripple in the pass band and in the stop band. Like the inverse Chebyshev, the stop band rejection has some bounce back.

 

Bessel response has less rolloff in the stop band than the other types, and is not as flat in the pass band. Therefore, it has not been a very popular filter response.

2-pole Chebyshev low pass filter (source) 1-pole/2-pole RC Filter (source) Sallen-Key Filter