2022-10-05 09:57 Status: # Basic Electrical Noise Theory Plays a vital role in high performance circuits. ## Example: 'Perfect'current source   Noise is not easy to deal with in the time domain. ## RMS $v_{N,RMS}=\sqrt{\frac{1}{T}\int_{0}^{T} v_n^2(t) dt}$ Is an estimate of the standard deviation. Also $\sigma^2 = \frac{1}{T}\int_{0}^{T} v_n^2(t) dt$ is called the "noise-power". ## Noise Addition RMS noise term for multiple sources contains a [cross-correlation](cross-correlation.md) term. For most uncorrelated noise,  Variance of sum of two stochastic variable is equal to the sum of the variance of the two *independent* random variables. (uncorrelated sources). ## Frequency Domain Normally something known - the fourier transform of the square of the noise signal. $v_n^2(f)=F(v_n^2(t))$ Noise power spectral density (actually a voltage/current spectral density). Units: $V^2/Hz$ or $A^2/Hz$ To get the average, we integrate: $v_{N,RMS}^2=\int_0^\infty v_n^2(f) df$  ### White Noise Flat line - const across the mid frequency range. ### Pink Noise 1/f noise - from transistors. ### Finite Bandwidth Rolloff occurs at high frequencies. ## Shaped Noise   The phase of noise never matters - it's the rms value that sums up (use the magnitude of the TF). ## Total Output Referred RMS Noise Formula  Noise is always small signal - can consider it linear. $V_{noise,RMS}^2=\sum_{k=1}^M\int_0^\infty v_{nk}^2(f)|H_k(2\pi if)|^2 df$ [^1] --- # References [^1]: [vr-4602-wk03-sc07-basicnoise](../../Spaces/University/ELEC4602%20–%20Microelectronics%20Design%20and%20Technology/Lectures/W3/vr-4602-wk03-sc07-basicnoise.mp4)