1. Electronic Noise Noise phenomena Device noise models
Representation of noise (2-ports):
Motivation
Output spectral density
Input equivalent spectral density
Noise figure
Sampling noise (“kT/C noise”)
SNR versus Bits
Noise versus Power Dissipation
Dynamic range
Minimum detectable signal

2. Noise in Devices and Circuits
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.

3. Noise vs 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

4. Time domain description of noise

5. What is signal and what is noise?

6. Signal and noise power:

7. Physical interpretation
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.
power

8. Signal to noise ratio SNR = 0 dB when signal power = noise power
Absolute noise level in dB:
w.r.t. 1 mW of signal power

9. SNR in bits A sine wave with magnitude 1 has power = 1/2.
Quantize it into N=2n equal levels between -1 and 1 (with step size = 2/2n)
Quantization error uniformly distributed between +–1/2n
Noise (quantization error) power =1/3 (1/2n)2
Signal to noise ratio = 1/2 ÷ 1/3 (1/2n)2 =1.5(1/2n)2 = n dB or n bits

10. C=0: n1 and n2 uncorrelated C=1: perfectly correlated

11. Adding uncorrelated noises
Adding correlated noises

12. For independent noises

13. Frequency domain description of noise
Given n(t) stationary, its autocorrelation is:
The power spectral density of n(t) is:
For real signals, PSD is even.  can use single sided spectrum: 2x positive side
↑ single sided PSD

14. Parseval’s Theorem: If
If x(t) stationary,

15. Interpretation of PSD
Pxf1 = PSDx(f1)
PSDx(f)

18. Types of “Noise” “man made” “intrinsic” noise Interference
Supply noise …
Use shielding, careful layout, isolation, …
“intrinsic” noise
Associated with current conduction
“fundamental” –thermal noise
“manufacturing process related”
flicker noise

19. 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

20. Thermal noise dominant in resisters
Example:
R = 1kΩ, B = 1MHz, 4µV rms or 4nA rms

21. 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?

22. 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 a
white noise source and typically larger than thermal noise.
− Zero mean
– Gaussian pdf
– Power spectral density flat
– Proportional to current
– Dependent on temperature

23. Example:
ID= 1mA, B = 1MHz, 17nA rms

24. MOS Noise Model

25. 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

26. BJT Noise

27. Sampling Noise • Commonly called “kT/C” noise
• Applications: ADC, SC circuits, … R
von C
Used:

28. Filtering of noise
x(t)
y(t)
H(s)
|H(f )|2 = H(s)|s=j2pf H(s)|s=-j2pf

29. Noise Calculations 1) Get small-signal model
2) Set all inputs = 0 (linear superposition)
3) Pick output vo or io
4) 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:

30. Example: CS Amplifier Von=(inRL +inMOS)/goT VDD goT = 1/RL + sCL RL M1

31. wo=1/RLCL

32. Some integrals

33. 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.