What input impedance for R2R I/V converter?

I am designing a transistor, low cost, high performance I/V converter for NOS DACs.
The DAC in question is the 16bit AD1856 R2R Iout, +/-1ma impedance, 1.7k
I started by the simple circuit from Linear Audio,
https://www.linearaudio.net/simple-high-quality-iv-converter
The distortion is too high and perfect hfe matched transistors not necessary.
I am at this stage with input impedance of 50ohm, full scale THD 0.0005%.
IV converer.JPG

I am wondering how the 50ohm impedance will effect the distortion of the R2R?
If I decrease, the distortion increases, so, there is a minimum.
Andrea Ciuffoli has tested with 200ohm resistor.
https://www.audiodesignguide.com/DacNoOverSampling/
The THD is 0.01% for 116mv rms instead of 140mv full scale that this DAC can go down to 0.002% THD+N.
 
R3 generates noise, converts base shot noise current of T1 to voltage and reduces loop gain, why is it there? If it's meant to be a base stopper, its value is about 1000 times the usual values.

When you reduce R3 to 100 ohm or so, you need to change R5 to get the input DC voltage back to 0. Replacing it with a diode-connected (collector shorted to base) transistor of the same type as the input transistor in series with a 200 ohm or 250 ohm trimming potmeter with its wiper shorted to the positive side should do the trick.
 
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The distortion without R3 is 0.03%. The noise iwith 100k s horrible.
I tried with mosfet. I get 0.0014% but the impedance has fell to 5ohm.
The noise 10-20k bw is 1uv.
I tried every parameter except the mosfet type, the stubborn 0.0014 doesn't want to alter.
R5 adjust the input potential and I3 the operating point 6v.

mosfet iv.JPG
 
The principle of Linear Audio publication is to have input current from common base, amplified by the output transistor and feedbacked to the current input. To get 0v input potential, it uses current mirror. I replaced the current mirror to have the input potential adjustable. Maybe a servo can be added if the DC compliance is very low. The DS doesn't speak about it.
R4 is emitter or source degenerator, biasing at high current, the ratio R4 to internal square low impedance becomes very high , hence low distortion.
I replaced the 2n7000 with BS170, The input impedance could be adjusted to 30ohm while the distortion is near 0%. Strange that if I decrease the R4 more, the distortion suddenly flies to 0.03%.
 

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Maybe it starts oscillating.

If R4 is degeneration for the input transistor, then node VF2 must be the input, but the DC voltage there is about 7.5 V or so rather than the 0 V that the DAC needs.

Why do you want a 50 ohm input impedance rather than as low as possible?
 
Now I have the ideal I/V. Input impedance 40mohm, THD 0.00006%.
The reason why the R4 is to provide the mosfet 10v d-s operating voltage. Bellow it gets distorted. I decoupled the R4 and the impedance crashed to 40 mohm without increase in THD.
decoupled.JPG

As you can see the input VF2 is 1.8mv adjusted by R5.
 

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Now I have the ideal I/V. Input impedance 40mohm, THD 0.00006%.
The reason why the R4 is to provide the mosfet 10v d-s operating voltage. Bellow it gets distorted. I decoupled the R4 and the impedance crashed to 40 mohm without increase in THD.
View attachment 1253946
As you can see the input VF2 is 1.8mv adjusted by R5.

OK, so that's why you introduced the negative voltage source. The circuit of post #1 will definitely not have 0 V at node VF2.

The sensitivity to variations of IS2 and IS3 might be problematic. If needed, you could probably solve that by making the ratio of the bias currents of T1 and T2 smaller, shorting R4 and C3, adjusting the gate bias voltage and increasing the positive supply voltage to whatever is needed to keep T1 in saturation in the signal peaks.
 
In post1, if R5 is 3.15k the input is
post 1.JPG

The operating point of the pnp is 8v/ma CCS. The max excursion of the signal is 2.8vP. If I accept +/-1v drift of the operating point 6v, it will correspond the CCS to be +/-0.125ma from 18.5ma drift. It is 0.7%.
 

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I see. I had overlooked the large voltage drop across R3 that the base current of T1 causes.

How accurate do the current sources have to be to keep the input DC voltage between -50 mV and +50 mV and how much does the input DC voltage vary with temperature?
 
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Done.
With servo, the input impedance is 0.1 ohm, see graph bellow.
I still don't have an idea what is the compliance should be. The input offset is 24uv without input and 300uv with +/-1ma.
The distortion is still 0.00006%.
IVCONVERTER MOSFET.JPG
 

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I found something scary about DC compliance for R2R.
Screenshot_20240102_113653_Samsung Notes.jpg

This shows how desasterous is the offset voltage and the bias current.
Another aspect of IV converter is the setteling time which requires high slew rate well dampened character.
 

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I measured on simulator,the input impedance of several opamps I've seen used as IV converter for 1map 20khz.
NE5534 with 22pF. OPA627, THS4011, AD829, AD8007.
 

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As I know 0.7 ohm is acceptable, I decreased the bias current to 4+1.5ma. The 4ma passes through the MOSFET, is temperature dependent and both vary in the same way where the 1.5ma that passes through the output is compensated.
The input impedance is 0.08 ohm to reach 0.4 ohm at 20khz, see graph.
The distortion at 2.8v is 0.0005% now, sufficient for 16bit.
I replaced the voltage drop resistor by leds and tl431 to avoid offset pumping. The noise of LED is 10 times higher.
Once the servo inputs balanced, the offset is 4uv.
IVCONVERTER MOSFE2T.JPG
 

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HYAK, FYI -

For some interesting DIY advice on implementing the AD1856, perform a search on this site with the subject ‘PCM56’, by member ‘Bernhard’. The AD1856, of course, being an Analog Devices drop-in replacement for the Burr-Brown PCM56. Bernhard has measured most of the old multi-bit, non-Sigma-Delta, DAC chips. Although, I don’t recall whether he verified the performance of the AD1856 is essentially the same as the PCM56. Anyhow, a search will produce posts with spectrum analyzer display photos of multi-bit DAC distortion measurements performed and posted by Bernhard. Show the excellent real-world DAC distortion capability of the PCM56 when the MSB-trim feature is utilized. Bernhard was a tireless advocate for the PCM56. You’ll also find a resistor I/V + passive filter circuit suggested by him.
 
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