INTRODUCTION
Noise, defined in the broadest practical terms, is any signal present in the
receiver other than the desired signal or any unwanted disturbance that masks,
corrupts, reduces the information content of or interferes with the desired
signal. In the optical wireless communication environment, it is known as “ambient
noise”. The sources of noise available in a receiver circuit are divided
into two classes (Alexander, 1997):
• 
Intrinsic noise sources arising from fundamental physical
effects in optoelectronic and electronic devices used to construct the receiver 
• 
Coupled noise sources arising from interactions between receiver
circuitry and the surrounding environment 
In addition, noise in a receiver can be described as either additive or signaldependent.
Additive noise is a source of noise that is present whether there is a signal
at the receiver or not, while a signaldependent noise is one that is observed
only when there is a signal present at the receiver. Figure 1
illustrates a simple model for an optical receiver and the major contributors
to the noise present in the receiver. The received signal and any optical background
that may be present, are photodetected and then amplified in a linear signal
path.
The implications of each noise source will be addressed, shown right to left
in Fig. 1. Receiver electronic noise consists of three primary
components: thermal noise, electronic shotnoise and 1/f noise. Thermal
noise is the type most often associated with receivers. Also known as Johnson
noise, it is a result of thermallyinduced random fluctuations in the charge
carriers in a resistance. The power spectraldensity for thermal noise is white
for all frequencies within a defined bandwidth and, since thermal noise inherently
results from the accumulated effect of large quantity of individual charge motions,
it exhibits Gaussian statistics. Nyquist showed that the open circuit RMS voltage
produced by a resistance R is as follows (Nyquist, 1928;
Baker, 2005):
where, k is Boltzmann’s constant, T is absolute temperature in Kelvin and B is the observation bandwidth in Hz.

Fig. 1: 
Simple receiver model and noise sources in the receiver (Alexander,
1997) 
Electronic shot noise is that associated with the passage of carriers across
a potential barrier. This means that any photocurrent in the photodiode will
have electronic shotnoise associated with it. Based strictly on the characteristics
of the noise, it is impossible to distinguish between the quantum shot noise
arising from photons being detected with a photodiode and the electronic shot
noise arising from the photocurrent flowing through the junction in the photodiode.
Therefore, the total electronic shot noise associated with a current, I_{DC},
flowing through a potential barrier is given as follows (Baker,
2005):
where, q is the electronic charge and B is the bandwidth 1/f noise has
been observed as low frequency fluctuations in the resistance of a semiconductor.
In resistors it is called “excess noise” and has been a concern in
optical receiver design when the receiver is required to have a low frequency
cutoff that is less than a few tens of MHZ. The amount of 1/f noise
present depends on the choice of transistors used in the first stages of the
receiver. A Si bipolar transistor’s 1/f noise is noticeable in the
tens of kHz region.
The noise in an optical wireless receiver can be influenced by additional nonsignal
related sources of optical energy that fall on the photodetector, namely quantum
shot noise and optical background noise. Quantum shot noise is the result of
the discreteness of photon arrivals. It is due to background light sources,
such as sunlight, fluorescent lamp light and incandescent lamp light, as well
as the signaldependent source. Since the background light striking the photodetector
is normally much stronger than the signal light, the dependency of noise on
the input signal may be neglected and the photon noise can be considered to
be additive white Gaussian noise (Carruthers, 2002).
The amount of background radiation collected by a freespace optical receiver
is dependent on the receiver’s fieldofview, as well as its optical bandwidth.
LITERATURE REVIEW
Noise model of a transimpedance amplifier: Amplification of lowlevel signals is a critical function of any receiver, due to the noise sources mention earlier. The overall noise performance of an amplifier is related to the noise characteristics of the individual devices and components that form the amplifier circuit. Two established techniques have been used as indicators of the noise performance of an amplifier. The first, known as the noise figure, NF, is simply the noise factor, F, expressed in terms of dB:
The first formula for the overall noise factor for a three stage amplifier combination is given by:
where, F_{1} and G_{1} are noise factor and power gain of first stage amplifier.
F_{2} and G_{2} are noise factor and power gain of second stage amplifier etc and all amplifiers are assumed to have the same bandwidth.
Equation 4 shows that if the gain of the first stage is large, the noise performance of a cascade of subsystems will be dominated by the noise performance of the firststage. In an optical wireless receiver, the photodetector and the first stages of the amplifier are known as the receiver frontend. This will generally be the principal factor in determining the overall noise performance and sensitivity of the receiver. Unfortunately, noise figure has some drawbacks when used to describe noise performance of amplifiers intended for an optical wireless receiver. It is defined using a resistive source, but a photodiode is dominated by capacitance, so the magnitude of the source impedance varies with frequency in the first stage amplifier in the receiver. Therefore the second technique that overcomes the noise figure drawbacks is to model an amplifier using equivalent noise sources, V_{n}(ω) and I_{n}(ω), as illustrated in Fig. 2 for a receiver consisting of a signal source such as a photodetector and an amplifier.
Assuming only amplifier noise, using the noise analysis principles approach
discussed by Motchenbacher and Fitchen (1973) and the
principle of superposition in linear circuits, the noise power at the amplifier
output is given by:
Replacing V_{n}(ω) and V_{nr}(ω) as short circuits, where Z_{f} = R_{f}/C_{f}
Then, the output noise for voltage noise is given by:
Replacing I_{n}(ω) as an open circuit and V_{nr}(ω)
as a short circuit

Fig. 2: 
Noise model of amplifier 
Replacing I_{n}(ω) as an open circuit and V_{n}(ω) as a short circuit
The transfer function:
The total output source and amplifier noise is:
Substituting (5) and (6) into (8), the simplified equivalent input currentnoise:
Since a photodetector is a capacitive current source, Z_{s}(ω) = jωC_{d}, setting Z_{f}(ω) = R_{f}:
Equation 11 shows that the influence of voltagenoise increases
with frequency. The detector capacitance acts as high pass filter to the voltage
noise sources of the amplifier. At low frequencies the contribution of voltage
noise to the overall current flowing is small, due to the large impedance of
the capacitor. At high frequencies, the amounts of circulating current due to
voltage noise increase because the capacitor’s impedance decreases. The
implications of noises for the frontend of an optical wireless receiver can
be summarised in Fig. 3.
Assume an optical signal and background noise impinge on the photodetector inducing a current in the external load resistor. If P_{t} is the average optical power, then I_{p} the photocurrent, is given by:
where, q is the electron charge, η is the quantum efficiency, h is Planck’s constant and v is the optical frequency of the light.
Therefore, the expressions for the current sources in the models illustrated
in Fig. 2, assuming that a PIN photodetector is being used
in the receiver, are as follows:
Where:
I_{dk} 
: 
is photodiode dark current 
I_{dm} 
: 
is unmultiplied dark current 
I_{b} 
: 
is DC photocurrent due to optical background 
I_{nb} 
: 
is optical background noise 
I_{neq} 
: 
is equivalent input currentnoise from the receiver amplifier including
photodiode thermal noise 

Fig. 3: 
An equivalent noise model of input stage of preamplifier,
where I_{p} is the photocurrent, I_{nd} is the detector
noise, I_{nb} is the background noise, C_{d}, R_{d}
are capacitance and resistance of a detector, I_{n}, V_{n}
are current noise and voltage noise of a preamplifier, R_{i}, C_{i}
are input resistance and input capacitance of a preamplifier, G is the voltage
gain of a preamplifier (Bielecki et al., 2003). 
If the general expression for I_{Total}(ω) is converted to frequency f in Hz, the equivalent input currentnoise can be expressed as a power series:
where, I_{shot} is the spectral density of the unmultiplied quantum
shotnoise associated with the signal and the coefficients x_{j} may,
depending on the details of the receiver and system implementation, be proportional
to received signal power, optical background, etc. The 1/f noise has
been excluded in the above expression, since the receivers are used at high
frequencies (Park et al., 1988; Su
et al., 1983). In practical cases, Eq. 14 can
be limited to (Muoi, 1987):
From Eq. 15, a figure of merit for an optical wireless receiver can be defined and used to describe the noise performance of the system, by assuming the amount of signal related quantum shot noise is essentially constant:
I^{2}_{shot} is unmultiplied quantum shotnoise associated with the signal and I^{2}_{rcvr}(f) is the equivalent input current noise due to all other noise sources present in the receiver.
Parameter k(f) is indicative of the difference between the receiver’s total equivalent input current noise density and the noisedensity due to the quantum shot noise of the signal as:
Using Eq. 10 to describe the amplifier noise and Eq. 13 to describe photodetector noise, the signal photocurrent and dark current, then the equivalent input currentnoise at the receiver’s input is given by:
where, Z_{s}(ω) = jωC_{d}, Z_{f}(ω)
= R_{f}, neglecting C_{f},:
Assuming that the receiver is illuminated by a signal with a constant power level P_{t} and ignoring any optical background, the equivalent input current noise density is:
Where:
From Eq. 16, the degradation from the quantum shotnoise limited current density is then given by:
The total equivalent input current noise is:
where, H_{t}(f) is the amplitude normalized frequency dependent portion of the overall receiver transimpedance, given by H_{t}(f) = 1 for 0<f<B, 0 for f > B.
METHODOLOGY
In this section, the discussion is focussed on the noise analysis for adjustable
bootstrap transimpedance and voltage feedback amplifier circuits. The analysis
is facilitated by the consideration of the input equivalent noise voltage and
noise current. Bipolar Junction Transistors (BJTs) and Fieldeffect Transistors
(FET) are one of the key building blocks of electronic amplifiers. The noise
sources present in both the components have been extensively studied (Motchenbacher
and Fitchen, 1973; Muoi, 1984; Smith
and Personick, 1982; Sze, 1981; Abdullah
et al., 2004; Abdullah and Green, 2010).
The smallsignal model for the FET and the BJT are shown in Fig.
4 and 5, respectively. To simplify the analysis of the
FET, direct effects from the gatedrain feedback capacitor will be ignored.
This is usually valid, since in most devices the gate source capacitance is
approximately ten times the gate drain capacitance (Alexander,
1997).
For the BJT, the base spreading resistance, r_{x}, accounts for any resistance between the base terminal contact and the actual active base region of the device. The base current and collector current shot noises are accounted for by two noise current generators i_{bBJT} and i_{cBJT}. The resistances r_{μ}, r_{μ} and r_{0} are dynamic resistances, they do not dissipate energy and do not contribute thermal noise. In this analysis, secondary effects that are introduced by the internal feedback r_{μ} and C_{μ} will be ignored for simplicity. C_{π} is composed of two contributions from the space charge in the emitter junction and the diffusion capacitance of the emitter junction that increases with emitter current.
The bootstrapped transimpedance amplifier is connected in series with a voltage
feedback amplifier, the LMH6624. An RC filter is used as a termination as shown
in Fig. 6.

Fig. 4: 
FET smallsignal model 

Fig. 5: 
BJT smallsignal hybridπ model 

Fig. 6: 
Composite bootstrap transimpedance amplifier with VFA 

Fig. 7: 
Frequency response composite transimpedance amplifier 
The first stage of the BTA produces a cutoff frequency of 94.5 MHZ, with a
gain of 51.5 dB. By varying the capacitor, C_{filter}, of the RC filter
between 50pF to 1nF, the bandwidth of the composite circuit can be controlled.
The cutoff frequency obtained by this RC filter on the composite amplifier
is from 9.5 to 103.5 MHZ, as shown on the frequency response plot of Fig.
7. The overall gain is reduced to 12.3 dB. There is a tradeoff between
gain and bandwidth, as the bandwidth is increased the gain of the circuit is
reduced.
Assuming that the gain stages and the emitter follower can be approximated by the simplified amplifier model as shown in Fig. 8., R_{b1}, R_{b2}>>R_{e1} and frequencies are considered where C_{dc} and C_{b} are short circuits, than the transimpedance gain, A_{z}, for the circuit is approximated using the following assumption where A is the voltage gain of the first stage amplifier and A_{1} is the voltage gain of the second stage amplifier:
From (22) and (23):
Equation 24 shows that the feedback resistor plays an important
part in determining the gain of the circuit. As the feedback resistor, R_{f,}
increases, the gain of the overall system increases but, as the second stage
amplification feedback resistor, R_{f1,} increases, the overall system
gain reduces.
ANALYSIS AND RESULTS
The combination of a bootstrap transimpedance amplifier with the feedback impedance
(R_{f} in parallel with the parasitic C_{f}) has been referred
back to the input, such that the input impedance is equal to R_{f}//C_{d}//C_{f}.
The gain set for the voltage feedback amplifier is:
And the calculated noise figure for the voltage feedback amplifier will be 2.6, where, R_{f} = 1k Ω, R_{1}=25 Ω and R_{G}=50 Ω. Therefore, the input equivalent noise current density, is:
where, R_{T}=R_{f}//r_{π}

Fig. 9: 
Input and Output noise density for bootstrap transimpedance
amplifier with voltage feedback amplifier 
Figure 9 shows the simulated input and output noise density
for bootstrap transimpedance amplifier and voltage feedback amplifier. The input
noise current density shows a flat 380 pV/
from 1 Hz to 10 GHz and starts to increase. In simulation the output noise density,
shows a flatness of 1.1 nV/
from 1 Hz to 80 MHZ when it starts descending according to the capacitor value
which adjust the bandwidth. The simulated results also showed that the output
noise density remains constant during the bandwidth adjustment process.
CONCLUSION
This study has discussed the noise performance analysis and simulation for transimpedance amplifier using the composite amplifier techniques. Results showed that the bootstrapped transimpedance with voltage feedback amplifier exhibits an identical output noise density.
ACKNOWLEDGMENT
The author would like to thank Faculty Electrical & Electronic Engineering, Universiti Tun Hussein Onn Malaysia (UTHM) for this project sponsorship.