INF4420 Noise and Distortion Jørgen Andreas Michaelsen Spring 2013 1 / 45 Outline • Noise basics • Component and system noise • Distortion Spring 2013 Noise and distortion 2 2 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen ([email protected]) Introduction We have already considered one type of noise in the layout lecture: Interference—Other circuits or other parts of the circuit interfering with the signal. E.g. digital switching coupling through to an analog signal through the substrate or capacitive coupling between metal lines. We mitigate this interference with layout techniques. True noise is random and zero mean! Spring 2013 Noise and distortion 3 3 / 45 Introduction TV Static Stock Video by REC Room Spring 2013 Noise and distortion 4 4 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen ([email protected]) Introduction We do not know the absolute value, but … • We know the average value • We know the statistical and spectral properties of the noise Spring 2013 Noise and distortion 5 5 / 45 Introduction • Noise (power) is always compared to signal (power) • How clearly can we distinguish the signal from the noise (SNR) Spring 2013 Noise and distortion 6 6 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen ([email protected]) Introduction • Why is noise important? • Signal headroom is reduced when the supply voltage is reduced. • Supply voltage is reduced because of scaling (beneficial for digital, less power consumption) • Noise is constant. • Noise limits performance of our circuits (along with mismatch, etc.) Spring 2013 Noise and distortion 7 7 / 45 Signal power • Sine wave driving a resistor dissipates power • The average voltage of the sine wave is zero • The average power dissipated is not zero 2휋 2 2 1 푉 sin 푥 Mean square 퐴 푉 value, RMS is 퐴 푃 = 푑푥 2 2휋 0 푅 1 2휋 푉2 2 2 2 퐴 푣 = 푉퐴 sin 푥 푑푥 = 2휋 0 2 Spring 2013 Noise and distortion 8 8 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen ([email protected]) White noise White refers to the spectrum, constant PSD 푉푛 푓 = constant Resistors exhibit white noise only (ideally). Random thermal motion of electrons (thermal noise) 4푘푇 푉2 푓 = 4푘푇푅 ⇔ 퐼2 = 푅 푅 푅 nV 1 kΩ resistor ≈ 4 @ RT (useful to remember) Hz Spring 2013 Noise and distortion 9 9 / 45 Filtering noise • In most circuits we have capacitors (noise free) • There is always some parasitic capacitance present. • White noise is filtered: the constant PSD is shaped. Spring 2013 Noise and distortion 10 10 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen ([email protected]) Filtering noise Spring 2013 Noise and distortion 11 11 / 45 Total noise We find the total noise by integrating from 0 to ∞. This is a finite value because of the filtering. ∞ 1 2 푘푇 4푘푇푅 푑푓 = 0 1 + 푗2휋푓푅퐶 퐶 Resistor 1st order lowpass noise filter magnitude Important! response Total noise is independent of R and defined by C! Spring 2013 Noise and distortion 12 12 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen ([email protected]) Noise bandwidth Find a frequency, such that when we integrate the ideal constant PSD up to this frequency, the total noise is identical. This is the equivalent noise BW. 휋 휋 1 1 For 1st order filtered noise: 푓 = = 2 푐 2 2휋푅퐶 4푅퐶 Spring 2013 Noise and distortion 13 13 / 45 Adding noise sources If the noise sources are uncorrelated (common assumption): 2 2 2 푉푛표 = 푉푛1 + 푉푛2 Generally: 2 2 2 푉푛표 = 푉푛1 + 푉푛2 + 2퐶푉푛1푉푛2 퐶 is the correlation coefficient. Spring 2013 Noise and distortion 14 14 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen ([email protected]) Signal to noise ratio signal power SNR ≡ 10 log dB 10 noise power Example: 푉 푘푇 Best case signal swing, 푉 = 퐷퐷, noise is . 퐴 2 퐶 퐶푉2 SNR = 퐷퐷 8푘푇 If 푉퐷퐷 is reduced, 퐶 must increase: More power (-) Spring 2013 Noise and distortion 15 15 / 45 Sampled noise When sampling signals, the sampled spectrum only represents frequencies up to the Nyquist frequency (half the sampling frequency). Frequencies beyond are aliased down to this range. (More on this in a later lecture). The total noise is 푘푇 still the same, . 퐶 Spring 2013 Noise and distortion 16 16 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen ([email protected]) 1/f noise So far, we have considered white noise (with filtering). Transistors exhibit significant flicker (1/f) noise. The PSD is proportional to the inverse of the frequency. constant 푉2 푓 = 푛 푓 Spring 2013 Noise and distortion 17 17 / 45 Components • Resistors exhibit white noise where voltage noise is proportional to resistance. • Diodes exhibit white noise (shot noise) where noise current is proportional to diode current. Spring 2013 Noise and distortion 18 18 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen ([email protected]) MOSFET noise White noise (channel resistance) 2 4푘푇 Triode: 퐼푑 푓 = 푟푑푠 γ is process dependent, 2/3 for long-channel 2 2 4푘푇훾 Active: 퐼푑 푓 = 4푘푇훾푔푚 or 푉푔 푓 = 푔푚 Flicker noise (different models are used, we use the one from the textbook) 2 퐾 K is process dependent 푉푔 푓 = 푊퐿퐶표푥 푓 Spring 2013 Noise and distortion 19 19 / 45 MOSFET noise • Total MOSFET noise is white noise + flicker noise • Higher 푔푚 attenuates the white noise contribution • Larger devices (gate area) reduces the flicker noise • We can reduce flicker noise using circuit techniques. E.g. in sampled analog systems we can sample the noise and subtract (correlated double sampling). Spring 2013 Noise and distortion 20 20 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen ([email protected]) Input referred noise Amplifier not only amplifies the signal, but adds noise. Even though the amplifier noise is not physically present at the input, we can calculate an equivalent input noise, 푣푖푛. 푣표푛 푣표 푡 = 4 × 푣푖 푡 + 푣표푛 푡 푣푖푛 = , 퐴0 = 4 퐴0 Amplifier noise × 4 푣푖 푡 = sin 휔0푡 Spring 2013 Noise and distortion 21 21 / 45 Input referred noise Spring 2013 Noise and distortion 22 22 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen ([email protected]) Noise figure (NF) A “figure of merit” for how much noise the amplifier adds, compared to the source. 2 4푘푇푅푠 + 푣푎푖 푓 NF 푓 = 10 log10 4푘푇푅푠 Source noise Input referred amplifier noise Spring 2013 Noise and distortion 23 23 / 45 Input referred noise The amplifier may be a cascade of gain stages. High gain at the input stage attenuates noise contributed by later stages (important). Spring 2013 Noise and distortion 24 24 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen ([email protected]) Amplifier system example Resistive feedback and noiseless opamp 2 푉표 푅2 2 2 푅1 2 = − , 푉푛푖 = 푉푛1 + 푉푛2 푉푖 푅1 푅2 푅2 푅1 푉푖 푉표 Noiseless Spring 2013 Noise and distortion 25 25 / 45 Amplifier system example 푅 2 2 2 2 2 푓 푉푛표1 푓 = 퐼푛1 푓 + 퐼푛푓 푓 + 퐼푛− 푓 1 + 푗2휋푓푅푓퐶푓 2 푅 푅−1 2 2 2 2 2 푓 1 푉푛표2 푓 = 퐼푛+ 푓 푅2 + 푉푛2 푓 + 푉푛 푓 1 + 1 + 푗2휋푓푅푓퐶푓 2 2 푉푛표 푓 = 푉푛표1 푓 2 + 푉푛표2(푓) Spring 2013 Noise and distortion 26 26 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen ([email protected]) Differential pair example Input stage → most significant noise Several noise sources, we want the total input referred noise, 2 푉푛푖 푓 , assuming device symmetry. Spring 2013 Noise and distortion 27 27 / 45 Differential pair example • Ignore 푉푛5, just modulates the bias current • 푉푛1 and 푉푛2 are already at the input • Find how 푉푛3 and 푉푛4 influence the output 2 푔푚3 (푔푚3푅표) and input refer, 푔푚1 2 2 2 2 푔푚3 푉푛푖 푓 = 2푉푛1 푓 + 2푉푛3 푓 × 푔푚1 2 2 훽3 푔푚 = 2훽퐼퐷 → = 2푉푛1 푓 + 2푉푛3 푓 × 훽1 Spring 2013 Noise and distortion 28 28 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen ([email protected]) Differential pair example 4푘푇훾 Contribution from white noise, 푔푚 1 푔푚3 • Maximize 푔 (small overdrive) 8푘푇훾 + 8푘푇훾 푚1 2 • Minimize 푔 (large overdrive) 푔푚1 푔푚1 푚3 퐾 Contribution from flicker noise, 푊퐿퐶표푥푓 2 퐾1 휇푛 퐾3퐿1 • Big devices helps + 2 • Especially increased 푊1 and 퐿3 퐶표푥푓 푊1퐿1 휇푝 푊1퐿3 Spring 2013 Noise and distortion 29 29 / 45 Distortion • So far we have discussed noise, which is an important performance constraint • The degree of non-linearity is another important performance limitation • SNR improves with “stronger” input signals (because the noise remains constant) • However, larger input amplitude adds more non-linearity. • The sum of noise and distortion is important (SNDR). Increasing the amplitude improves SNDR up to some point where the non-linearity becomes significant. Beyond this point the SNDR deteriorates. Spring 2013 Noise and distortion 30 30 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen ([email protected]) Distortion Amplification and non- linearity depends on the biasing point. • Soft non-linearity (compression and expansion) • Hard non-linearity (clipping) Spring 2013 Noise and distortion 31 31 / 45 Common source amplifier example Spring 2013 Noise and distortion 32 32 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen ([email protected]) Harmonic distortion Using Taylor series allows us to study distortion independent of the specific shape of the non- linearity (e.g. common source). Generic expression for total harmonic distortion (THD). The non-linearity adds harmonics in the frequency domain. Spring 2013 Noise and distortion 33 33 / 45 Harmonic distortion Spring 2013 Noise and distortion 34 34 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen ([email protected]) Harmonic distortion Using Taylor expansion we write the output of the amplifier as: 2 3 푣표 푡 = 푎 0 + 훼1푣푖 푡 + 훼2푣푖 푡 + 훼3푣푖 푡 + ⋯ Output DC Ideal gain Distortion level (This is the signal we (harmonics) want) (Not important) In fully differential circuits, the even order terms, 훼2, 훼4, …, cancels out.