Differential amplifier and random signals

I would like to ask if I can amplify a random signal (picture 1 right hand) with a differential amplifier(picture 1 left hand) and how this will work.I know how the differential amplifier will work with sinusoidal signal but I have no idea with a random signal.Can someone help me?

Example of simulation result when input signals is sinusoidal and when input signals is random

• Try reducing your "random signal" amplitude variation to something much smaller (like your linear "sinusoidal signal" amplitude). For small signals, your amplifier appears linear. – glen_geek Aug 18 '17 at 19:40
• Sinusoidal signals are used in datasheets because they demonstrate the operation of the device, and we all know what they should look like. The use of sinusoidal signals in datasheets does not imply that an amplifier is only capable of handling sinusoidal signals. – Peter Bennett Aug 18 '17 at 19:44
• Also, any signal (random noise included) can be described as a sum of many sine waves all with different frequencies, amplitude and phase. Look up Fourier transformation to learn more. So the response to a random signal can be derived if you know the response to sinusoidal signals and the frequency response of the circuit. – Bimpelrekkie Aug 18 '17 at 21:20
• @Bimpelrekkie: what you wrote is only true for linear systems (i.e. such systems that satisfy $af(x) + bf (y) = f(ax + by)$). First you have to make sure that this is the case here (see also glen_geeks comment). – Curd Aug 19 '17 at 8:26
• Thank you so much glen_geek your comment was so useful!You are right!Also, Peter Bennett this is true you are right! – gr1 Aug 19 '17 at 9:41

Deferentially amplifying a random signal is identical amplifying a sinusoidal one essentially, but with a complication. Output = gain (in1 - in2) as long as the inputs fall within the amplifier's input range. The output will simply be the difference between them, so just as random.

Therein lies the problem you'll face. Specifically, determining the gain you want. It's very hard if the signal is random such as white noise. If the input signals are 1Vp-p, you will not get 2Vp-p with a gain of 2. The amplifier's gain bandwidth product /slew rate complicates the calculation very much. The amplifier ends up amplifying some of the component frequencies, whilst attenuating others. It's a complicated non linear trade off.

Anecdotally, doubling the amplitude of 1Vp-p noise requires a TL082 op amp to have a gain of ~4. I've never seen a gain formula that applies to random signal amplification, and gain is only determined either by simulation or experimentation.

You will find that even with a unity gain, it is likely that a very broadband random signal will come out with a lower peak to peak than it went in with. This is the effect of frequency attenuation due to gain bandwidth product /slew rate limitation. This may matter or not to you, depending on your use of the signal. But if for example you're looking to maximise range on an analogue to digital converter, the gain calculation becomes important.

Here is 0db SNR random noise + sinwave, run through a standard integrator OpAmp circuit with Rfeedback to implement DC gain of 13. Noise bandwidth is 1GHz, sin frequency is 20MHz, OpAmp bode 3dB is 50KHz.