The effect of voltage noise rises because of rising noise gain with frequency, as Terry Brown points out. This is true even though the voltage noise is itself flat with frequency.

But the effect of current noise also rises with frequency. This is true not because of rising noise gain, but because the input current noise itself rises with frequency. Examples of this rising current noise can be seen in the plots of Noise Current vs Frequency in the LTC6240 and LTC6244 data sheets, which can be obtained at linear dot com.

Measurement techniques for current noise at low and high frequency can be found in the sidebar of my article "Signal Conditioning for High Impedance Sensors" on the EDN website.

In the case of this present design idea, the input current noise is about 28fA/rtHz at 28kHz, so it is rearing its head but still below the 43fA/rtHz surface. And still well well below the 130fA/rtHz of the "conventional" TIA.

Regarding voltage noise, the 10pF or so total input capacitance (Cpd+Ccm+Cdm) at 28kHz constitutes about 568kOhm of shunt impedance, for a noise gain of 1+10M/0.568M = 18.6 to the 10Meg node (ie before attenuation). That multiplies the 7nV/rtHz input voltage noise to equate to 130nV/rtHz before attenuation, or 13nV/rtHz after attenuation, or 13fA/rtHz input referred.

So the input voltage noise is having less impact than the input current noise. This reality would shift as the photodiode size (capacitance) is increased.

In the upper frequency regions where both of these phenomena occur (rising noise gain and rising input current noise), we can actually calculate the optimum total input C, "C_opt", where the effects of voltage noise and current noise equate. (Called optimum because neither dominates - but it may not be optimum for you.) Looking at the LTC6240 current noise plot for example, you can see the rate of current noise rise with frequency is about 1fA/rtHz per kHz. That reduces to 1aA*Hz^-3/2 ("one attoAmp Hertz to the minus three half") of current noise slope, which we can call m for simplicity. The C_opt can be found to be
C_opt = m / 2*pi*en
where en is the input voltage noise.

I completely agree that active circuits shouldn't be relied on entirely to limit noise bandwidths.

(The underscore in C_opt is there hopefully to avoid search engine confusion with our friends in Egypt.)

Yes, I failed to consider the dynamic range. The virtue of the 50-volt circuit is 10 times more dynamic range.

I agree that the current noise terms (shot noise current, amplifier bias current noise, and feedback resistor noise) all roll off with the transimpedance bandwidth. This is NOT true for the amplifier input voltage noise. The amplifier input voltage noise is multiplied up by the noise-gain (non-inverting gain) of the amplifier. Even though the TIA bandwidth is 28 kHz, the noise-gain bandwidth is considerably higher and integrates to a significant value. This noise term can be easily low pass filtered after the amplifier.

Terry Brown

Thank you for all of your comments, and Terry Brown for your hard work. I am truly consoled that there still exist individuals ready to spend effort to correct an error when they see it, or in this case when they think they see it. I love the truth, and consider all those friends who seek to defend it.

A critic should always consider not only the faults but also the merits of the object under discussion. Otherwise he risks trashing a straw man. The fact that nobody analyzed the circuit where it in fact outperforms the conventional circuit means that nobody was looking for the merit. In this case effort was spent on calculations shoring up an initial hasty dismissal. For that fact I am at least partly to blame, for I should have anticipated that such an ambitious title would have been met with quick suspicion, and I should have pointed out exactly where the circuit is lower noise and where the boundaries of its benefits lay. For that omission I readily apologize.

But the article is correct. The circuit of Figure 2 has lower noise than the conventional TIA of Figure 1. That means that it can resolve SMALLER photocurrents, where noise matters most. All of the critical analyses were done at HIGHER currents, where indeed the photo-shot noise dominates. But while high photocurrent shot noise may set the noise floor of some "systems", it is not the identical with the noise floor of the circuit.

The circuit was intended for applications involving a wide range of photocurrents. My impression from the people posting unfavorable (and quite correct) observations is that they are working with higher fixed photocurrent "systems", and have no use for small signals. In fixed photocurrent applications you wouldn't use a circuit like this. You would just use a feedback resistor calculated for that current level. This circuit supports smaller currents than the conventional TIA does, and it also works up to 5uA. The combination of 43fA/rtHz at small signal levels with linear large signal capability to 5uA in one circuit is a real achievement, and actually does require 50V. It is only "overkill" if you don't want that combination of specificiations.

The 130nV/rtHz of a conventional 1M TIA is equivalent to the shot noise of a 53nA photocurrent. The 43nV/rtHz output noise floor of Figure 2 is equivalent to the shot noise of a 5.8nA photocurrent. Put in those terms, my circuit has 9 times the dynamic range of the conventional circuit.

Put another way, the circuit offers the low noise of a well designed 10M TIA, while supporting the input current capability of a 1M TIA. It also offers the poorer bandwidth of the 10M TIA, but that's actually fortunate because the opamp's input current noise rises at high frequency anyway and that would have degraded higher frequency performance. Note that the bandwidth was included as the final noun in the article. (That was intentional, as it is indeed one of the tradeoffs.)

Put yet another way, the circuit IS a well-designed 10M TIA, (Didn't anyone notice that?) so it has the lower noise floor of a 10M TIA. It gets extended large signal range by working on 50V, and then squeezes it all down into a hopefully more manageble 0-5V range.

Please note that I did indeed take into account the amplifier's voltage noise and input capacitance, as well as its current noise at high frequency. (That's why I didn't mind the fact that the bandwidth was only 28kHz. Above that, the input current noise gets near the surface.)

Then I built it up and tested it, which is the discipline here at Linear Technology. Indeed, the first version I built up used a high voltage opamp in place of the discretes. But I didn't like the performance (in partial answer to K. Slotkowski). (Does anybody care to suggest why the 10k:10k resistive divider is necessary?)

So, anyway, the circuit works and it does what I said it does. I apologize that I didn't clarify exactly "where" it does which thing. Design Ideas are intentionally short. In summary: below 53nA it is lower noise than the conventional TIA. Above 53nA it is shot noise limited.

Best Regards,
Glen BriseboisApplications Engineer
Linear Technology
408-432-1900 x3755
gbrisebois@linear.com

It requires 5µA of photocurrent to produce 5V output. This level of current would have a shot noise of 1.3pA which would produce 1300nV/rt-Hz output noise. It would seem pointless to try ro reduce the resistor Johnson noise, when it is an order magnitude smaller than the shot noise. Both circuits produce the same noise output - 1300nV.