Question 8.12: Estimate the output noise in the circuit seen in Fig. 8.27a.......
Estimate the output noise in the circuit seen in Fig. 8.27a. Verify your answer with SPICE. Assume that the diode’s minority carrier lifetime (see Ch. 2) is 10 ns.
Figure 8.27b shows the circuit used for noise analysis. The diode is forward-biased at roughly 0.7 V. One volt is dropped across the 1k resistor and so 1 mA of current flows in the circuit. The diode’s small-signal resistance is
r_{d}={\frac{V_{T}}{I_{D C}}}={\frac{k T}{q I_{D C}}}\approx2{5}\ \Omeganoting that the small-signal resistance of the diode does not generate thermal noise (it’s a model) but that any diode series resistance will. (We set the diode’s series resistance to zero in the SPICE model statement for this example.) The diode’s storage capacitance is
C_{S}={\frac{I_{D C}}{V_{T}}}\cdot\tau_{T}={\frac{\tau_{T}}{r_{d}}}=400\,p FThe diode’s shot noise PSD is
The resistor’s thermal noise PSD was calculated in Ex. 8.5 as 16.66\times10^{-24}A^{2}/H z\,.
The circuit output PSD is then the sum of the thermal and the shot noise contributions times the parallel connection of the 1k and 25 ohm resistors or
V_{o n o i s e}^{2}(f)=336.6\times10^{-24}\cdot(25\vert\vert{1}k)^{2}=200\times10^{-21}\,V^{2}/HzTo calculate the output RMS noise voltage, we need to integrate this PSD from DC to infinity as indicated in Fig. 8.12. However, notice that this circuit has a single time constant of (1k\vert\vert25)\cdot 400\ pF or approximately 10 ns (the diodes minority carrier lifetime). The noise equivalent bandwidth, NEB from Eq. (8.15), is roughly
V_{o n o i s e,R M S}^{2}=V_{L F,n o i s e}^{2}\cdot f_{3d B}\cdot{[tan^{-1}2\pi f/f_{3d B}]}^{\infty }_0
=V_{L F,n o i s e}^{2}\cdot\ \overbrace{f_{3dB}\cdot \frac{\pi}{2} }^{NEB} (8.15)
N E B={\frac{1}{2\pi\cdot10n s}}\cdot{\frac{\pi}{2}}=25~M H zThe RMS output noise is then
V_{o n o i s e,R M S}=\sqrt{25\times10^{6}\times200\times10^{-21}}=2.23\ \mathrm{\mu }VThe SPICE netlist and simulation output are seen below.
* ” Example 8.12 CMOS: Circuit Design, Layout, and Simulation * “
.control
destroy all
run
print all
.endc
.noise V(Vout,0) Vs dec 100 1 100G
Vs Vs 0 dc 1.7 ac 1
Rs Vs Vout 1k
D1 Vout 0 Diode
.model Diode D TT=10n Rs=0
.print noise all
.end
TEMP=27 deg C
Noise analysis … 100%
inoise_total = 3.592225e-05
onoise_total = 5.257612e-12
The RMS output noise calculated using SPICE is \sqrt{5.26\times 10^{-12}} =2.28\ \mu V\ .
Again note that the input-referred noise is meaningless in this example, as seen in Eq. (8.19) and the associated discussion.
V_{i n o i s e}^{2}(f)={\frac{V_{o n o i s e}^{2}(f)}{|A(f)|^{2}}}={\frac{V_{L F,n o s i e}^{2}}{1+(f/f_{3d B})^{2}}}\cdot{\frac{1+(f/f_{3d B})^{2}}{A_{D C}^{2}}}={\frac{V_{L F,n o s i e}^{2}}{A_{D C}^{2}}} (8.19)
