DDS Selection

Actually notches are great inside feedback loops, because their phase shifts go away at frequencies more than a few notch widths away. Long long ago, when I was designing atomic force microscopes, we got a factor of about 4 increase in speed by notching out the mechanical resonance of the silicon cantilever.

If you have a resonant actuator, a notch filter can be a _big_ win.

Cheers

Phil Hobbs

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You can do that sometimes, especially when the noise is nearly white. Photodiode capacitance makes the noise of TIAs rise steeply with frequency, though, so once you get past the point where the differentiated TIA voltage noise e_N*(2*pi*f*C_diode) dominates the shot noise, you start losing SNR by increasing BW.

Cheers

Phil "CW guy at heart" Hobbs

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What is a Hobsonian Laser Noise Canceler? Is it a Phil Hobbs invention?

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This is not necessarily true. FFT can be done at a single frequency. If the number of samples per cycle is a power of two there is a symmetry in that there are repeated values of the sine function to multiply the sample by. They repeat symmetrically about the 1/4 point in the first 1/2 of the waveform, and again at the 3/4 point in the second half of the waveform. Also the absolute values of the first 1/2 of the waveform are the same as in the second half of the waveform. This enables the multiplications to be factored out of all the summations, greatly reducing the number of multiply operations. This is what I intend to do at the carrier frequency of each channel. I am not interested in the other frequencies.

Depending on the sample rate the repeat values may be spread out over two or more periods. The more periods the less efficient the FFT but also the lower and more random the quantization noise.

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What kind of lock-in are you referring to? Is it a Homodyne where the input signal to be measured is essentially multiplied by a square wave in analog circuits?

I am now considering filtering higher harmonics and noise by using a switched capacitor filter such as described here:

I am concerned about switching noise. In prior experience with switched capacitor filters I have observed switching noise in the output. I would like the switching frequency to be well above the cutoff of the anti-alias filter. For this to be I figure I would need at least 10,000:1 ratio of switching frequency to cutoff frequency. In the filters I have seen 100:1 is typical and 1000:1 is rare. I have not found one with 10,000:1. Does it exist?

Failing that I could make the switching frequency a multiple of 1/T where T is the length of time the FFT is done over. That would put the switching frequency in one of the notches in the sync function that is the frequency response of a Fourier Transform.

I could create a switched capacitor filter out of several chips. But it would make the board too large. I would need it in a single chip.

There would also be the 6 different switching frequencies to generate. I know how to do this with several counter and logic chips. But any lower chip count suggestions are welcome, especially a singe chip with several channels of output.

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It's not a synchronising function but sinc - sine(x)/x which gives the resistor value at each tap.

Google wasn't too helpful, until I remembered that the structure is also known as a transversal filter

shows one at Fig 25

goes into the theory.

It's more compact, and you can get 0.1% tolerance resistors, while 1% tolerance capacitors are as good as you can buy. It's also a finite impulse response filter, with a linear phase shift.

-- Bill Sloman, Nijmegen

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Agreed. You just have to want to notch out a frequency that has nothing to do with your modulation frequency, which doesn't happen all that often.

-- Bill Sloman, Nijmegen

What frequencies are you talking about? I'd sample the signals using an ADC and do the whole filtering and processing digitally. In the analog domain you get extra noise and errors with every stage you add.

That's the same as sqrt(t) right? Like the stability specifications you sometimes get with references.

So the graph of typical long-term drift has a square root shape.

Hmm, is this related to the random walk sqrt(N)?

Given what you're trying to do, you really, really ought to get his book.

John

Not so--that's exactly what it's good for. You can't notch out the modulation frequency before the demod, obviously, but you can widen the lowpass on the output if you notch out the ripple components.

Cheers

Phil Hobbs

Yes, it's random walk drift, sometimes called "Brown noise". Uniform drift doesn't have a Fourier transform, strictly speaking, but you can compute it formally by integrating a delta function twice. That gives you 1/f**2 in amplitude, so 1/f**4 in power. The random version doesn't always go the same direction, so if you do some stochastic Fourier integral that I'd have to look up, it winds up being 1/f**2.

Cheers

Phil Hobbs

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OK to answer my own question... Reading the spec sheet in the light of day I found the ouput 'power' of 22 cd. Which is 62mW/sr, and with the 4 degree 1/2 angle about 0.1mW of power. So total power is something like 0.2mW

George H.

I am looking for low noise sine wave generation to drive an LED light source. Frequencies will be somewhere between 100Hz and 1kHz. I will set the frequencies in the part of the noise spectrum where noise is lowest.

ADC does not apply. DAC and DDS does. But I have decided not to use them for this for reasons I will give in another reply.

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How many resistors would it take to get the equivalent quantization noise of 16 bits_

A photodiode of, say, 0.5 A/W would give 2 mA, for a CTR of 4%, again sort of reasonable.

John

I have decided not to use a DDS. I recognize now that the same quantization noise equation with its white noise approximation that would apply to the 16 bit ADC would apply to the DDS. So if I use a 10 bit DDS I will get the quantization noise performance of 10 bits, not

There has been mention in another reply of an LTZ1000 reference. I have looked at the specs and it looks like a very good one. I plan to use one them to voltage reference both the ADCs and the square wave generators. Thanks for bringing this one up.