AN61-1 Application Note 61 August 1994 Practical Circuitry for ...

Application Note 61When casually constructing a wideband amplifier with afew mini-DIPs, the reader will do well to recall the pain andskill expended by the HP3400A’s designers some 30 yearsago.Incidentally, what were you doing in 1965?Copyright 1965 Hewlett-Packard Co. Reproduced with permission.APPENDIX BSymmetrical White Gaussian Noiseby Ben Hessen-Schmidt,NOISE COM, INC.White noise provides instantaneous coverage of all frequencieswithin a band of interest with a very flat outputspectrum. This makes it useful both as a broadbandstimulus and as a power-level reference.Symmetrical white Gaussian noise is naturally generatedin resistors. The noise in resistors is due to vibrations ofthe conducting electrons and holes, as described byJohnson and Nyquist. 1 The distribution of the noise voltageis symmetrically Gaussian, and the average noisevoltage is:Vn =2 kT ∫ R(f) p(f) df (1)Where:k = 1.38E–23 J/K (Boltzmann’s constant)T = temperature of the resistor in Kelvinf = frequency in Hzh = 6.62E–34 Js (Planck’s constant)R(f) = resistance in ohms as a function of frequencyhfpf ()=kT exp(hf/kT) −1[ ]Note 1: See “Additional Reading” at end of this section.(2)p(f) is close to unity for frequencies below 40GHz when Tis equal to 290°K. The resistance is often assumed to beindependent of frequency, and ∫df is equal to the noisebandwidth (B). The available noise power is obtainedwhen the load is a conjugate match to the resistor, andit is:2N = V n=4R kTB(3)where the “4” results from the fact that only half of thenoise voltage and hence only 1/4 of the noise power isdelivered to a matched load.Equation 3 shows that the available noise power is proportionalto the temperature of the resistor; thus it is oftencalled thermal noise power, Equation 3 also shows thatwhite noise power is proportional to the bandwidth.An important source of symmetrical white Gaussian noiseis the noise diode. A good noise diode generates a highlevel of symmetrical white Gaussian noise. The level isoften specified in terms of excess noise ratio (ENR).( )ENR ( in dB)=Log Te −29010290(4)AN61-38