The transimpedance circuit has some noise and you want to measure it. If that be so, determine the bandwidth of this set up, using as you have done, a voltage source with a large series resistance which makes it a current source.

measure the noise using an rms voltmeter . Then  divide by pi/2 times the -3dB bandwidth and express the result as xx nV/ sqroot hz. [This is because noise bandwidth is (pi/2) times the -3dB frequency]. As an example if the output is 1e-15  with feedback as 1 meg || 10 pf, the noise bandwidth is 1/4RC= 25kHz, then noise per hz is 1e-15/25000 Volt/sqrt Hz. The noise is expressed as xx/sqrt(hz)

 You might recap about noise measurements as it can be due to shot noise or flicker noise. the flicker noise density  has a dependence on frequency .. It has constant power in any octave at low frequencies typically < 100 hz.

http://www.jensign.com/noisebandwidth/index.html

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 Xianqian:

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I think before you make a lot of measurements and create a lot

of data, you should ask some hard questions. Noise has always

been viewed as an elusive subject but the one thing that usually

makes it a less complicated challenge is that because in many

cases it's possible to use superposition methods; that is, noise

sources are generally individually small, and therefore they can

be calculated individually and summed later , either using linear

summation if the noise metric is power, or summed in an RMS

fashion if the preceding metric has been voltage or current. 

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But in asking the question "How does one measure ....

                   the noise of the transimpedance circuit" ....

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   this sounds like a practical question - not a design challenge.

If so, the most revealing tests will be provided by  the use of a

spectrum analyzer at the output of the op amp, while you vary

several parameters of the system.

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Would you like to be clearer as to which of these objectives is

behind the question you originally asked?

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Barrie

V.s.V：

Now I have known the bandwidth measurement method.  Unfortunately, I don`t have an rms voltmeter, but I have read the paper about noise bandwidth. Thank you very much.

Barrie:

Firstly, I should explain that the circuit have been designed and the photo detector is the photomultiplier.

The circuit design referred to the book "Photodiode amplifiers op amp solutions". It consists of two stage amplifications: the first stage has an op amp, a feedback resistor R1 and a feedback capacity C1; the second stage is a voltage amplifier. To meet the high gain requirement, the R1 used the metal film resistor of 100k. The C1 prevents the oscillation and reduces the noise, but it would be limit the bandwidth. The noise calculation learned from the book “Operational Amplifier Noise Techniques and Tips for Analyzing and Reducing Noise”. Can you explain the “superposition methods”? I want to learn these methods and use them.

After calculation, I used the oscilloscope to measure the noise of the circuit, but I not sure if the input terminal should be short or open it. A professor told me that a 1G ohm should be as the input resistor in series because the extremely large resistor would be produce the extremely small current noise. And then when this small current noise flows the circuit, the total output noise approximately regard as the noise floor of the circuit.      

Now I am using the spectrum analyzer to measure the noise, so I desire for some advices from you.

Thank you very much!

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Xianqian:

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The matter of measuring the noise properties of a transimpedance

amplifier is something of great importance to me, as I've designed

a related family products at Analog Devices: the "translinear log

amps”, so called because they exploit the highly reliable IC to VBE

characteristic of bipolar transistors. This specific type of log amp

transforms a large range (200dB = one trillion) of a photodiode's

current to an equivalent decibel form, relative to some reference

current. The data sheet for the ADL5304 (attached) discusses this

in general terms; I suggest you start at page 16.

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Measuring the output noise of these log amps is difficult, partly

because when one’s signal is only a few pA (which means only

a relatively few electrons are involved in carrying information) the

fluctuation in it – the noise current – is necessarily relatively large.

Figure 40 on page 20 of the attached Data Sheet suggests a

method for measuring the noise at the final output of a log amp;

but there is no escaping the fact that measuring the noise of any

type of low-current interface is fraught with challenges.

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It is usually easier to calculate the noise spectral densities of the

principal noise-generating mechanisms, and sum them after they

have been appropriately weighted, followed by integration over the

frequency range of interest. These include the noise of the photo-

diode, the thermal noise of the feedback resistor, the voltage and

current noise at the input of the op amp, and perhaps you also

need to consider the finite noise rejection ratio of the op amp’s

supply voltage(s) – again, all as NSDs which are integrated over

the bandwidth you are seeking to achieve.

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If these notes fail to answer your original question please feel

free to say so. You may also find the following link helpful:

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http://www.analog.com/en/products/optical.html

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Barrie