EXAM Flashcards
Poisson equation
P(r)=N^r/r! e^-N
N in the poisson equation
Describes the expectation value, or the average number of events one can expect to occur in a given timeframe
P(r)
is the probability that an event occurs r times
what events does poisson distribution describe
Poisson distribution describes discrete and uncorrelated events
standard distribution of poisson
The standard deviation of poisson distribution is given by sqrt(N)
what is Poisson mainly used for
used to describe rare events
poisson and Gauss
for a large number of events the poisson and gauss distribution look very similar
shot noise and Poisson
Shot noise is a type of noise which originates from discrete nature of events such as electric charge, particles occurring in radioactive decay or photon counting in optical devices, due to particle nature of light. Shot noise is dominate for rare events hence is well described by the poisson distribution.
How silicon pn junction acts as a photodetector by converting photons into electron-hole pairs
Incident light is absorbed by the semiconductor as long as the incoming photon energy is higher than the bandgap energy of the semiconductor. The absorbed photon energy promotes electrons from the valence band to the conduction band. THe in-build-field of the diode separates the electrons from the holes.
NEP (noise equivalent power)
NEP describes the noise power spectral density of a photodetector and relates to the noise power
p_noise = NEP x sqrt(B)
With B the bandwidth of the detecro
Detectivity D*
Detectivity is the inverse of the NEP normalised to the area of the detector,
D* = sqrt(A_det)/NEP
White noise
White noise refers to the fact that noise is independent of frequency. This means that each frequency component contributes equally to the noise power generated. by the detector.
why noise current of a photodetector depends on the sqrt of the bandwidth
As noise power scales linearly with bandwidth and since current is proportional to the sqrt of the power, the photocurrent noise scales as the sqrt of the bandwidth
How the cut off frequency of a photodector depends on the reverse voltage
A photodetector can be understood as a capacitor. The doped n and p regions represent the two capacitors plates and the depletino region represents the spacer. THe frequency is then given by the RC time constant of the device. As the fromula shows and increase in Vext will increase . As d is increased te capacitance drops according to C=e0erA/d as C decreases the RC time constant becomes shorter so the bandwidth increases.
sampling theroem
if a continuous function contains no frequencies higher than fmax it is completely determined by its value at a series of points taken less than 1/2fmax apart
nature of alpha particle and charge state
Alpha particles consist of two protons and two neutrons bound together into a particle identical to a helium nucleus. positively charged
nature of beta particles and charge state
Beta particles are high-energy speed electrons or positrons. Beta particles are also cahrged eiether positively (positron) or negatively (electrons)
gamma particles
Gamma particles are high energy photons so they are not charged.
Neutrons
Are one of the fundamental building blocks of the atomic nucleus, together with protons. Neutrons are not charged.
Quantum efficiency
Describes the efficiency of the detector of converting photons into electron hole pairs.
Responsivity
The responsivity measures the ability of the detector to convert an optical power into a photocurrent
difference between responsivity and quantum efficiency
The difference is that the responsivity takes the erngy of the photon into account while the quantum efficiency does not. Therefore the maximum value of the quantum efficiency is unity or 100% (1 photon in =1e-h pair out) while the responsivity can assume any positve value up to infinity
Transducer
converts energy from one form into another
examples of transducers
Scales measure weight via the compression of a spring. Spring is a transducer
signal
combined multiple measurements in time to get a sequence of measurments
noise
additional unwanted signal
SNR
signal to noise ratio used to describe the quality of a signal
Noise in digital siganl
Noise is less of a problem in digital signal. Noise usually disturbs the amplitude. In a digital signal the information is not contained in the amplitude
sigma in gauss equation
describes the width of the curve
mu in gauss equation
expectation value
Gaussion function
describes the likelyhood of a particular argument
shot noise
type of electronic noise which can be modeled by a poisson process.
shot noise caused by
enegetic particles not emitting in regular intervals.
key property of poisson
sigma =sqrt(N)
noise and signal strength
As a signal get’s stronger the noise gets weaker
Signal power proportional to
to signal amplitude squared
Bandwidth
describes the maximum data transfer rate of a network or internet connection.
Bandwidth equation
B= I / delT
colour of shot noise
Shot noise is white
shot noise can be mitigated how>
by increasing the signal strength, as the SNR is proportional to sqrt(signal) or by decreasing the dector bandwidth as shot noise power like any white noisesscales as the bandwidth
Thermal noise
Arises from the presence of thermal energy in the detecor e.g. brownian motion of the electrons. some electrons thereby assume sufficient energy to mimic a detection event. THe spectral density of thermal noise is flat. i.e. thermal nnoise is white TO mitigate decrease bandwidth or cool down
1/f noise
also called, flicker or pink noise. occurs in many physical, biological and economic systems. It does not have a single origin. A key characteristic is that there is equal energy in all octaves. Since 1/f noise drops as the bandwidth, it is best mitigated by decreaseing the bandwidth of the detector.
Lock in detection
improves the SNR by modulating the signal at a particular frequency and using a bandpass filter that coincides with the lock in frequency. The spectral width of the bandpass filter is given by the bandwidth of the signal to. be measured.
three ways lock in detection reduces noise
1) the bandpass filter reduces Johnson noise, which is proportional to the detected bandwidth.
2) The frequency offset provided by the modulation does reduce the 1/f noise, as it shifts the detection to higher frequencies, where the 1/f noise is lower
3) Background noise sources are not modulated and are therefore eliminated from the measurement. 50/100Hz noise arising from the mains and background light is a particular problem in this respect, and lock in detection, for example allow for the use of daylight in laboratories.
frequency filter that uses RC
Highpass and lowpass filters are voltage dividers that use the fact that impedance of a capacitor depends on frequency RC=1/omegaC.
For low frequencies Rc>R so most or all of the voltage drops across the capacitor while for high frequncies the impedance of the capacitor is low so the voltage drops across the resistor.
