1. Home
  2. Electronics Design
  3. "silly" RCL noise question

"silly" RCL noise question

So say you have an RCL circuit and are looking at the Johnson noise (Created by the R) that is across the capacitor. And assume that the circuit has a decent Q. Then the voltage noise at (and near) the resonance frequency will be Q times higher than it would be without the L and C. This implies (by energy conservation if nothing else) that the voltage noise at frequencies not near the resonance must be reduced.

It's like the resonance sucks up all the nearby noise. (I think this is right.) Could you then use this effect to reduce the Johnson noise in some frequency band you were interested in, by sticking an LC at some point outside that band?

(Or is there some fatal flaw in my logic?) TIA George H.

Reply to
George Herold
Loading thread data ...

OK scratch that, I can't measure across the cap in one case, and the resistor in the other and then compare the two. (More thinking required.)

Geo

Reply to
George Herold

The noise at resonance will be the noise of the resistor itself at that frequency, not multiplied by Q.

Replace the resistor by a Thevenin-equivalent source, and do the math.

--

Tim Wescott 
Wescott Design Services 
http://www.wescottdesign.com
Reply to
Tim Wescott

Well, it bandpass filters it.

Again, you'd be making a filter.

If the RLC are all in parallel, the LC looks open at Fr, so the noise voltage is unloaded at Fr and pretty much unloaded nearby.

You can Spice this. A resistor can have noise in LT Spice in the frequency domain. In the time domain, LT Spice resistors are noiseless, and LT Spice doesn't have a time-domain noise generator, but you can make one; we had a thread about that a while back.

--

John Larkin         Highland Technology, Inc 
picosecond timing   precision measurement  

jlarkin att highlandtechnology dott com 
http://www.highlandtechnology.com
Reply to
John Larkin

The resonant mode is a single classical degree of freedom, so it has a mean excitation of kT/2. Changing the Q let's you trade off peak PSD vs bandwidth, but that's all.

I ran into the mechanical equivalent of this with attractive-mode atomic force microscopes in about 1987.

Cheers

Phil Hobbs

Reply to
Phil Hobbs

Hi Tim, (I'm already eating humble pie, 'cos my mistake.) The noise across the resistor won't change, if I measure the voltage across the cap it'll be Q times bigger, at resonance.

George H.

Reply to
George Herold

Yeah thanks, my mistake. (JL too) I was thinking about a BP filter in frequency space, and watching* the response change w/ Q.

More L's or C's are just another "degree of freedom" which gets it's 1/2 kT sooner or later.

My mistake did cause me to re-read "Who wakes the bugler?" by C. Battjes, in J William's 2nd book.

George H.

*watching in "my mind", as faulty as youtube :^)
Reply to
George Herold

You can Spice this. A resistor can have noise in LT Spice in the frequency domain. In the time domain, LT Spice resistors are noiseless, and LT Spice doesn't have a time-domain noise generator, but you can make one; we had a thread about that a while back.

You can easily 'add' noise and be able to include any non-linear effects in the circui by setting up the circuit to run .tranoise, which combines the .tran and the .noise into a single analysis run, EXCEPT it enables you to see the effects of non-linear operation, unlike the .noise analysis.

Great for looking at non-linear operation and yielding calibrated FFT noise floors.

The attached .asc shows an example of .tranoise to analyze a VERY simple RLC circuit.

Note the two independent gaussian white noise sources have VERY flat spetrums.

go through clear out the two sets of 'spaces' and straighten out the word wrap! those two lines are LONG!

Version 4 SHEET 1 27404 680 WIRE 1184 -288 1136 -288 WIRE 1296 -288 1264 -288 WIRE 1008 -192 992 -192 WIRE 1136 -192 1136 -288 WIRE 1136 -192 1008 -192 WIRE 1184 -192 1136 -192 WIRE 1296 -192 1296 -288 WIRE 1296 -192 1264 -192 WIRE 1392 -192 1296 -192 WIRE 1504 -192 1392 -192 WIRE 1696 -192 1504 -192 WIRE 1952 -192 1696 -192 WIRE 1984 -192 1952 -192 WIRE 1696 -176 1696 -192 WIRE 1824 -176 1696 -176 WIRE 992 -160 992 -192 WIRE 1392 -160 1392 -192 WIRE 1504 -160 1504 -192 WIRE 1696 -160 1696 -176 WIRE 1824 -160 1824 -176 WIRE 1696 -64 1696 -80 WIRE 1824 -64 1824 -80 WIRE 1824 -64 1696 -64 WIRE 992 -48 992 -80 WIRE 1392 -48 1392 -96 WIRE 1504 -48 1504 -80 WIRE 1696 -48 1696 -64 FLAG 992 -48 0 FLAG 1952 -192 out FLAG 1392 -48 0 FLAG 1696 -48 0 FLAG 1008 -192 in FLAG 1504 -48 0 SYMBOL res 1280 -208 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName Rsource SYMATTR Value {R1} SYMBOL bi2 1264 -288 R90 WINDOW 3 32 40 Invisible 2 WINDOW 0 -32 40 VBottom 2 SYMATTR Value

I={sqrt(4.8*k*T/R1/dt)*(rand(time/dt)+rand(tstop/dt+1+2*int(time/dt))

+rand(3*(tstop/dt+1)+3*int(time/dt))+rand(6*(tstop/dt+1)+4*int(time/dt)) +rand(10*(tstop/dt+1)+5*int(time/dt))-2.5) }

SYMATTR InstName BnoiseR1 SYMBOL voltage 992 -176 R0 WINDOW 0 -93 28 Left 2 WINDOW 3 -242 104 Left 2 WINDOW 123 -108 67 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName Vin SYMATTR Value SINE(0 1.414uV 1kHz) SYMATTR Value2 AC 1 SYMBOL cap 1376 -160 R0 SYMATTR InstName C1

SYMBOL res 1680 -176 R0 SYMATTR InstName Rload SYMATTR Value {R2} SYMBOL bi2 1824 -160 R0 WINDOW 3 24 81 Invisible 2 SYMATTR InstName BnoiseR2 SYMATTR Value

I={sqrt(4.8*k*T/R2/dt)*(rand(15*(tstop/dt+1)+time/dt)+rand(16*(tstop/dt+1)

+2*int(time/dt))+rand(18*(tstop/dt+1)+3*int(time/dt))+rand(21*(tstop/dt+1) +4*int(time/dt))+rand(25*(tstop/dt+1)+5*int(time/dt))-2.5) }

SYMBOL ind 1488 -176 R0 SYMATTR InstName L1

SYMATTR SpiceLine Rser=100u TEXT 1328 -128 Right 2 !.param R1=1k TEXT 312 -400 Left 2 !.options plotwinsize=0\n.param k=1.38e-23 T=300\n.param N=1000000 dt=1uS TEXT 304 -296 Left 2 !.param fstart={1/N/dt} fstop={1/2/dt}\n.param tstart={0.1*N*dt} tstop={1.1*N*dt} TEXT 304 -136 Left 2 !.tran 0 {tstop} {tstart} {dt/10}\n.ic V(ou)=0 I(L1)=-88.6161nA\n.save V(out) I(L1) TEXT 1616 -216 Left 2 !.param R2=100k TEXT 840 -400 Left 2 ;Note fstart=1Hz or BW of FFT, fstop=500kHz, FFT is irrevelant above 500kHz\n tstart=100mS to allow stabilizing, and tstop=1.1 to allow 'window' of 1 second total TEXT 304 -216 Left 2 ;.ac lin 10001 990 1010 TEXT 304 -176 Left 2 ;.noise V(out) Vin dec 10000 {fstart} {fstop} TEXT 800 -456 Left 3 ;TRANOISE EXAMPLE Simple RLC Circuit

Reply to
RobertMacy

ElectronDepot website is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.