# HW_9 - EE338K HOMEWORK ASSIGNMENT#9 Random Noise in...

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1 EE338K HOMEWORK ASSIGNMENT #9 Random Noise in Amplifiers Introduction The accurate sensing of small electrical signals is limited by the presence of noise in the form of random current and voltage fluctuations in both the resistors and the active devices that makeup an electronic amplifier circuit. An excellent discussion of the sources of these noises and how they affect the performance of Op Amp amplifiers is presented in Chapter 12 of the reference book “Op Amps for Everyone” available online at http://focus.ti.com/general/docs/litabsmultiplefilelist.tsp?literatureNumber=slod006b The nomenclature and notations used in this homework assignment for random noise voltages and currents are as follows: 1. The quantity ( ) f e 2 ( ) [ ] f i 2 written with a bar above the square of a lower case letter indicates the power density spectrum of a noise voltage [current.] The power density spectrum has the units V 2 /Hz [A 2 /Hz.] It is generally a function of frequency including the case where it is a constant. When the power density spectrum is constant with respect to frequency the noise is referred to as white noise. 2. The quantity 2 E [ ] 2 I written as the square of an upper case letter and with over-bar refers to the Mean Square (MS) value of a noise voltage [current] developed in a band of frequencies extending from f 1 to 2 . It has the units V 2 [A 2 ]. The relationship to the power density spectrum is ( ) ( ) ] [ 2 2 2 2 2 2 2 2 = = f f f f df f i I df f e E (1) The quantity BW = 2 - 1 is referred to as the bandwidth of the MS voltage [current]. 3. The quantity E [ ] I is the Root Mean Square (RMS) value of the noise voltage [current] and is simply the square root of the MS value. 4. The quantity ( ) f e , ( ) [ ] f i written with a lower case letter and an over-bar, designates the spectral density of a noise voltage [current] and has the units V/Hz 1/2 [A/Hz 1/2 ]. The spectral density is simply the square root of the power density spectrum. 5. The notation for any of the quantities introduced above, whether it is a power density spectrum, MS or RMS value, or spectral density may have subscripts that provide identification of the component with which the quantity is associated. 6. The power density spectrum of the open circuit noise voltage, 2 R e , generated by a resistor of R Ohms is kTR e R 4 2 = V 2 /Hz (2)

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2 2 Because it is independent of frequency it is white noise. It is referred to as Johnson noise after the first person that characterized this type of noise experimentally. 7. The noise model of the Op Amp contains three noise sources as shown below.
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## This note was uploaded on 10/26/2009 for the course EE 338k taught by Professor Bostick during the Fall '09 term at University of Texas.

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HW_9 - EE338K HOMEWORK ASSIGNMENT#9 Random Noise in...

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