How high is too high?

[elki]

In the op amp data sheets there are recommendations for the feedback resistor values to provide a stable operation of the amplifier. The recommended configurations typically do not go beyond the gain of 10. I wonder what are the pros and cons of driving the amplifier circuit to provide the very high gain of 100 vs having a two-stage amplifier configuration (e.g. 10x10). The op amp in question is https://www.analog.com/media/en/technical-documentation/data-sheets/ad8000.pdf.

[Benta]

A gain of 100 or 1000 is normally not a problem, but you need to keep in mind that input bias and offsets are amplified as well.
Also, you may run into gain/bandwidth issues.

[TimFox]

As noted above, bandwidth is an important parameter to answer your question.
As is DC offset.
A cheap op-amp, with 1 MHz unity-gain frequency, will then have 1 kHz bandwidth at gain 1000.
Also, that cheap op-amp may well have an initial DC offset voltage of 5 mV (referred to the input), so at gain 1000 the quiescent output will be 5 V DC.
Old textbooks go into the optimization for multiple stages, each of which is characterized by a gain-bandwidth product (normally equal to the unity-gain frequency for an unconditionally-stable op amp), to choose the appropriate number of stages and division of the required gain between them.
If you use multiple stages, and the amplifier is not to be used down to DC (e.g., an audio amplifier), then you can place coupling capacitors between stages to remove the DC offset.

[ejeffrey]

The AD8000 is a current feedback amplifier so the bandwidth doesn't scale linearly with gain.  Instead The bandwidth is set by the feedback resistor and high gain requires an obnoxiously small ground resistor, and at some level the parasitic inductance of that resistor will limit bandwidth.  In the end it's just hard to make a high bandwidth 1000:1 voltage divider.

[elki]

Thanks a lot for your replies. As was mentioned by several of you, the input offset will be amplified as well and it becomes rather cumbersome to correct for it when going to high gains. Having the non-linear dependence of the bandwidth on the gain for this specific amplifier, I guess the choice between the one- and two-stage gain configurations should be done in practice as the data sheet does not seem to provide enough information. My main two worries about going to the two-stage option were the increased noise and energy consumption.

[elki]

Somewhat related question. While trying to include the AD8000 model within a netlist for ngspice simulation (XU1 N006 N011 N015 N009 N012 N015 AD8000), I get the following error:

Error: no such function 'xu1.x1.'

which seem to point to some inconsistencies between the notation used in the official AD8000 cir model and ngspice?

[ejeffrey]

A two stage amplifier will definitely draw more power, but as long as the first stage has a reasonable gain the second won't add significant noise.  A first stage gain of 10 is easily enough for that.

[Kleinstein]

A 2 stage amplifier can use lower speed OP amps and select different types: e.g. a slower low noise, low bias or low drift one for the input and a high speed one for the output. The 1st amplifier may also use a lower supply, though this is rare in practice. Overall the power consumption could even be lower.
E.g. instead of the AD8000 at a gain of 100 one could use something like an AD8065 and AD8001 with a gain of 10 each with lower total power.
The super fast amplifiers often have limitations, e.g. with drift or lower frequency noise.

For high gain at high speed there may just not be a suitable OP-amp with enough GBW.

Besides the simple 2 stages in series there is also the option with a compound amplifier, with the 2nd amplifier insider the FB loop. This can be beneficial with accuracy (e.g. combine an AZ amplifier with a fast non AZ type for high gain, use only 1 pair of resistors to set the total gain). Daves µC would be such an example with could have well used this.

[shapirus]

Somewhat related question. While trying to include the AD8000 model within a netlist for ngspice simulation (XU1 N006 N011 N015 N009 N012 N015 AD8000), I get the following error:

Error: no such function 'xu1.x1.'

which seem to point to some inconsistencies between the notation used in the official AD8000 cir model and ngspice?

Most likely it means that the symbol's pin ordering doesn't match the model's one. You need to check both and reassign them as necessary in the symbol properties.

[TimFox]

If the two amplifiers in cascade are identical, and the first amplifier has a voltage gain of 10 V/V, then the total noise referred to the input is the noise of the first stage plus (1/10) of the noise of the second stage, but that sum must be done in quadrature (noise powers add directly).
Therefore, the total noise voltage is
N_tot² = N₁² + (N₂ / 10)²
where
N₁ = N₂
so
N_tot = N₁ x (1 + 0.1²)^1/2 =  N₁ x (1.005)
which is a negligible extra noise.
Even with a gain of only x2 in the first stage, the extra noise is a factor of (1 + 0.5²)^1/2 = 1.12

[elki]

Indeed; your calculations make perfect sense.

[elki]

Thanks again to all for the very useful feedback.