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•Noise is any unwanted excitation of a circuit, any input that is not an information-bearing signal.• External noise: Unintended coupling with other parts of the physical world; in principle, can be virtually eliminated by careful design.• Intrinsic noise: Unpredictable microscopic events inherent in the device/circuit; can be reduced, but never eliminated. •Noise is especially important to consider when designing low-power systems because the signal levels (typically voltages or currents) are small.
Noise vs random process variations
• random process variations– Variations from one device to another– For any device, it is fixed after fabrication
• Noise– Unpredictable variations during operation– Unknown after fabrication– Remains unknown after measurement during
operation– May change with environment
Time domain description of noise
What is signal and what is noise?
)()()( tntstx
srmsT
s PSrmsSdttsT
P )(,)(102
nrmsT
n PNrmsNdttnT
P )(,)(10
2
Signal and noise power:
Physical interpretation
power
If we apply a signal (or noise) as a voltage source across a one Ohm resistor, the power delivered by the source is equal to the signal power.
Signal power can be viewer as a measure of normalized power.
Signal to noise ratio
)(log20)(log10 1010rms
rms
n
s
N
S
P
PSNR
SNR = 0 dB when signal power = noise power
Absolute noise level in dB:w.r.t. 1 mW of signal power
)log(10dB30
mW1log10din
n
nmn
P
PP
B
SNR in bits• A sine wave with magnitude 1 has power
= 1/2.• Quantize it into N=2n equal levels between
• “intrinsic” noise– Associated with current conduction– “fundamental” –thermal noise– “manufacturing process related” – flicker noise
Thermal Noise • Due to thermal excitation of charge carriers in a
conductor. It has a white spectral density and is proportional to absolute temperature, not dependent on bias current.
• Random fluctuations of v(t) or i(t)• Independent of current flow• Characterization:
– Zero mean, Gaussian pdf– Power spectral density constant or “white” up to about
80THz
Thermal noise dominant in resisters
Example:R = 1kΩ, B = 1MHz, 4µV rms or 4nA rms
HW
Equivalently, we can model a real resistor with an ideal resistor in parallel with a current noise source. What rms value should the current source have?
Show that when two resistors are connected in series, we can model them as ideal series resistors in series with a single noise voltage source. What’s the rms value of the voltage source?
Show that two parallel resistors can be modeled as two ideal parallel resistors in parallel with a single noise current source. What’s the rms value of the current source?
Noise in Diodes Shot noise dominant– DC current is not continuous and smooth but
instead is a result of pulses of current caused by the individual flow of carriers.
It depends on bias, can be modeled as awhite noise source and typically larger than
thermal noise. − Zero mean – Gaussian pdf – Power spectral density flat – Proportional to current – Dependent on temperature
Example:ID= 1mA, B = 1MHz, 17nA rms
MOS Noise Model
Flicker noise
–Kf,NMOS 6 times larger than Kf,PMOS
–Strongly process dependent
−when referred to as drain current noise, it is inversely proportional to L2
BJT Noise
Sampling Noise • Commonly called “kT/C” noise
• Applications: ADC, SC circuits, …
von
R
C
Used:
Filtering of noise
H(s)x(t) y(t)
|H(f )|2 = H(s)|s=j2f H(s)|s=-j2f
Noise Calculations 1) Get small-signal model2) Set all inputs = 0 (linear superposition)
3) Pick output vo or io4) For each noise source vx, or ix Calculate Hx(s) = vo(s) / vx(s) (or … io, ix)5) Total noise at output is
6) Input Referred Noise: Fictitious noise source at input: 22
,2, )(/ sAvv Toneffin
Example: CS Amplifier
CL
VDD
RL
Von=(inRL +inMOS)/goT
goT = 1/RL + sCL
LBnR RTki
L
142
mBnMOS gTki3
242
o=1/RLCL
Some integrals
HW
In the previous example, if the transistor is in triode, how would the solution change?
HW
If we include the flicker noise source, how would that affect the computation? What do you suggest we should modify?
HW
In the example, if RL is replaced by a PMOS transistor in saturation, how would the solution change? Assume appropriate bias levels.