Hi Its been a while since last I did calculations on analog circuits, maybe you can help with the following: Consider the non-inverting amplifier on the drawing below (hope you can see it). When calculating the resistors' thermal noise contribution to the total noise voltage, En_total, I have seen application notes calculate each resistors thermal noise and adding them (in the sum of squares way), like: En_thermal = SQRT[ 4kTdf( R1 + R2 + R3 + R4) ], k:Boltzmann's constant, T:temperature, df:bandwidth Others calculate it by using the parallel resistances, R1||R2 and R3||R4: En_thermal = SQRT[ 4kTdf( R1||R2 + R3||R4) ] Which method is correct? | \ o-R1-------------| + \______out | |---| - / | R2 | | / | | | | GND |--R3------| | R4 | | GND If you feel you are moving to far from the digital world - feel free to answer '01' for the first method, '10' for the second, '00': I got it all wrong. Best regards Jan

# OPamp noise calculations

Started by ●June 26, 2003

Reply by ●June 26, 20032003-06-26

"Jan R�rg�rd Hansen" <jrh(IngenSpam)@(NoSpamTak)person.dk> wrote in message news:<bdfr20$1s6a$1@news.cybercity.dk>...> Hi > > Its been a while since last I did calculations on analog circuits, maybe you > can help with the following: > Consider the non-inverting amplifier on the drawing below (hope you can see > it). > > When calculating the resistors' thermal noise contribution to the total > noise voltage, En_total, I have seen application notes calculate each > resistors thermal noise and adding them (in the sum of squares way), like: > > En_thermal = SQRT[ 4kTdf( R1 + R2 + R3 + R4) ], k:Boltzmann's constant, > T:temperature, df:bandwidth > > Others calculate it by using the parallel resistances, R1||R2 and R3||R4: > En_thermal = SQRT[ 4kTdf( R1||R2 + R3||R4) ] > > Which method is correct? > > | \ > o-R1-------------| + \______out > | |---| - / | > R2 | | / | > | | | > GND |--R3------| > | > R4 > | > | > GND > > > If you feel you are moving to far from the digital world - feel free to > answer '01' for the first method, '10' for the second, '00': I got it all > wrong. > > Best regards > JanI can't seem to make out your schematic! Try using a monospaced font next time. But in any case the equivalent noise is just the equivalent resistance applied to the equation. En_thermal = SQRT[ 4kTdfR) ] Regards, Paavo Jumppanen

Reply by ●June 27, 20032003-06-27

"Jan R�rg�rd Hansen" <jrh(IngenSpam)@(NoSpamTak)person.dk> wrote in news:bdfr20$1s6a$1@news.cybercity.dk:> Hi > > Its been a while since last I did calculations on analog circuits, > maybe you can help with the following: > Consider the non-inverting amplifier on the drawing below (hope you > can see it). > > When calculating the resistors' thermal noise contribution to the > total noise voltage, En_total, I have seen application notes calculate > each resistors thermal noise and adding them (in the sum of squares > way), like: > > En_thermal = SQRT[ 4kTdf( R1 + R2 + R3 + R4) ], k:Boltzmann's > constant, T:temperature, df:bandwidth > > Others calculate it by using the parallel resistances, R1||R2 and > R3||R4: En_thermal = SQRT[ 4kTdf( R1||R2 + R3||R4) ] > > Which method is correct? > > | \ > o-R1-------------| + \______out > | |---| - / | > R2 | | / | > | | | > GND |--R3------| > | > R4 > | > | > GND > > > If you feel you are moving to far from the digital world - feel free > to answer '01' for the first method, '10' for the second, '00': I got > it all wrong. > > Best regards > Jan > >The thermal noise of the Rs will be the second equation. -- Al Clark Danville Signal Processing, Inc. -------------------------------------------------------------------- Purveyors of Fine DSP Hardware and other Cool Stuff Available at http://www.danvillesignal.com

Reply by ●June 27, 20032003-06-27

"Jan R�rg�rd Hansen" wrote:> > Hi > > Its been a while since last I did calculations on analog circuits, maybe you > can help with the following: > Consider the non-inverting amplifier on the drawing below (hope you can see > it). > > When calculating the resistors' thermal noise contribution to the total > noise voltage, En_total, I have seen application notes calculate each > resistors thermal noise and adding them (in the sum of squares way), like: > > En_thermal = SQRT[ 4kTdf( R1 + R2 + R3 + R4) ], k:Boltzmann's constant, > T:temperature, df:bandwidth > > Others calculate it by using the parallel resistances, R1||R2 and R3||R4: > En_thermal = SQRT[ 4kTdf( R1||R2 + R3||R4) ] > > Which method is correct? > > | \ > o-R1-------------| + \______out > | |---| - / | > R2 | | / | > | | | > GND |--R3------| > | > R4 > | > | > GND > > If you feel you are moving to far from the digital world - feel free to > answer '01' for the first method, '10' for the second, '00': I got it all > wrong. > > Best regards > JanUsenet requires a fixed-width font and no tabs. It's the only standard there is. The Johnson noise power from a resistive source depends on the equivalent resistance (and Bolzmann's constant and the absolute temperature too, but you know what I mean), whether that be a series connection, a parallel connection, or some combination. Noise power from individual sources adds directly. If you keep the math straight, you will see that applying either basis leads to the same result. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������

Reply by ●June 27, 20032003-06-27

Jan: For input referred noise density calculations the straightforward approach is always to work from first principles and find/calculate the "equivalent" source resistance Req. The equivalent source resistance is the total source resistance in series with the Op Amp inputs. In the particulare case of your circuit this would be calculated as the parallel connection of R1 and R2 in the non-inverting lead and the parallel connection of R3 and R4 in the inverting lead. Adding these two together gives the equivalent single value of the total source resistance seen by the amplifier inputs i.e. Req = R1||R2 + R3||R4. Then if en is the input referred Op Amp noise spot density is en expressed in V/rtHz and in is the input referred Op Amp current spot density expressed in A/rtHz, then the total input referred spot noise density will be: vn = sqrt[ en^2 + in^2*Req + 4*k*T*Req] There are several practical application things to watch out for with resistor noise... "In theory theory and practice are the same but in practice they are different." -- Yogi Berra. Only *purely metallic* conductors exhibit the so-called Johnson noise [quantum/thermal noise] calculated by the Nyquist celebrated formula i.e. conductors in which the current is carried by free electrons above the valence band and not bound by other forces in the conductor material. Essentially only metals exhibit this kind of pure noise. All other kinds of conductors exhibit this quantum noise *plus* one or more other, usually larger, noises which can only be determined empirically. The celebrated Nyquist formula for the Johnson [quantum thermal noise] is simply: vrn^2 = k*T*R*B [Nyquist's formula for the quantum/thermal "Johnson" noise power of a resistance R in Volts squared at temperature T degrees Kelvin in bandwidth B Hertz. k is Boltzman's constant.] Most commonly available resistors are *not* metallic conductors and usually exhibit *considerably* more noise than that indicated by Nyquist's formula. Thus you will be surprised by any measured results in low noise situations if you are depending upon the Nyquist formula to predict your noise floor. Your noise floor will be *way* off your Nyquist formula predictions by lot's of dB's *unless* you are using metallic resistors! In most resistors there are two other noises which are far larger than the Johnson noise. There is the generally larger so-called "shot noise" which is proportional to the current through the resistor and which unlike the white [flat] Johnson noise actually gets larger below a certain corner frequency, i.e. it's a 1/f noise effect, plus there is also the larger so-called current noise which is proportional to the voltage applied and is usually rated in uVoltsrms/Volt which also rises below a corner frequency, i.e. also a 1/f effect! These latter two noises are not well characterized and as far as I know do not have a simple physics based formula to predict their values, instead one must rely on empirical measurements for these latter two 1/f noises. So for most practical resistors which you purchase or have available in your lab [e.g. carbon composition, carbon film, metal film, etc... ] there are the three noises to consider, two of which are generally larger than the Johnson noise and which also grow as 1/f below corner frequencies. Metal film resistors are the most quiet of the three common resistor technologies mentioned above, but... if you want really quiet resistors you must use/buy bulk metal resistors! Only bulk metal either of the wire wound or metal foil type] resistors will exhibit the pure Johnson noise predicted by the Nyquist formula! Bulk metal resistors [Either metal foil or wire wound resistors] are available but are more expensive than the common garden variety resistors. See for instance the web site of Vishay which is a large passive component manufacturer. Vishay manufactures all kinds of resistors, carbon comp, carbon film, metal film, [in both thick film and thin film styles] as well as bulk metal resistors in both wire wound and metal foil formats. If you are trying to work down near the quantum noise levels without using bulk metal resistors you will be sorely disappointed and will get noise floor results far above that predicted by Nyquist's formula, unless... you are using *bulk metal* resistors! "In theory theory and practice are the same but in practice they are different." -- Yogi Berra. -- Peter Consultant Indialantic By-the-Sea, FL "Jan R�rg�rd Hansen" <jrh(IngenSpam)@(NoSpamTak)person.dk> wrote in message news:bdfr20$1s6a$1@news.cybercity.dk...> Hi > > Its been a while since last I did calculations on analog circuits, maybeyou> can help with the following: > Consider the non-inverting amplifier on the drawing below (hope you cansee> it). > > When calculating the resistors' thermal noise contribution to the total > noise voltage, En_total, I have seen application notes calculate each > resistors thermal noise and adding them (in the sum of squares way), like: > > En_thermal = SQRT[ 4kTdf( R1 + R2 + R3 + R4) ], k:Boltzmann's constant, > T:temperature, df:bandwidth > > Others calculate it by using the parallel resistances, R1||R2 and R3||R4: > En_thermal = SQRT[ 4kTdf( R1||R2 + R3||R4) ] > > Which method is correct? > > | \ > o-R1-------------| + \______out > | |---| - / | > R2 | | / | > | | | > GND |--R3------| > | > R4 > | > | > GND > > > If you feel you are moving to far from the digital world - feel free to > answer '01' for the first method, '10' for the second, '00': I got it all > wrong. > > Best regards > Jan > >

Reply by ●June 30, 20032003-06-30