7.4 TRANSRESISTANCE PREAMPLIFIER NOISE ANALYSIS
7.4.3 Summary of Results for the Common-Emitter
We are now in a position to determine the complete input referred noise current from all the noise sources in the amplifier. A schematic of a typical transresistance preamplifier using a common-emitter front-end was shown in Fig. 7.11. A small signal model of this amplifier, with all the non-neglible noise sources, is shown in Fig. 7.19. The spectral density of the input noise current is found to be
SnB(f) = 4 kT
RF + 2 qIC
+ 4kTrb(2fCds)2+
2qIC+ 4 kT RC
2fCTB
gm
2
(7.159) We have discussed each of these terms previously, expect the noise due to the base resistancerb. This noise has the same functional form as the noise due tore. However,
rbis generally much larger thanreand can not be ignored.
Simulated and calculated values of this spectrum are shown in Fig. 7.20(a). This plot shows that (7.159) can be used to accurately predict noise performance over the useful bandwidth of the device. The first term in (7.159) is due to thermal noise in the feedback resistor. The second term results from base-current shot noise. These two terms are dominant at low frequencies, and their respective spectral densities are plotted in Fig. 7.21.
The remaining terms of (7.159) all increase with frequency. The third term is due to thermal noise in the base resistance. This is normally smaller than the other frequency dependent noises, but it can be large if care is not taken to minimizerb. This noise
362 Chapter 7
101 102 103 104 105
104 105 106 107 108 109 1010 1011
total noise, Ic=4.95mA beta=36.48 cpi=1.3pF cd=1pF rf=10k rc=520
pA^2 / Hz
Frequency
Calculated Simulated
10-9 10-6 10-3 100 103 106 109
104 105 106 107 108 109 1010 1011
Ic noise, Ic=4.95mA beta=36.48 cpi=1.3pF cd=1pF rf=10k rc=520
pA^2 / Hz
Frequency Calculated Simulated
(a) (b)
Figure 7.20 Input referred noise spectral density of a transresistance preamplifier with a common-emitter front-end: (a) total noise, (b) contribution due to shot noise.
100 101
104 105 106 107 108 109 1010 1011
Rf noise, Ic=4.95mA beta=36.48 cpi=1.3pF cd=1pF rf=10k rc=520
pA^2 / Hz
Frequency
Calculated Simulated
101 102 103
104 105 106 107 108 109 1010 1011
Ib noise, Ic=4.95mA beta=36.48 cpi=1.3pF cd=1pF rf=10k rc=520
pA^2 / Hz
Frequency
Calculated Simulated
(a) (b)
Figure 7.21 Input referred noise spectral density of a transresistance preamplifier with a common-emitter front-end due to: (a)RFthermal noise, (b)Ibshot noise.
Low-Noise Preamplifier 363
10-9 10-6 10-3 100 103 106 109
104 105 106 107 108 109 1010 1011
Rb noise, Ic=4.95mA beta=36.48 cpi=1.3pF cd=1pF rf=10k rc=520
pA^2 / Hz
Frequency Calculated Simulated
10-11 10-8 10-5 10-2 101 104 107
104 105 106 107 108 109 1010 1011
Rc noise, Ic=4.95mA beta=36.48 cpi=1.3pF cd=1pF rf=10k rc=520
pA^2 / Hz
Frequency Calculated Simulated
(a) (b)
Figure 7.22 Input referred noise spectral density of a transresistance preamplifier with a common-emitter front-end due to: (a)rbthermal noise, (b)Rcthermal noise.
is plotted in Fig. 7.22(a), and the thermal noise due toRc is shown in Fig. 7.22(b).
The fourth term results from collector-current shot noise. This is the dominant noise at high frequencies, and its spectral density was shown in Fig. 7.20(b), where it can be compared directly with the total noise. We have omitted the dc contributions of these frequency-dependent terms because they are much less than the noise terms due toRF
andib. However, the noise begins to increase at a break frequency determined by the dominant pole of the open-loop amplifier, because the forward gain, which keeps the input-referred noise low, starts to fall off. (This effect is similar to the reduction of the common-mode-rejection ratio or the power-supply-rejection ratio of an opamp.) For an FET input device the result is
SnF(f ) = 4 kT RF +
4kT ,gm+ 4 kT RC
2fCTF
gm
2: (7.160)
(7.160) ignores the contributions due to the base-current shot noise and thermal noise in the base resistor that we saw in (7.159). For a broadband amplifier, the frequency dependent terms become increasingly important. Therefore it is desirable to minimize the following terms:
Bip olar= CTB=gm; (7.161)
FET= CTF=gm: (7.162)
These are equivalent delay times which are determined by the capacitance to transcon- ductance ratio. With all else equal, the device with the highest speed (the lowestC=gm ratio) will exhibit the lowest noise.
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Qualitative Explanation for Frequency Dependence of Noise
A photodiode generates electron-hole pairs in proportion to the number of photons incident on the device. We would like to make use of all of these electron-hole pairs to evaluate the strength of the incoming signal. However, many of these charges are lost at the outset, and are used to fill empty lattice sites in the depletion region of the photodiode. The reason these charge carriers are lost is because a voltage swing must appear at the input of the amplifier to steer the current through the feedback resistor.
This voltage can only be generated by the accumulation of charge in the depletion layer. At higher frequencies more current from the diode will be lost to the depletion capacitance and the signal strength will weaken.
The noise power at the output will contain a constant term due to the shot-noise from the collector current. As the signal is reduced in magnitude at higher frequencies, the input referred noise power will therefore increase — a weaker signal with constant noise at the output is equivalent to a constant signal with increasing noise at the input. The equivalent input noise will increase with the square of the capacitance. The noise will also depend on the transconductance, which determines how large the input voltage has to swing in order to switch a fixed amount of current. If the transconductance is high, only a small voltage is needed; therefore, few charges are lost in the depletion capacitance and a larger percentage can be detected as a signal at the output. We have reasoned that the rms noise will increase with the capacitance and with frequency, but will be inversely proportional togm. The noise power will vary with the square of these quantities. Therefore, we expect a term in the input-referred noise spectral density of the form(C=gm)2f2.