Ultra low noise filters
I've been working some numbers, and I'd like to put some of them in front of the forum along with some questions. I hope some knowledgable folks will be able to help me out.
My situation is specific to op-amp based LPF, but applies equally to any kind of filter/buffer/transmitter. With today's ultra low noise opamps (AD797 at [0.9/sqrt(Hz)]) resistor noise can (usually) dominate even a simple circuit.
(even an 8nv/sqrt(Hz) opamp sees a sqrt(2) increase in noise with a 4k resistor)
I would like to keep resistor values low (~1k) but such low input impedences mean that significant current (~5mA) is flowing and as a result excess (1/f) noise tends to dominate even in metal film resistors.
My first thought is wirewound resistors, but I am unsure of the inductance of the average wirewound (e.g. Vishay-Dale 3W RS) or its effect at the input, or (worse) in the feedback loop.
Can anyone comment on using WW resistors in this kind of application? Are there other ways of achieving 20-bit S/N?
Thanks for any insights.
LPF moise issue
You can not bend the laws of physics and as most things in life it is a compromise. I think you are just right with the 1k to 2k range of metalfimresistors. Don't use wire wound, they will scew up things as they have significant <B>inductance</B>
BTW is this a practical example or theoretical one of you?
The powersupply should be low moise too. And the circuit bandwith limited as RFI can cause noise too.
..and don't forget to include current noise. If memory serves me, the formula is:
sqrt[ e(n)^2 + (i(n)*R)^2 + 4kRT ]
Where k is boltzmann's constant = 1.38 x 10^-23
T is temperature in Kelvin
R is the source resistance
e(n) is the voltage noise density
i(n) is the current noise density
so the noise of a resistor on it's own is about sqrt(4kRT)
You can use this convenient little formula along with some gain equations to figure out what the total noise of your circuit will be.
Most importantly, beware taking a single number (0.9nv/rt Hz) as the sole specifier of a device's performance. That figure is taken at 1kHz according to Analog Device's datasheet. The noise of the AD797 starts to rise at frequencies below about 200Hz. The datasheet lists input noise of 50nV peak-peak at frequencies of 0.1Hz to 10Hz.
Also, remember that noise at the input will be multipled by the operating gain of the op-amp at the output. So, 0.9nV/rt Hz noise at the input becomes 0.9mV/rt Hz at the output if you use a gain of 1000.
The problem with many op-amps for audio use is that they have a huge gain-bandwidth product. High gain at audio bandwidths means you will be greatly mulipltying the input noise. Lowering the gain to reduce this noise-multiplying effect opens up the bandwidth; at a gain of 10, the AD797 has a bandwidth of 8MHz! From the datasheet, the input noise between 10Hz to 1MHz is 1uV RMS.
Given that you wanted a LPF, you may be better of with an op-amp that has a lower gain-bandwidth product, even if the noise density specs are slightly worse - you may end up with less total noise. Then again, you'd may be even better off with a discrete solution - possibly higher noise density but very much lower gain-bandwidth may give you lower output noise.
In terms of resistors, I'd go with values in the order of 1-10k. At meg-ohm resistances, the signal to noise ration drops considerably.
Re: LPF moise issue
I believe C1 is attempting to shunt HF noise to ground.
The Butterworth filter below is from the Crystal AN48. They used rather small capacitors (220pF/1000pF). It seems to me that capacitors in the nF range would be easier to spec (less parasitic capacitance, easier to obtain tight tolerances). Is there a reason for using pF values?
Re: 1/f noise
a) 50nV p-p is probably on the order of 12nV RMS
b) the noise at 10Hz is only 1.7nV/rt(Hz)
c) my amplifier input filter is already -3dB at 10Hz
d) my loudspeakers cannot get near these frequencies
As such I am relying on integration by parts across the range 20-20,000Hz for the total noise figure; is this reasonable? Due to the effects of feedback, can the super sonic noise voltages create audible noise?
I am obviously struggling to understand the correct application of these opamps, so I certainly thank everyone for their assistance.
Thanks again for everyone's input.
The practical circuit you gave makes it much easier to discuss.
You can design the lowpassfilter <B>MUCH</B> more easy with FilterPro(R) now from Texas Instruments (was Burr Brown).
You can even make the first "pole" in the IV-converter. If you want low noise you have to use low value resistors in the range 1k-2k or lower. Let the program calcute for you capvalue's and see how you get in the pF values. If you use caps lower than about 50 pf stray capacitance in the circuit spoils things, as your values aren't accurate any longer.
Discrete circuits like Sonnya's folded cascode with JFET inputs sound better and can be low noise too. See this forum. Of course discrete takes up more boardspace. Discrete or IC, both can be low noise. What matters to me more, is <B><I>soundquality</B></I>. Measurements mean nothing to me I just listen to the music and the circuit and if I like the result I keep it that way.
Thanks Elso. That is some nice software. I am planning on sticking with 2 poles, as the OOB noise attentuation is acceptable and the phase variation is less pronounced.
I still have a question about capacitor size though, because the ratio K=C1/C2 is more important than their values. i.e. I can choose C1, C2 in pF or nF range and get acceptable resistance values, but is their a reason to prefer smaller/larger caps? I can easily obtain film caps at 2% tolerance for values >=1nF, but such accuracy is more difficult in the pF.
If larger values are fine, I will probably use 10% dip mica for the I-V and 2% polyester film for the LPF, then 1% MF resistors as recommended here. I was planning on the MFB topology as I posted above...any reasoning against that?
I will definitely consider your recommendation about a discrete solution, but I think it best for me to first construct a filter with good numbers and then tackle the more elusive "quality" later. (walk before run?)
One of the nice things of the FilterPro program is it can calculate for any range of R or C values.
You can start with 100, 1k, 10k, 100k and see what happens. The values are calculated in a fraction of a second.
I have been using 10nF silvermica caps for the IV-converter but abandoned that idea as a good quality polypropylene sounded less harsh and more pleasant to my ears.
For the other caps I do use 470pF and 2200pF 1% polypropylene made by BC-Components(formerly Philips) I also used silvermica's here but gave them up for the same reason. [BTW I use a f-3dB=10k third order Bessel MFB lowpass filter for my non oversampling KWAK-DAC with AD1865.] It is a balanced filter two IV-converters, one outputbuffer per channel along the lines you sketched.
These 1% polyprop. caps are availabe from www.conrad.com in the range of values of 47pF to 4700pF. Also a nice feature of the program is that you can use standard C values; and if a certain value is not available using a other value and resistor values are recalculated.
Re: 1/f noise
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