Noise equivalent input

For gas or ions, FET sensors response speed is not the main prerequisite because of the relatively long time constants associated with chemical measurements. However, the ON-OFF conductance ratio, as well as the transconductance IJ Vg should be maximized. As far as noise is concerned, attention shold be paid to reducing both the noise-equivalent input current zn and voltage vn generators of the sensor. In fact, the total rms input noise for unity bandwidth of such a device can be expressed in a first approximation as (Motchenbacher and Fitchen, 1973)... 

The achievable signal-to-noise ratio Vs/Vn, which is, in principle, limited by the noise of the incident radiation. It may, in practice, be further reduced by inherent noise of the detector. The detector noise is often expressed by the noise equivalent input power (NEP), which means an incident radiation power that generates the same output signal as the detector noise itself, thus yielding the signal-to-noise ratio S/N = 1. In infrared... 

This is 10" to 10 times higher than the noise equivalent input power of standard IR detectors. 

The detectivity D [cm/s / -W ] gives the obtainable signal-to-noise ratio Vg/Vn of a detector with the sensitive area A and the detector bandwidth Af, at an incident radiation power of P = 1 W. Because the noise equivalent input power is NEP = P V /Vg the detectivity of a detector with the area 1 cm and a bandwidth of 1 Hz is D = 1/NEP. 

Jones, R. C. (1952). Detectivity, the reciprocal of noise equivalent input of radiation. Nature, 170, 937-8, see also Journal of the Optical Society of America, 42, 286. 

The fundamental performance parameter of any detector is its noise equivalent power (NEP). This is simply the input irradiance power necessary to achieve a detector output just equal to the noise. This NEP is dependent on a number of detector and signal variables such as modulation frequency and wavelength (the input signal is defined as sine wave modulated monochromatic light), and detector area, bandwidth and temperature. 

If the input of an amplifier is connected to a device with a correctly matched electrical impedance, then even in the absence of any useful signal from the device there will be noise in the output of the amplifier equivalent to a noise power input (Robinson 1974)... 

It is evidently insufficient to consider only the response of a detector when analysing its usefulness for a particular application. It is generally necessary to analyse both intrinsic and extrinsic noise signals and compare them with the response. The result of this comparison can be expressed in many different ways. One of the most useful is the noise-equivalent power nep which is the power of an rms signal input (in watts) required to give a response equal to the total rms noise voltage AVN. Then ... 

Typical detectivity values as a function of wavelength for PbS photoconductive and various photovoltaic detectors. is a figure of merit defined as A /NEP, where A is the detector area and NEP is the noise-equivalent power, the rms radiant power in watts of a sinusoidally modulated input incident on the detector that gives rise to an rms signal equal to the rms dark noise in a 1-Hz bandwidth. Data from Hughes Aircraft Company. 

The noise from I bias has been omitted for simplicity. Using the same parameters as above and Vg = 1 V and B= 1 kHz, the standard deviation of the equivalent input noise of the circuit is 0.63 aF. Since noise follows a Gaussian distribution, there is a 32 percent probability that a particular error sample is larger than this value. Datasheets usually specify a three times larger value, 2 aF, to reduce the probability for larger errors to 0.3%. Note that thermal noise from the amplifier is the only error source included in this analysis. In practice, other error sources are often relevant also. 

In the ideal case of a noiseless detector of 100% absorption efficiency the DQE= 1. For a noiseless detector but with an entrance window which attenuates the input and/or with a fractional absorption efficiency, then the DQE decreases from 1 to e where 0< <1. In this case, the time needed to make a measurement to a desired accuracy, q, for a fixed count rate onto the specimen, increases as 1. If, in addition, the detector contributes a noise equivalent to the signal given by tj photons, then the DQE is further reduced according to the relation ... 

This signal should be larger than the noise equivalent power NEP (this is the input power of the detector which gives the same detector output as the noise). 

The minimum still detectable concentration Ni of absorbing molecules is determined by the noise-equivalent power NEP, the radiation input power Pq, the absorption cross section ct, of the absorbing transition and the length L of the absorption... 

Noise equivalent power, NEP That optical power which produces a detector output current equal to the total noise current. A detector with input power, NEP, produces an output signal-to-noise ratio of unity. 

Fortunately, the bandwidth-dictated load resistance, R, can be supplied by the amplifier and the net noise decreased substantially because of the gain in the amplifier first stage. One of the preferred amplifier types is the transimpedance amplifier, which presents an appropriate input resistance using negative feedback, but has an equivalent input noise current smaller than that of a real resistor. Commercial low noise amplifiers for optical detection are usually characterized by an effective input noise current, sometimes called the spot noise current, (/ )usually quoted in pA/VHz, with 1 pA =10 A. Since the amplifier now includes the load resistance, R, of Fig. 2(b), its contribution is included in the effective input noise current. The amplifier limited noise equivalent power, NEPal, is then... 

JcT/C. Second, the amplifier has an equivalent input noise voltage, shown here as that of a field effect transistor (FET), the most common input device for a low-noise amplifier. 

Noise equivalent power (NEP) The amount of light equivalent to the noise level of the device. Responsivity (R) The ratio of the output current to the input optical power, amperes per watt. 

Both instrumentation and operational amplifiers are available as single-package devices. These incorporate laser-trimmed resistors that are critically matched for optimum performance. Fixed and adjustable gain units are offered with gains up to 1000 (60 dB), equivalent input noise of —128 dB, and total harmonic distortion (THD) of 0.0001% at 20 kHz. 

The major noise sources for a typical pyroelectric detector are the dielectric or Johnson noise, the amplifier current and voltage noise, and the thermal noise, caused by fluctuations in the power flow from the element to its heat sink. Each of these has an equivalent voltage generated at the amplifier input V y (given by equation (5.9)), and and Vj. respectively. These combine to give the total equivalent input noise according to the equation... 

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