One of the first things you learn about operational amplifiers (op amps) is that the op amp's gain is very high. Now, let's connect a feedback resistor across it, from the output to the −input. When you put some input current into the −input (also known as the summing point), the gain is so high that all of the current must go through the feedback resistor. So, the output will be VOUT = −(IIN × RF). That's neat (Fig. 1). While we used to call this a "current-to-voltage converter," which it is indeed, it's also sometimes referred to as a "transimpedance amplifier," where the "gain" or "transimpedance" is equal to RF.
There's a whole class of applications in which this configuration is quite useful and important. An important case is when you need an op amp to amplify the signal from a sensor, such as a photodiode. Photodiodes put out current at high impedance (high at dc), but often they have a lot of capacitance. If you just let the photo diode dump its current out into a resistor, there are two problems (Fig. 2). If the sense resistor is large, then the gain can be fairly large, but the response will be slow and the time-constant will be large: τ = RL × CS. But if you choose a small sense resistor to get a small τ, the gain will be low. The signal-to-noise ratio (SNR) may also be unacceptable. How can you avoid poor gain and/or poor response? Kay garney? (That's Nepali for "What to do?")
To avoid this terrible compromise, it's a good idea to feed the photodiode's output current directly into the summing point of a transimpedance amplifier (Fig. 3). Here, the response time is not RF × CS, but considerably faster. Plus, the gain can be considerably larger, because now you can use a larger RF. This helps improve the signal-to-noise ratio too!
When you connect up the diode like this, the first thing you realize is that the darned thing is oscillating! Why? Well, it's well known that the input capacitance of an op amp (and its circuitry) can cause instability when the op amp is used with a feedback resistor. You usually need to add a feedback capacitor across RF to make it stable. In the old days, it was stated that:
CF × RF = CIN × RIN
So if you have a unity-gain inverter with RIN = RF = 1 MΩ, and the input capacitance of the op amp is 10 pF, then you're supposed to install a feedback capacitor of 10 pF. That's what people said for years. The LF156 data sheet stated this, and it still does. But that's not exactly true. A complete explanation is a bit beyond the scope of this column, but in practice you can usually get away with a much smaller feedback capacitor. In many cases, you can get a response that's improved by a factor of five or 10, and still not get excessive (more than 5% or 10%) overshoot. In practice, you have to tweak and optimize the feedback capacitance as you observe the response.
The formula for the optimized amount of CF is, if:
then:
but if:
the feedback capacitor CF should be:
Reprints
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