Video Lectures: - http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-002-circuits-and-electronics-spring-2007/video-lectures/lecture-20/
Lecture Notes: - http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-002-circuits-and-electronics-spring-2007/lecture-notes/
We first look at the subtractor circuit. There are five steps in the first method of obtaining v_O.
Another way is the superposition method which is the easier way. The two input voltages are shorted one at a a time, v_1 is set to zero, then v_2 is set to zero. After that the output voltages are added.
Next, we look at how to build an integrator. As voltage output is proportional to the integral of the current, we need to somehow convert voltage v_I to a current. First, we try using a resistor to do so. This can happen when v_O is very small compared to v_R..
However we will find that that this is not possible as the capacitor tends to charge up v_O to a certain value.
The better way is an op amp integrator. With KVL, v_O=v_C.
To build a differentiator as current is proportional to the differential of the input voltage , we need to somehow convert current to a voltage v_O. The circuit is somewhat similar to the integrator except the resistor and capacitor are swapped.
Filters can be built with op amps as well. The problem with passive filters is that it is difficult to get v_O equal to H of j omega v_I.
The moment a load resistance is connected to the filter circuit, the j omega of the filter has changed.
When a a source with an internal resistance R_I is connected to the filter circuit, the filter characteristic will change as well. Worse is that the filter resistance loads the source, so the source may not be able to supply current.
The other issue is that it is difficult to build an inductor in an integrated circuit. As many filter circuits require inductors , we need to look at some other approach of doing such things. The approach is to use op amps and the first approach is known as the brute force approach. In this approach a buffer is used. A buffer can be connected to the input and the output but it is a bit inefficient.
We will see how op amps work with impedances. and sketch a graph for values of low and high omega. In this case, a bandpass filter is obtained.
We can build non linear circuits with op amps. With an inverting amplifier, it is possible to build an exponentiator with the Expodweeb device.
With that in mind, it is possible to build a logarithmic amplifier.
Summing amplifiers can be used to build digital to analog converters.
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