Need stiff low noise bias voltage for scope frontend

[Martinn]

Recently, I have started designing a USB oscilloscope frontend https://www.eevblog.com/forum/projects/few-mhz-scope-frontend/msg4957573/ . To make up for the lowish 10 MHz bandwidth, I threw in a few extras to make life more interesting. One is a wide input offset shift - a few volts (+2 -5)  on top of the 20 mVpp max input range (x1/10/100/1000). To achieve this, I added a bias voltage at the first FET input amplifier (x5) stage.

I had my doubts about this LM358 bias buffer (bias1 in the schematic), and indeed it shows lots of ripple and crossover distortion.
Thinking about it, the bias1 point should be stable to 0.1% (8 bit ADC and x5 gain), which means its impedance should be 1000 times lower than the feedback divider R12, R13, R49, which are 850 Ohms according to AD8065 datasheet spec for x5 gain.
So I need the bias to have an impedance of about 0.8 ohms from DC to 10 MHz. I found two ways how others did that:

First would be scopefun https://gitlab.com/scopefun/scopefun-hardware/-/blob/master/KiCadSource/Scopefun_v2.pdf?ref_type=heads using a OPA692 video buffer. This is kind of brute force - but why not? Unfortunately it would add lots of extra noise due to its large bandwidth and filtering the output of a fast unity gain buffer is out of the question, these things are allergic to single digit pFs. Also these things are expensive and I have four bias points (one for each amplifier stage - I figured connecting those would create cross-coupling, making a nice oscillator).

Second solution I found in a reverse engineered scope schematic (can't remember where I found it), where the bias was buffered with a 220 uF capacitor, driven by an opamp followed by a BJT class B follower.

So I could either find a low enough noise/bandwidth (video?) buffer or try to drive a large enough capacitor. A 220 uF capacitor would have an impedance of 0.8 ohms at 904 Hz, so I'd have to design an opamp circuit driving those 220 uF and providing less than 0.8 ohms closed loop impedance below 900 Hz. (some literature on that: https://www.analog.com/media/en/training-seminars/design-handbooks/Practical-Analog-Design-Techniques/Section2.pdf).

Not sure what the best way to proceed is here. As this will most likely stay and educational exercise, part cost actually does not matter but still it would feel inapproriate throwing several $5 parts into a design of such pedestrian bandwith (the original USB mixed signal scope sells for $20 on Ali).

Any ideas?

[MasterT]

Input impedance for external driver at Bias1 is 170 Ohm not 850. Inverting input of the AD is "virtual ground".
IMHO,  driving so high load at high frequency  is not easy task, BJT emmiter follower is the chipest solution, But better alternative is inject bias directly to non-inverting input of AD, there about 1 kOhs, so 5k brought from LM358 output should be o'k. Freq. linearity is easy to achieve splitting 5k by /2 and setting cap to ground

[Martinn]

I don't see how I could inject a voltage at U1 noninverting input - that's the scope input, could be low impedance (50 ohms+) or high impedance (up to 1 meg set by R3).

[nctnico]

Also don't try to clamp input voltages using the supply lines. Regulators can't sink current so this is utterly useless and likely to damage the rest of the circuit. Just put a bi-directional, low capacitance TVS diode in there. Or use a few biased zeners to create positive / negative voltages because zeners can sink current. Use low capacitance diodes to couple the signal into the biased zeners for a low capacitance solution.

A simpler solution to create and offset is to use a buffer amplifier followed by an inverting amplifier and put the offset on the positive input. Basically half an instrumentation amplifier.

[Martinn]

I did a simulation of a typical capacitive drive circuit: An arbitrary opamp (voltage mode dominant pole compensated, unity gain stable), C2 tuned to no overshoot (critical damping).
Interestingly, the output impedance curve shows a peak of 30 ohms (the value of the series isolation resistor) at 31 kHz. To the right, the impedance drops according to the C1 value.
To the left, impedance drops probably according to increasing gain of U1.
So if this is correct, it is impossible in this configuration to achieve a lower peak impedance than the isolation resistor R3. In my case, this would need to be below 0.2 ohms which is practically impossible (no high GBW opamp will have that low open loop output impedance). Any objections?
This would mean that unless I change the topology as suggested by nctnico the only way to go is a low noise, fast buffer.

Also don't try to clamp input voltages using the supply lines. Regulators can't sink current so this is utterly useless and likely to damage the rest of the circuit. Just put a bi-directional, low capacitance TVS diode in there. Or use a few biased zeners to create positive / negative voltages because zeners can sink current. Use low capacitance diodes to couple the signal into the biased zeners for a low capacitance solution.

Good point, haven't thought that through obviously. A TVS probably would not work as they have rather loose voltage specifications (more geared towards ESD) and the input diodes of the AD8065 will also clamp towards VCC/VEE. So diode clamping would have to be to lower voltages as the supplies (4.7 V zeners sound like a good idea)!
The critical path is when both input attenuators are set to 1:1 and the opamp input is effectively connected to the input via a 50+2x510 ohms resistor. The AD8065 input diodes are specified as max. 30 mA, which results in about 30 V of overvoltage. Just checked - my RTB2000 has an input voltage specification of 400 Vp - I wonder how they do that. The only way I see for that is increasing the input protection resistors. The input current noise of the AD8065 is only 0.6 fA/rtHz so current noise over a 11.7 meg resistor would equal the opamp input voltage noise. However, the 1000 ohms in the current design already add 4 nV/rtHz, so this approach does not work if I want to keep the noise low.