Difference between revisions of "229-A2.2"

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{{NumBlk|::|<math>\overline{v_R^2}=4kTR\Delta f</math>|{{EquationRef|1}}}}  
 
{{NumBlk|::|<math>\overline{v_R^2}=4kTR\Delta f</math>|{{EquationRef|1}}}}  
  
Thus, for a resistor <math>R=1\mathrm{k\Omega}</math> and a temperature <math>T=300K</math>, and with <math>k=1.38\times 10^{-23}\mathrm{\tfrac{J}{K}}</math>the spot noise is equal to:
+
Thus, for a resistor <math>R=1\mathrm{k\Omega}</math> and a temperature <math>T=300K</math>, and with <math>k=1.38\times 10^{-23}\mathrm{\tfrac{J}{K}}</math>, the spot noise is equal to:
  
{{NumBlk|::|<math>\frac{\overline{v_R^2}}{\Delta d}=4kTR=1.66\times 10^{-17}</math>|{{EquationRef|2}}}}  
+
{{NumBlk|::|<math>\frac{\overline{v_R^2}}{\Delta f}=4kTR=1.66\times 10^{-17}\mathrm{{V^2}{Hz}}</math>|{{EquationRef|2}}}}  
  
Thus, the total output integrated noise, shaped by the transfer function of the RC circuit is:
+
Thus, for a capacitor <math>C=1\mathrm{\mu F}</math>, the total output integrated noise, shaped by the transfer function of the RC circuit is:
  
 +
{{NumBlk|::|<math>\overline{v_{o,T}^2}=\int_0^\infty 4kTR \left|\frac{1}{1 + sRC}\right|^2 df = \frac{kT}{C} = 4.144\times 10^{-15}\mathrm{V^2}</math>|{{EquationRef|3}}}}
  
 +
Or equivalently,
 +
 +
{{NumBlk|::|<math>v_{o,\mathrm{rms}}=\sqrt{\overline{v_{o,T}^2}}=64.4\mathrm{nV}</math>|{{EquationRef|4}}}}
 +
 +
If we change the value of the resistor to <math>R=10\mathrm{k\Omega}</math>, the resistor spot noise changes to:
 +
 +
{{NumBlk|::|<math>\frac{\overline{v_R^2}}{\Delta f}=4kTR=1.66\times 10^{-16}\mathrm{{V^2}{Hz}}</math>|{{EquationRef|5}}}}
 +
 +
But the total integrated noise should remain the same since the bandwidth of the RC circuit is reduced by the same amount.
 +
 +
To verify our calculations, we can use SPICE to simulate the noise of the RC circuit. Using this netlist and this Python script, we get the following ngspice results:
 +
 +
<source lang="bash">
 +
******
 +
** ngspice-31 : Circuit level simulation program
 +
** The U. C. Berkeley CAD Group
 +
** Copyright 1985-1994, Regents of the University of California.
 +
** Please get your ngspice manual from http://ngspice.sourceforge.net/docs.html
 +
** Please file your bug-reports at http://ngspice.sourceforge.net/bugrep.html
 +
******
 +
ngspice 1 -> source RC_noise.sp
 +
 +
Circuit: * noise simulations
 +
 +
Doing analysis at TEMP = 27.000000 and TNOM = 27.000000
 +
 +
 +
No. of Data Rows : 9001
 +
 +
No. of Data Rows : 1
 +
inoise_total = 1.661427e-11
 +
onoise_total = 4.143579e-15
 +
Doing analysis at TEMP = 27.000000 and TNOM = 27.000000
 +
 +
 +
No. of Data Rows : 9001
 +
 +
No. of Data Rows : 1
 +
inoise_total = 1.661428e-10
 +
onoise_total = 4.143808e-15
 +
ngspice 2 ->
 +
</source>
  
 
== Noise in MOSFETs ==
 
== Noise in MOSFETs ==

Revision as of 13:11, 9 October 2020

Activity: Noise Analysis

  • Instructions: This activity is structured as a tutorial with a design problem at the end. Should you have any questions, clarifications, or issues, please contact your instructor as soon as possible.
  • At the end of this activity, the student should be able to:
  1. Understand and observe the effects of noise in electronic circuits.

Simulating Resistor Noise

Consider a simple RC circuit shown in Fig. 1. The noise generated by the resistor is:

 

 

 

 

(1)

Thus, for a resistor and a temperature , and with , the spot noise is equal to:

 

 

 

 

(2)

Thus, for a capacitor , the total output integrated noise, shaped by the transfer function of the RC circuit is:

 

 

 

 

(3)

Or equivalently,

 

 

 

 

(4)

If we change the value of the resistor to , the resistor spot noise changes to:

 

 

 

 

(5)

But the total integrated noise should remain the same since the bandwidth of the RC circuit is reduced by the same amount.

To verify our calculations, we can use SPICE to simulate the noise of the RC circuit. Using this netlist and this Python script, we get the following ngspice results:

******
** ngspice-31 : Circuit level simulation program
** The U. C. Berkeley CAD Group
** Copyright 1985-1994, Regents of the University of California.
** Please get your ngspice manual from http://ngspice.sourceforge.net/docs.html
** Please file your bug-reports at http://ngspice.sourceforge.net/bugrep.html
******
ngspice 1 -> source RC_noise.sp

Circuit: * noise simulations

Doing analysis at TEMP = 27.000000 and TNOM = 27.000000


No. of Data Rows : 9001

No. of Data Rows : 1
inoise_total = 1.661427e-11
onoise_total = 4.143579e-15
Doing analysis at TEMP = 27.000000 and TNOM = 27.000000


No. of Data Rows : 9001

No. of Data Rows : 1
inoise_total = 1.661428e-10
onoise_total = 4.143808e-15
ngspice 2 ->

Noise in MOSFETs