1. Noise

2. Resistor Thermal Noise

3. Example Vnr1sqr=2.3288 x 10-19 Vnr3sqr=7.7625 x 10-20
Vnoutsqr= x10-19

4. Analytical Versus Simulation

5. Popular Interview Question

6. Noise Spectrum Shaping by a Low Pass Filter
As R increases, 4kTR increases, but the bandwidth decreases.
Therefore, the bandwidth is constant.
Pn,out can only be decreased by increasing C.

7. Alternative Representation of Resistor Thermal Noise

8. MOSFETS (Typically 2/3, not to be confused with
body effect coefficient)

9. 𝛾 as a function of length
Let’s sweep the gamma as a function of gmoverid and length and see how gamma is affected.
We can sweep the gmoverid by adjusting the VGB between 0 and VDD.
We fix VDS and VSB at 0.2 V.
Let’s look at the horizontal axis. Gmoverid is approximately equal to 1 over the Vgs-Vth.
A gmoverid of 10 will take a device into strong inversion; a gmoverid of 20 will take a device into weak inversion.
A gmoverid close to 30 is usually an indication that the device in subthreshold region.
Let’s look at gamma at a gmoverid of 20.
Gamma is approximately 1 for a length of 120 nm.
Gamma is approximately 0.75 for a length of 180 nm.
[The curvature of gamma vs. gmoverid depends on the degree of iinversion along the channel.]
You can generate similar plots by changing VDS and VSB. I am not going to show those plots here in the interest of time.

10. Noise Voltage Generated Per Device
VDS=0.6
I1=100 uA
gm/ID
gm(mS)
gm/gds
Vn(nV/sqrt(Hz))
Gamma 5
0.5
12.045
84.83
1.4976 10 1
15.707
64.5
1.018 15
1.5
17.19
52.40
0.84 20 2
17.55
44.27
0.76 25
2.5
17.05
38.22

11. Flicker Noise

12. Flicker Noise Model
The flicker noise is modeled as a voltage source in series with the gate:
The trap-and-release phenomenon associated with the dangling
bond occurs at low frequencies more often.
Device area can be increased to
decrease noise due to flicker noise.

13. Corner Frequency
Definition: the frequency at which the thermal noise equals the flicker noise.

14. Corner Frequency (fco)
So let us look at the second noise parameter.
The corner frequency represents the frequency at which the thermal noise equals the flicker noise. It is also a function of gmoverid. It is a key parameter in low noise circuit design because it can be used to determine the flicker noise at a given frequency. Similar to thermal noise, it is bias sensitive and depends on process characteristics.
Once thermal noise and fco are known, flicker noise at any frequency can be determined.
A is usually a process dependent number close to 10.
For NMOS, it is For PMOS, it is 11.5.

15. fco as a function of length
Using the same set up as before, we can extract the corner frequency as a function of gmoverid and look at its dependence on length and bias parameters such as Vds and Vsb.
The expression of for the corner frequency can be a little misleading. Because it seems to suggest that the corner frequency will increase with gmoverid. But what really happens is that at the current density levels of pretty quickly at large gmoverid. So at large gmoverid, the fco levels off pretty quickly with gmoverid.
For gmoverid of less than 20, the corner frequency decreases with the length of a transistor because the length appears in the denominator of the expression.
You can also generate similar plots to show the corner frequency as a function of VDS and VSB. But I will skip those plots for now because they don’t add much to this talk.

16. Representation of Noise in Circuits
Output noise
Input noise
Voltage noise source
Current noise source

17. Output Noise

18. Problem of Output Noise
Output noise depends on the gain of the amplifier, for example.

19. Input-Referred Noise Voltage
Problem: only valid for when source impedance is low.

20. Input Voltage Calculation

21. Calculation of Input-Referred Noise
Low source
impedance
High source impedance

22. Input Current
More significant at
High frequencies!

23. Noise in Single Stage Amplifier
Equivalent CS Stages CS CG SF
Cascode
Differential Pairs

24. Equivalent CS Stages

25. Common Source Amplifier
The transconductance of M1 must be maximized in order to
minimize input-referred noise.

26. Input Referred Thermal Noise Voltage
M2 acts as the current source.
The gm of M2 should be minimized.
M1 acts as the amplifier.
The gm of M1 should be maximized.

27. Noise Simulation
Thermal
noise
3.758 nV/sqrt(Hz)
Av=28.711

28. Noise Simulation
3.126 nV/sqrt(Hz)
Av=33.42

29. Comparison
(simulated input-referred
thermal noise)
Av=33.42

30. Flicker Noise
Dominated by
Flicker noise
Dominated by
Thermal noise

31. Common Gate Amplifier Need to consider Input referred voltage source
Input referred current source

32. Gain of CG
If RS=0 and channel length modulation is ignored, Av is

33. Input-Referred Voltage Source

34. Input-Referred Current Source
Does not produce
a current to the output

35. Input-Referred Thermal Noise

36. Input-Referred Flicker Noise

37. Design Example Design criteria: gm/ID=5 for M0, M2, M3 and M4.
I1=10 uA
I2=10 uA
I(M1)=40 uA

38. Source Follower with a NMOS CS Load (Review)

39. Source Followers High Input impedance,
noise current source is negligible.

40. Cascode Stage (At Low Frequencies)

41. Cascode Stage (At High Frequencies)

42. Differential Pair
(negligible)

44. Analysis