6Noise 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.
7Alternative Representation of Resistor Thermal Noise
8MOSFETS (Typically 2/3, not to be confused with body effect coefficient)
9𝛾 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.
10Noise Voltage Generated Per Device VDS=0.6I1=100 uAgm/IDgm(mS)gm/gdsVn(nV/sqrt(Hz))Gamma50.512.04584.831.497610115.70764.51.018151.517.1952.400.8420217.5544.270.76252.517.0538.22
12Flicker Noise ModelThe flicker noise is modeled as a voltage source in series with the gate:The trap-and-release phenomenon associated with the danglingbond occurs at low frequencies more often.Device area can be increased todecrease noise due to flicker noise.
13Corner FrequencyDefinition: the frequency at which the thermal noise equals the flicker noise.
14Corner 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.
15fco 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.
16Representation of Noise in Circuits Output noiseInput noiseVoltage noise sourceCurrent noise source