# What would be the peak voltage value of two combined signals (one noise and one sinusoidal signal)?

As I learned before, the peak voltage value of two combined sinusoidal signals is the sum of the two amplitudes, for example, $0.6\sin(ax) + 0.8 \cos(bx)$ can be $+1.4$V or $-1.4$V. Would it be the case for the noise?

For example, if now the output noise signal is $1$Vpp and my desired signal is $1$V at $1$kHz. Would the peak value of output become $+2$V or $-2$V?

One more question: If the answer of the above question is yes, would an amplifier which limits its output to the range $\pm1.5$V saturate at that time?

• Simple answers are yes, yes, yes. Add noise maximums. Peak value is +2 and -2 at various times so 4V p-p. A 1.5 V max rail amp will saturate. – Russell McMahon Oct 14 '14 at 5:47
• Thank you!. If the amplifier would be saturated, does that mean my 1kHz signal would distort at that time? – billyzhao Oct 14 '14 at 7:03
• Yes. When the summed signal clips, then all components can be considered to have clipped as well, even if none of them actually are by themselves. You can see/hear this by playing 100Hz and 1kHz into a mixer/amplifier and cranking the 100Hz until the output clips. Listen to the 1kHz; what happens to it? – AaronD Oct 14 '14 at 18:17
• @AaronD: Thank you! But why would all components be clipped? Any reference or recommended book? – billyzhao Oct 15 '14 at 2:50
• When the output clips, it basically flatlines at its max or min value. It can't do anything else until the sum of all inputs is inside the limits. As long as the total is outside, nothing else gets through. – AaronD Oct 15 '14 at 2:56

## 1 Answer

Most of the noise that occurs in electronic instruments and in environment is additive noise, so yes, if a noise is of same amplitude as signal, both will add to generate higher voltage signal and yes it can saturate the output level. Usually, at any instant of time the value of output signal is equal to signal value plus noise value at that instant of time. But with the use of current op-amps which are compensated with higher input impedance, lower output impedance, rail to rail, higher PSRR, CMRR etc. u can get lower noise generated within amplification device. The other noise u may find is phase noise where phase of signal fluctuates to create jitter. U can go through noises from here http://en.wikipedia.org/wiki/Noise_%28signal_processing%29

• You ought to be clearer in saying that the noise you are talking about is peak-to-peak - RMS noises are not additive. – Andy aka Oct 14 '14 at 7:20