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Noise

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**Resistor Thermal Noise**

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**Example Vnr1sqr=2.3288 x 10-19 Vnr3sqr=7.7625 x 10-20**

Vnoutsqr= x10-19

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**Analytical Versus Simulation**

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**Popular Interview Question**

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**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.

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**Alternative Representation of Resistor Thermal Noise**

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**MOSFETS (Typically 2/3, not to be confused with**

body effect coefficient)

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**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.

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**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

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Flicker Noise

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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.

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

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**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.

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**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.

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**Representation of Noise in Circuits**

Output noise Input noise Voltage noise source Current noise source

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Output Noise

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**Problem of Output Noise**

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

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**Input-Referred Noise Voltage**

Problem: only valid for when source impedance is low.

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**Input Voltage Calculation**

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**Calculation of Input-Referred Noise**

Low source impedance High source impedance

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Input Current More significant at High frequencies!

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**Noise in Single Stage Amplifier**

Equivalent CS Stages CS CG SF Cascode Differential Pairs

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Equivalent CS Stages

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**Common Source Amplifier**

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

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**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.

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

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

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

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Flicker Noise Dominated by Flicker noise Dominated by Thermal noise

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**Common Gate Amplifier Need to consider Input referred voltage source**

Input referred current source

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

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**Input-Referred Voltage Source**

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**Input-Referred Current Source**

Does not produce a current to the output

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**Input-Referred Thermal Noise**

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**Input-Referred Flicker Noise**

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**Design Example Design criteria: gm/ID=5 for M0, M2, M3 and M4.**

I1=10 uA I2=10 uA I(M1)=40 uA

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**Source Follower with a NMOS CS Load (Review)**

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**Source Followers High Input impedance,**

noise current source is negligible.

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**Cascode Stage (At Low Frequencies)**

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**Cascode Stage (At High Frequencies)**

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Differential Pair (negligible)

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Analysis

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Fig. 6.2 Different modes of operation of the differential pair: (a) The differential pair with a common-mode input signal vCM. (b) The differential.

Fig. 6.2 Different modes of operation of the differential pair: (a) The differential pair with a common-mode input signal vCM. (b) The differential.

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