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Bài giảng Mạch điện tử thông tin - Chapter 3: Low noise amplifier (LNA) - Đỗ Hồng Tuấn

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Chapter 3:  
Low Noise Amplifier (LNA)  
Dept. of Telecomm. Eng.  
Faculty of EEE  
CSD2020  
DHT, HCMUT  
Origin of Noise (1)  
Resistor thermal noise: Probably the most well known noise source is  
the thermal noise of a resistor (also called Johnson noise). It is generated  
by thermal energy causing random electron motion. It is white noise since  
the PSD of the noise signal is flat throughout the frequency band.  
The noise is also called Gaussian which means the amplitude of the noise  
signal has random characteristics with a Gaussian distribution. We are  
able to apply statistic measures such as the mean square values. The  
noise power is proportional to absolute temperature.  
The thermal noise spectral density in a resistor is given by  
where k is Boltzmann’s constant (1.38 × 10−23 J/K), T is the absolute  
temperature in Kelvin temperature of the resistor, and R is the value of the  
resistor.  
Dept. of Telecomm. Eng.  
Faculty of EEE  
CSD2020  
DHT, HCMUT  
2
Origin of Noise (2)  
Noise power spectral density is expressed using volts squared per hertz  
(power spectral density). In order to find out how much power a resistor  
produces in a finite bandwidth of interest f , we use:  
where vn is the rms value of the noise voltage in the bandwidth f . This can  
also be written equivalently as a noise current rather than a noise voltage:  
Maximum power is transferred to the load when RLOAD is equal to R. Then  
vo is equal to vn /2. The output power spectral density Po is then given by  
Thus, available noise power is kT, independent of resistor size. Note that  
kT is in watts per hertz, which is a power density.  
Dept. of Telecomm. Eng.  
Faculty of EEE  
CSD2020  
DHT, HCMUT  
3
Origin of Noise (3)  
To get total power out Pout in watts, multiply by the bandwidth, with the  
result that:  
Dept. of Telecomm. Eng.  
Faculty of EEE  
CSD2020  
DHT, HCMUT  
4
Origin of Noise (4)  
Available power from antenna: The noise from an antenna can be modeled  
as a resistor. Thus, the available power from an antenna is given by:  
at T = 290K, or in dBm per hertz:  
Example: For any receiver required to receive a given signal bandwidth, the  
minimum detectable signal can now be determined. From Pout = kTB, the  
noise floor depends on the bandwidth. For example, with a bandwidth of  
200 kHz, the noise floor is  
or in dBm:  
Dept. of Telecomm. Eng.  
Faculty of EEE  
CSD2020  
DHT, HCMUT  
5
Origin of Noise (5)  
Thus, we can now also formally define signal-to-noise ratio (SNR). If the  
signal has a power of S, then the SNR is  
Thus, if the electronics added no noise and if the detector required a SNR of  
0 dB, then a signal at -121 dBm could just be detected. The minimum  
detectable signal in a receiver is also referred to as the receiver sensitivity.  
However, the SNR required to detect bits reliably (e.g., bit error rate (BER)  
= 10-3) is typically not 0 dB. Typical results for a bit error rate of 10-3 (for  
voice transmission) is about 7 dB for quadrature phase shift keying  
(QPSK), about 12 dB for 16 quadrature amplitude modulation (QAM), and  
about 17 dB for 64 QAM. For data transmission, lower BER is often  
required (e.g., 10-6), resulting in an SNR requirement of 11 dB or more for  
QPSK.  
Dept. of Telecomm. Eng.  
Faculty of EEE  
CSD2020  
DHT, HCMUT  
6
Origin of Noise (6)  
Shot noise: Shot noise is generated if current flows through a potential  
barrier such as a pn junction. The square root of the shot noise current  
can be described by  
is2h 2qIdcf  
with q as the electron charge. As expected, the shot noise increases with  
DC current Idc since it determines the number of available carriers.  
Thus, shot noise can be minimised by reducing the DC current. However,  
a reduced DC current may decrease the maximum possible gain and large  
signal properties of transistors. Consequently, a tradeoff has to be found.  
Shot noise plays an important role in BJTs since they consist of pn  
junctions (especially for the forward biased base emitter junction).  
Dept. of Telecomm. Eng.  
Faculty of EEE  
CSD2020  
DHT, HCMUT  
7
Origin of Noise (7)  
Usually, the shot noise of FETs is very small since there are no relevant  
pn-junctions, and the current flowing through them is weaker than for  
BJTs. However, the aggressively scaling of MOSFETs can introduce a  
significant current from the gate to the channel, which may generate shot  
noise.  
In contradiction to thermal noise, shot noise does not occur in an ideal  
resistor.  
Dept. of Telecomm. Eng.  
Faculty of EEE  
CSD2020  
DHT, HCMUT  
8
Noise in Bipolar Transistors (1)  
Small-signal equivalent circuit of BJT at hight frequencies (without  
noise):  
rb = rbb‘, r= rb‘e, C= Cb‘e, C= Cb‘c ,  
Dept. of Telecomm. Eng.  
Faculty of EEE  
CSD2020  
DHT, HCMUT  
9
Noise in Bipolar Transistors (2)  
BJT with base shot noise, collector shot noise, and thermal noise at rb:  
Small-signal equivalent circuit of BJT with noise:  
Dept. of Telecomm. Eng.  
Faculty of EEE  
CSD2020  
DHT, HCMUT  
10  
Noise Figure (1)  
Noise from the electronics (e.g. thermal noise, shot noise…) is described  
by noise factor F, which is a measure of how much the signal-to-noise  
ratio is degraded through the system. We note that:  
where Si is the input signal power, So is the output signal power, and G is  
the power gain So/Si. Then, the noise factor is:  
where No(total) is the total noise at the output. If No(source) is the noise at the  
output originating at the source, and No(added) is the noise at the output added  
by the electronic circuitry, then we can write:  
Dept. of Telecomm. Eng.  
Faculty of EEE  
CSD2020  
DHT, HCMUT  
11  
Noise Figure (2)  
Noise factor can be written in useful alternative form:  
This shows that the minimum possible noise factor, which occurs if the  
electronics adds no noise, is equal to 1.  
Noise figure NF is related to noise factor F by:  
Thus, an electronic system that adds no noise has a noise figure of 0 dB.  
Dept. of Telecomm. Eng.  
Faculty of EEE  
CSD2020  
DHT, HCMUT  
12  
Noise Figure (3)  
Noise Figure of stages in series: Consider three stages in series as  
The output signal So is given by:  
The input noise is:  
The total output noise is:  
The output noise due to the source is:  
Dept. of Telecomm. Eng.  
Faculty of EEE  
CSD2020  
DHT, HCMUT  
13  
Noise Figure (4)  
Finally, the noise factor can be determined as:  
The above formula shows how the presence of gain preceding a stage  
causes the effective noise figure to be reduced compared to the measured  
noise figure of a stage by itself. For this reason, we typically design  
systems with a low-noise amplifier at the front of the system.  
Question: Derive the formula for N stages in series?  
Dept. of Telecomm. Eng.  
Faculty of EEE  
CSD2020  
DHT, HCMUT  
14  
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