Sallen-key filter and SNR

[Stephen Boulet]

I've designed a 6-pole Sallen-key op amp filter (so three stages) as a
reconstruction filter after a DAC. It's a low pass filter with a corner
near 90 kHz.

At the input to the filter, SNR is about 67 dB, and it goes down to 65.4
dB after stage 1, 60.1 dB after stage 2, and 55.4 dB after stage 3.

The last two stages have higher Q than the first stage.

Basically, the noise floor keeps creeping up across the stages (I'm
using a TL3474A op amp). It seems to me that the op amp noise isn't the
culprit, because at 40 nV/sqrt(Hz) it's over 100 dB below the signal.
Are there some general things I should be looking out that some of you
with more analog audio design experience can share? Thanks.

Stephen

 

[John Popelish]

I've designed a 6-pole Sallen-key op amp filter (so three stages) as a
reconstruction filter after a DAC. It's a low pass filter with a corner
near 90 kHz.

At the input to the filter, SNR is about 67 dB, and it goes down to 65.4
dB after stage 1, 60.1 dB after stage 2, and 55.4 dB after stage 3.

The last two stages have higher Q than the first stage.

Basically, the noise floor keeps creeping up across the stages (I'm
using a TL3474A op amp). It seems to me that the op amp noise isn't the
culprit, because at 40 nV/sqrt(Hz) it's over 100 dB below the signal.
Are there some general things I should be looking out that some of you
with more analog audio design experience can share? Thanks.

Low pass filters made with capacitors have shunt paths for stop band
signals to ground. If those ground points are not pristine, they also
bring noise signals into the filer. What are you using as a ground
reference for the filter.

 

[martin griffith]

I've designed a 6-pole Sallen-key op amp filter (so three stages) as a
reconstruction filter after a DAC. It's a low pass filter with a corner
near 90 kHz.

At the input to the filter, SNR is about 67 dB, and it goes down to 65.4
dB after stage 1, 60.1 dB after stage 2, and 55.4 dB after stage 3.

The last two stages have higher Q than the first stage.

Basically, the noise floor keeps creeping up across the stages (I'm
using a TL3474A op amp). It seems to me that the op amp noise isn't the
culprit, because at 40 nV/sqrt(Hz) it's over 100 dB below the signal.
Are there some general things I should be looking out that some of you
with more analog audio design experience can share? Thanks.

Stephen

I've just been mucking around in
http://beis.de/Elektronik/Filter/ActiveHPFilter.html and was wondering
what the midband gain of the SK filler is.




martin

After the first death, there is no other.
(Dylan Thomas)

 

[Frank Miles]

I've designed a 6-pole Sallen-key op amp filter (so three stages) as a
reconstruction filter after a DAC. It's a low pass filter with a corner
near 90 kHz.

At the input to the filter, SNR is about 67 dB, and it goes down to 65.4
dB after stage 1, 60.1 dB after stage 2, and 55.4 dB after stage 3.

The last two stages have higher Q than the first stage.

Basically, the noise floor keeps creeping up across the stages (I'm
using a TL3474A op amp). It seems to me that the op amp noise isn't the
culprit, because at 40 nV/sqrt(Hz) it's over 100 dB below the signal.
Are there some general things I should be looking out that some of you
with more analog audio design experience can share? Thanks.

What sort of R & C values are you using? If the C values are pretty
small, that could be the cause. Recall, for example, that the noise
voltage (in v rms/rt Hz) for a parallel RC circuit is sqrt(k*T/C)
{this assumes that the RC circuit controls the band-limiting}.

-frank
--

 

[Mark]

Stephen,

you need to analyze the noise and see what frequency range the noise is
in, is it in the passband or is it in the stopband.

What are you using to measure the SNR?

Maybe you need a simple passive Rc low pass filter at the very end of
the chain to get rid of the noise in the stopband that may be created
by the op-amps.

Mark

 

[Pooh Bear]

I've designed a 6-pole Sallen-key op amp filter (so three stages) as a
reconstruction filter after a DAC. It's a low pass filter with a corner
near 90 kHz.

At the input to the filter, SNR is about 67 dB, and it goes down to 65.4
dB after stage 1, 60.1 dB after stage 2, and 55.4 dB after stage 3.

The last two stages have higher Q than the first stage.

Basically, the noise floor keeps creeping up across the stages (I'm
using a TL3474A op amp). It seems to me that the op amp noise isn't the
culprit, because at 40 nV/sqrt(Hz) it's over 100 dB below the signal.
Are there some general things I should be looking out that some of you
with more analog audio design experience can share? Thanks.

Well... you don't state your operating level making it difficult to make any
use of S/N numbers.

40nV/rtHz isn't especially quiet for an op-amp - actually it's noisier than
any I can think of offhand..

Each filter stage will also add thermal noise too. Approximately what are
the component values for each stage ?


Graham

 

[John Larkin]

I've designed a 6-pole Sallen-key op amp filter (so three stages) as a
reconstruction filter after a DAC. It's a low pass filter with a corner
near 90 kHz.

At the input to the filter, SNR is about 67 dB, and it goes down to 65.4
dB after stage 1, 60.1 dB after stage 2, and 55.4 dB after stage 3.

The last two stages have higher Q than the first stage.

Basically, the noise floor keeps creeping up across the stages (I'm
using a TL3474A op amp). It seems to me that the op amp noise isn't the
culprit, because at 40 nV/sqrt(Hz) it's over 100 dB below the signal.
Are there some general things I should be looking out that some of you
with more analog audio design experience can share? Thanks.

Stephen

Terrible opamp! 49 nV + 0.22 pA per root Hz.

What are the resistor values like?

And why 90 KHz?

John

 

[Stephen Boulet]

Low pass filters made with capacitors have shunt paths for stop band
signals to ground. If those ground points are not pristine, they also
bring noise signals into the filer. What are you using as a ground
reference for the filter.

The same ground as the rest of the PCB. The caps that go to ground on
these two stages do couple straight to the non-inverting terminal. They
are 10 pF, which (at least I thought) should be a high impedance to audio.

I'll try to do what I can to isolate the ground and see whether there is
any improvement.

Stephen

 

[John Larkin]

The same ground as the rest of the PCB. The caps that go to ground on
these two stages do couple straight to the non-inverting terminal. They
are 10 pF, which (at least I thought) should be a high impedance to audio.

10 pF, 90 KHz, puts your resistor values in (roughly) the 200K
ballpark. Dump the opamp bias current noise into a bunch of 200K
resistors, stir in roughly 20 uV of Johnson noise per resistor, and
there's your noise.

Scale things down, and get a better opamp.

John

 

[Stephen Boulet]

Stephen Boulet wrote:




Well... you don't state your operating level making it difficult to make any
use of S/N numbers.

40nV/rtHz isn't especially quiet for an op-amp - actually it's noisier than
any I can think of offhand..

Each filter stage will also add thermal noise too. Approximately what are
the component values for each stage ?


Graham

The caps are:

Stage 1: 68, 100 pF
Stage 2: 10, 100 pF
Stage 3: 10, 150 pF

where the first cap goes to ground and the second is in feedback.

The resistors are 32K, 41.25K, and 40.3K for the first 3 stages (I'm
using equal value resistors in each stage).

Here is a pdf of the I/V conversion stage (the DAC outputs a
differential current) and the first stage of the filter:

http://www.theboulets.net/Sallen-key.pdf

My signal is 0.8 Vpp over an 18 kHz bandwidth, so:

49nV * sqrt(2) * sqrt(18kHz) would be the input noise voltage in
peak-to-peak terms. The input signal voltage is 0.8Vpp. So:

20*log10(9.3uV/800mV) = -98.7 dB

Are there other noise contributors that aren't reflected in the input
equivalent noise spec for an op amp?

Stephen

 

[Meredith Boulet]

Terrible opamp! 49 nV + 0.22 pA per root Hz.

What are the resistor values like?

And why 90 KHz?

John

Well, it's cheap. I'm not sure it's the weakest link though.

I posted a link to the first two stages earlier:

http://www.theboulets.net/Sallen-key.pdf

It's a band-limited audio signal (2-74 kHz) representing several voice
channels destined to be upconverted to an RF band. I *think* that the
noise power in one 18 kHz channel is much less than the signal power at
0.8 Vpp.

Stephen

 

[John Popelish]

John Popelish wrote:


The same ground as the rest of the PCB. The caps that go to ground on
these two stages do couple straight to the non-inverting terminal. They
are 10 pF, which (at least I thought) should be a high impedance to audio.

I'll try to do what I can to isolate the ground and see whether there is
any improvement.

I could have been more specific. I am trying to get you to think of
what else is sharing the ground, and how it is routed across the
board, and how ground currents will produce local voltage drops that
show up in unintended places.

Is the audio ground shared with digital chips, etc.?

 

[John Larkin]

Well, it's cheap. I'm not sure it's the weakest link though.

I posted a link to the first two stages earlier:

http://www.theboulets.net/Sallen-key.pdf

It's a band-limited audio signal (2-74 kHz) representing several voice
channels destined to be upconverted to an RF band. I *think* that the
noise power in one 18 kHz channel is much less than the signal power at
0.8 Vpp.

Stephen

You could try

Scaling the Rs down

Scaling the Cs up

Dump R13: it just adds noise.

Sweep the response to make sure you don't have a peak.

Use a better opamp!



How many bits in the DAC? If you have enough headroom to keep all N
voice signals from clipping the dac, you may be pushing each one down
into the quantization noise.

John

 

[John Popelish]

The caps are:

Stage 1: 68, 100 pF
Stage 2: 10, 100 pF
Stage 3: 10, 150 pF

where the first cap goes to ground and the second is in feedback.

The resistors are 32K, 41.25K, and 40.3K for the first 3 stages (I'm
using equal value resistors in each stage).

Here is a pdf of the I/V conversion stage (the DAC outputs a
differential current) and the first stage of the filter:

http://www.theboulets.net/Sallen-key.pdf

My signal is 0.8 Vpp over an 18 kHz bandwidth, so:

49nV * sqrt(2) * sqrt(18kHz) would be the input noise voltage in
peak-to-peak terms. The input signal voltage is 0.8Vpp. So:

20*log10(9.3uV/800mV) = -98.7 dB

Are there other noise contributors that aren't reflected in the input
equivalent noise spec for an op amp?

I suggest you plug in a MCP6044 higher performance opamp (especially
with a 5 volt supply) and with lower noise.
http://rocky.digikey.com/WebLib/Microchip/Web Data/MCP6021,2,3,4.pdf

 

[Pooh Bear]

The caps are:

Stage 1: 68, 100 pF
Stage 2: 10, 100 pF
Stage 3: 10, 150 pF

where the first cap goes to ground and the second is in feedback.

The resistors are 32K, 41.25K, and 40.3K for the first 3 stages (I'm
using equal value resistors in each stage).

As a 'rule of thumb' I'd avoid using R values > 10k where you want to avoid adding
much noise in such a filter and that's with a higher working reference level for
audio of around a Volt.

You might consider simply scaling those values by a factor of 10 for example.

Here is a pdf of the I/V conversion stage (the DAC outputs a
differential current) and the first stage of the filter:

http://www.theboulets.net/Sallen-key.pdf

Thanks - that gives me something to work with.

My signal is 0.8 Vpp over an 18 kHz bandwidth, so:

Well... that's 283 mV rms.

49nV * sqrt(2) * sqrt(18kHz) would be the input noise voltage in
peak-to-peak terms. The input signal voltage is 0.8Vpp. So:

There seems to be a term of sqrt(2) in your calcualtion that gives you *peak*
voltage but not peak to peak voltage.

I make the rms input noise of the op-amp over that bandwidth 6.57 uV

20*log10(9.3uV/800mV) = -98.7 dB

Which gives me -92.7 dB ! You made the error of comparing peak and peak to peak
voltages. Hence the 6 dB difference. For simplicity I always normalise to rms -
it's less trouble !

Are there other noise contributors that aren't reflected in the input
equivalent noise spec for an op amp?

Well... there's input bias current noise but I doubt that's the case here.

However you're only getting 67dB at the input to the filter stages. How much self
noise is there from the DAC I'm wondering ? You could simply load it with Rf and
measure directly.


Graham

 

[Pooh Bear]

I suggest you plug in a MCP6044 higher performance opamp (especially
with a 5 volt supply) and with lower noise.
http://rocky.digikey.com/WebLib/Microchip/Web Data/MCP6021,2,3,4.pdf

Seconded. I've recently become aware that Microchip do some curious stuff I
wasn't previously aware of.

For example I just discovered they do gate drivers for power fets.

Graham

 

[qrk]

Well, it's cheap. I'm not sure it's the weakest link though.

I posted a link to the first two stages earlier:

http://www.theboulets.net/Sallen-key.pdf

It's a band-limited audio signal (2-74 kHz) representing several voice
channels destined to be upconverted to an RF band. I *think* that the
noise power in one 18 kHz channel is much less than the signal power at
0.8 Vpp.

Stephen

1. Your opamp is really noisy. There are better choices out there.
Your opamp contributes at least 15 uV of noise over the bandwidth.

2. The resistors are a bit high in value creating more noise due to
thermal noise and opamp input current noise. If you need R13 for bias
reasons, bypass it. It's another noise source. BTW, R13 should be 64k
if your trying to minimize DC offset errors. Try use a spice simulator
and see what sort of noise you get. LTspice (free from Linear
Technology) is a good choice if you don't have a spice simulator. A
spice simulation of your circuit with a zero noise amplifier has about
40 to 50 nV/rtHz of noise because of your resistor values.

3. You could have PCB layout problems. Digital ground noise getting in
to your analog ground, digital signal passing by the analog section,
insufficiently bypassed/decoupled power supplies in the analog section
(i.e. running analog and digital stuff on the same power bus), and
misc layout issues could all be part of your problem.

4. You should rig up a noise test and try out different opamps and
component values. A superstrip bread board will work fine.

 

[Ban]

Stephen,

you need to analyze the noise and see what frequency range the noise
is in, is it in the passband or is it in the stopband.

What are you using to measure the SNR?

Maybe you need a simple passive Rc low pass filter at the very end of
the chain to get rid of the noise in the stopband that may be created
by the op-amps.

Mark

This is a very good advice, and you can make a 7th order filter this way.
What others have said is true as well. Get a better opamp(OPA4134), a new
layout(analog away from digital), low resistor values (3k3), and compensate
the opamps in the right way. You also have to consider the gain at higher
frequencies, so if your opamp will have 40nV/sqrtHz, the whole bunch of
opamps will be at around 100-200nV/sqrtHz. Even this should give you 94dB
S/N with 3k3 resistors and 75dB with high value resistors, so there must be
something wrong.

 

[Stephen Boulet]

Well, it's cheap. I'm not sure it's the weakest link though.

You could try

Scaling the Rs down

Scaling the Cs up

Dump R13: it just adds noise.

Sweep the response to make sure you don't have a peak.

Use a better opamp!


How many bits in the DAC? If you have enough headroom to keep all N
voice signals from clipping the dac, you may be pushing each one down
into the quantization noise.

John

I'll look into scaling the design.

The reason I started with 10 pF and 100 pF capacitors is that those
parts were available in 1% values. I don't think that 1% 1000pF caps are
avaible (surface mount, 0402 or 0603, but I might be mistaken there).

Trying to design a low ripple Chebyshev filter (several tenths of a dB
at most) with 5% caps is challenging.

I'll first try a lower noise op amp (maybe on semi's MC33079). Thanks so
much to eveyone for their suggestions.

Stephen

 

[John Larkin]

I'll look into scaling the design.

The reason I started with 10 pF and 100 pF capacitors is that those
parts were available in 1% values. I don't think that 1% 1000pF caps are
avaible (surface mount, 0402 or 0603, but I might be mistaken there).

A 10 pF 1% cap won't be anything like that once you put it on a board
and connect it to opamps. An opamp input runs several pF, typically.
The PCB pads and traces alone will add a good hunk of a pF, and FR-4
makes just about the worst capacitors on the planet.

There are filter configs that have lower component sensitivities than
Sallen-Key.

John