
Simple Amplifiers 

The basic OpAmp circuits. Simple OpAmp; Unity gain buffer; Inverting Amplifier; Noninverting Amplifier. 

Mathematical Operators 

Amplifier circuits to implement operators. Linear  Sum/Difference; Nonlinear  Log/AntiLog/Multiply/Divide (incomplete); Discontinuous  Greater than/Less than/Comparator/Absolute Value. 

Signalling & Comms 

Amplifier circuits for signalling and communication on long lines. Line driver; Line receiver. 

Working 

Some of the examples in this section include mathematical formulae. Where the full derivation is not included, my working is shown here. 

Operational Amplifiers

Operational Amplifiers 
Operational amplifiers are hugely important devices. If you're new to electronics, then they typically appear as the slightly mysterious small triangles, with either three or five terminals. Two of those terminals are typically associated with a power supply, and that just leaves two inputs and an output.
The real utility of the "opamp" lies in its generic nature. It's a fair bit more complicated inside than a transistor, and typically on the semiconductor an opamp is represented by perhaps 25 individual transistors. If you were to build such an amplifier out of transistors, which is possible, it would take up considerable board space, and require significant debugging.
As it is opamps are available in tiny little packages, from 5 pin SOT devices just 0.075" (2mm) in size, right through SOIC and DIP, up to old fashioned round metal cases 3/8" (10mm) in diameter. Because of their size they can be used in quantity, like simple transistors. Crucially, their internal complexity is largely hidden, and externally they are simple and straightforward to use. This is clearly a significant departure from the fairly basic transistor.
Logic gates too, follow the same conceptual idea. By integrating a few transistors, one can build a generic functional block which is somewhat easier, and more straightforward to use than the basic transistor. On the ladder of evolution, an opamp is a slightly more developed and complex beast than the logic gate. For this reason, whilst simple logic circuits easily stretch to 10's of MHz bandwidth without particular care, it is much rarer for proper opamp circuits to stretch beyond 4 or 5 MHz.
Even where high speed devices exist, and they exist with capabilities right up to microwave frequencies, they cannot offset the core signalling constraints that exist at elevated frequencies. These constraints make most of the elegant and simple analogue computation options, of interest here, impossible. At microwave frequencies, opamps are really limited to simple gain and buffering functions. Even though they are high frequency opamps they are not so far removed from their functional brethren, fixed gain amplifiers. In the past these may have been implemented in exotic IIIIV materials like Gallium Arsenide. Today, transistors are so small, anything is possible.
In the main, opamps are most useful and diverse in applications for low bandwidth, high stability instrumentation functions. As frequencies rise, fixed gain amplifiers, transmission lines, filters and attenuators become much more the practical norm. In the realm of base band analogue video, lays a complex mixture of functionality and transmission schemes. Simply, these are better implemented on analogue System on Chip semiconductors. Although it is possible to implement base band video in basic components, it's a fiddly business. Even television in the 1970's wasn't as good as it had become by the mid 1990's and that directly reflects increasing use of analogue Large Scale Integration. Today, the world has seen sense, and television has gone digital.
Proper opamps are truly generic. There are clear types, such as chopper amplifiers and current feedback amplifiers designed for particular performance enhancements. Nevertheless, all simple voltage feed back opamps, are the same thing with different performance enhancements. Some optimise the output swing, input range, isolation, bandwidth and input impedance. Many optimise combinations. Because opamps are generic, for these low bandwidth applications, there are many, many different uses for the same generic device.
From a design perspective, opamps simplify the design mathematics. In the limit they allow one to implement analogue computers. They can be used for addition and subtraction directly. They can implement logarithmic behaviours. By combining these capabilities the four rules of number are available.
In these pages, I'll enumerate some of the many functions that can be implemented with the simple opamp. With this one component type one can do pretty nearly anything one might want to when designing interfaces to real world sensors and transducers. Whilst computing is now fully digital, the real world will always be analogue. Opamps will always exist between computers and the real world. Personally I'd not be surprised in the long term if opamps, in some form, make a resurgence and actually replace the computer as we know it today. 