Now, whenever you have an op amp with a large CS, a large RF, and a small CF, the noise gain will rise at moderate frequencies. The definition of noise gain is the reciprocal of the attenuation from the output back to the −input. In other words, if the attenuation is ZIN/(ZIN + ZF), then the noise gain is 1 + ZF/ZIN.
At moderate frequencies, the ZF is determined by RF, and ZIN is established by CS. So, the noise gain will rise until the frequency where the impedance of CF becomes equal to RF. Then the noise gain flattens out, typically at a large number, such as 20, 40, or 80. We do this because if the noise gain kept rising at 6 dB/octave while the op amp's gain is rolling off at 6 dB/octave, the loop is going to be unstable, and it will oscillate. The reason that we choose a small value of CF is to make the noise gain flatten out, make the loop stable, and stop the oscillation and ringing (Fig. 4).
If you make CF = CIN, you can get the noise-gain curve to stay flat as in line A-E. It will be very stable but have a very slow response. If you add no feedback capacitor, the noise gain will tend to rise as per line A-B-C. This will cause instability. Selecting a suitable small value for CF can get the smooth results shown by line A-B-D. Yeah, it's as easy as ABD to get fast, stable response by picking a small CF. So, we have made the feedback capacitance big enough to stop the oscillation and minimize the overshoot. Now what?
There's a pretty good book by Jerald Graeme (ex-Burr-Brown) on the topic of the transconductance amplifier: Photodiode Amplifiers—Op Amp Solutions. Jerry and I have definitely come to the same basic conclusion. When you want to optimize a transimpedance amplifier, everything interacts. Therefore, every time you compute the response and the noise, and change any factor, the computations may change considerably. There's no simple or obvious way to compute or optimize the performance. The performance, in terms of response or bandwidth, in terms of peaking or overshoot, and in terms of noise or SNR, is an extremely complicated, nonlinear, and highly interacting function of:
- the feedback resistor
- the source capacitance
- the feedback capacitance
- the desired bandwidth
- the desired gain factor (which does predict the full-scale output voltage)
- the voltage noise of the op amp
- the current noise of the op amp
- the input capacitances of the op amp
- and the gain-bandwidth product of the op amp.
Jerry and I certainly agree on that. Jerry's book is well written, and for just $55, it's pretty much a bargain. I recommend it: ISBN = 0-07-024237-X (www.amazon.com/exec/obidos/ASIN/007024247X/o/qid=968200121/sr=8-1/ref=aps_sr_b_1_3/002-6674439-7948805).
But I also have worked on this general problem many times over the years and have several suggestions that go be-yond Jerry's book. More on this later.
There are several basic rules of thumb that Jerry and I agree upon:
(A) You want to avoid an op amp with high voltage noise (nV/√Hz).
(B) You want to avoid an op amp with high current noise (pA/√Hz). (Most bipolar op amps have much higher current noise than FETs.) It's a rare case when an op amp with bipolar input transistors is better, except when RS is very low or resistive (or in cases where the input is capacitive but the bandwidth is narrow).
(C) You usually want to avoid an op amp with large input capacitance. Unfortunately, most data sheets don't properly specify the op amp's input capacitances, neither differential-mode nor common-mode. But it's fair to assume that most "low-noise" op amps have a larger input capacitance than ordinary op amps. You may want to ask the manufacturer, or you might just decide to measure it yourself.
(D) Much of the noise of such a transimpedance amplifier is proportional to √BW &215; CSOURCE × VN of the op amp. So if you want to get low noise, you must optimize very carefully. Specifically, begin by computing the im-pedance ZS of your sensor at the maximum frequency of interest:
ZS = 1/2πFCS
For a good amplifier, the voltage noise and the current noise times ZS should both be as small as you can get. If one of these noises is much larger than the other, then you're probably far off optimum.
(E) If you have any choice of what sensor you employ, try to find a lower-capacitance sensor. Furthermore, make a low-capacitance layout between the sensor and the op amp.
If you want to get fast response, low noise, or wide bandwidth, Jerry's book offers some pretty good advice. More on that later.
But Jerry didn't include a list of good op amps that have low voltage noise, and/or low current noise, and/or low input capacitance. Because some are better than others, I bet you can use Paul Grohe's selector guide to find some low-noise op amps. See www.national.com/selguide for free "Selguide" software that can run on your PC to help you select a good, low-noise, inexpensive op amp.
Also, Jerry neglected to mention that you can design your own op amp with better, lower voltage noise and better bandwidth. I mean, op amps that you can buy off the shelf cover a wide array of cases where they are optimized for low VNOISE and low INOISE, wide bandwidth, low power drain, and so on. But you can "roll your own" surprisingly easily and accomplish even better performance for a specified application! I'm not proposing that you design a complete op amp, but it's simple to just add a new low-noise front end ahead of a suitable op amp.
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