What is the output voltage range, i.e., does it swing ± around ground, or is it unipolar? What are the maximum voltages?

my current design:

x1 input: 0~0.125 output: 0~0.125
x10 input: 0~0.125 output: 0~1.25

it's going to be unipolar from 0 ~ +v

Is that enough information?

 

Also, a 1 Meg resistor from output to inverting input would prevent the gain from being open loop if the switch if break before make.

Question: What about using a capacitor to ground instead? It will smooth out the switch bounce, so I was thinking it could also provide the voltage level for several nanoseconds.

 

Question: What about using a capacitor to ground instead? It will smooth out the switch bounce, so I was thinking it could also provide the voltage level for several nanoseconds.

These is a very good chance that the circuit will go into oscillation/unstable state.

 

Question: What about using a capacitor to ground instead? It will smooth out the switch bounce, so I was thinking it could also provide the voltage level for several nanoseconds.

A capacitor to ground would generate peaking and possible circuit instability as bug13 noted.

But that brings up an alternate approach. Instead of a resistor between the minus input and output, add a small capacitor. You may want to limit the frequency response of the circuit anyway to minimize noise. For example the worst-case bias current for a run-of-the-mill LM324 op amp is 100nA. Assume that the worst-case open circuit is 1μs (likely maximum for most solid-state switches) and assume a feedback capacitor is 10pF. The voltage drift during this switch time would then be (100nA * 1μs) / 10pF = 10mV, a very small glitch.

Of course the capacitor can be made larger, for an even smaller glitch, depending upon the maximum frequency response you need.

 

So I just one or two switch, the mux I found are usually 8 channels, can I do that with transistor or something?

The gain I'm interested in are unity gain and x10

For gains of 1 and 10 you only need one switch (from the output to the minus input for the gain of 1). The connection from the junction of the two resistors to the minus input for the gain of 10 can be permanent.

You could use one switch of the four in a CD4016 or CD4066 quad bilaterial switch.

 

You could use one switch of the four in a CD4016 or CD4066 quad bilaterial switch.

I haven't use any of those, so if I understand the datasheet correctly, they can be operated under 5V, and a 5V control signal?

 

I haven't use any of those, so if I understand the datasheet correctly, they can be operated under 5V, and a 5V control signal?

With a 5V supply they can carry a signal from 0 to 5V and are controlled by a 5V signal. The signal can be equal to but can't exceed either the positive or negative (ground) supply voltage.