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 viewed 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 amplitude 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(2n)2 = n dB or n bits

10. -1<= C <=+1
C=0: n1 and n2 uncorrelated
C=1: perfectly correlated
C=-1: n1 and –n2 perfectly correlated

11. Adding uncorrelated noises
Adding correlated noises

12. For independent noises

13. Autocorrelation of a random process
Given n(t), its autocorrelation is defined as:
If n(t) (wide sense)stationary, then:

14. Power spectral density of noise
The power spectral density of n(t) is:
For real noise,

15. Ergodicity and time average of noise
A random process is Ergodic if its ensemble statistics can be computed from time samples.

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

17. Filtering of noise
x(t)
y(t)
H(s)

20. Three ways to view noise
For a given t,
n(t) could take various, random values
These values have a distribution pdf, e.g., uniform in [N1, N2], or Gaussian N(m, s), or just 0/1.
If a large number of these values taken, can use histogram to obtain approximate pdf
Take one value of n(t) at each t, plot n(t) ~ t  we get n(t)’s time waveform
Can look at statistics of n(t) over t
Translate into frequency domain PSD
White: spectrum is flat ~ f
1/f noise: spectrum has 1/f shape near low frequency

21. 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

22. 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

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

24. 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

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

26. MOS Noise Model

27. Flicker noise As a gate voltage,  1/Gate-Cap
– Kf,NMOS 6 times larger than Kf,PMOS
– Strongly process dependent
– When referred to as drain current noise, it is inversely proportional to L2
Nominal values for AF and EF are both 1.

28. Channel thermal noise current
A modified model of noise current
Qinv

29. BJT Noise

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

31. Noise Calculations 1) Get small-signal model
2) Set all inputs = 0 (linear superposition)
3) Pick an output variable vo or io
4) For each noise source vx, or ix
Calculate TF Hx(s) from input x to output
5) Total noise at output is
6) Input Referred Noise: Fictitious noise source at input:

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

33. wo=1/RLCL

34. Some integrals

35. 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?

36. 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.

37. NOISE IN MOS INVERTERS

38. To minimize:
L2 >>L1
en1 small

41. For thermal noise

43. NOISE Model

44. Input equivalent noise source

45. Total output noise current is found as,
Let
Then

47. How does this affect Av4 and go?

49. Did noise computation in class for this amp
VDD
Did noise computation in class for this amp
IN-
IN+ CC CC
Vo+
Vo-

50. VDD
VbP
VbPc
IN-
IN+
VbNc CC
VbNc Vo
VbN