Noise and distortion
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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 (jorgenam@ifi.uio.no) 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 (jorgenam@ifi.uio.no) 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 (jorgenam@ifi.uio.no) 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 1 π= 2π π£2 1 = 2π Spring 2013 2π 0 ππ΄2 sin2 π₯ ππ₯ π 2π 0 ππ΄2 sin2 π₯ ππ₯ Noise and distortion Mean square π value, RMS is π΄ 2 ππ΄2 = 2 8 8 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen (jorgenam@ifi.uio.no) White noise White refers to the spectrum, constant PSD ππ π = constant Resistors exhibit white noise only (ideally). Random thermal motion of electrons (thermal noise) ππ 2 π = 4πππ ⇔ πΌπ 2 = 1 kΩ resistor ≈ 4 Spring 2013 4ππ π nV @ RT (useful to remember) Hz 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 (jorgenam@ifi.uio.no) 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. ∞ 0 1 1 + π2πππ πΆ 1st order lowpass filter magnitude response 2 4πππ ππ = Resistor noise ππ πΆ Important! 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 (jorgenam@ifi.uio.no) 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. π 2 For 1st order filtered noise: ππ = Spring 2013 Noise and distortion π 1 2 2ππ πΆ = 1 4π πΆ 13 13 / 45 Adding noise sources If the noise sources are uncorrelated (common assumption): 2 = π2 + π2 πππ π1 π2 Generally: 2 = π 2 + π 2 + 2πΆπ π πππ π1 π2 π1 π2 πΆ is the correlation coefficient. Spring 2013 Noise and distortion 14 14 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen (jorgenam@ifi.uio.no) Signal to noise ratio SNR ≡ 10 log10 signal power dB noise power Example: Best case signal swing, ππ΄ = ππ·π· , 2 noise is ππ . πΆ 2 πΆππ·π· SNR = 8ππ If ππ·π· is reduced, πΆ 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 ππ still the same, . πΆ Spring 2013 Noise and distortion 16 16 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen (jorgenam@ifi.uio.no) 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. ππ2 π = Spring 2013 constant π 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 (jorgenam@ifi.uio.no) MOSFET noise White noise (channel resistance) Triode: πΌπ2 π = 4ππ πππ γ is process dependent, 2/3 for long-channel Active: πΌπ2 π = 4πππΎππ or ππ2 π = 4πππΎ ππ Flicker noise (different models are used, we use the one from the textbook) ππ2 π = Spring 2013 πΎ ππΏπΆππ₯ π K is process dependent Noise and distortion 19 19 / 45 MOSFET noise • Total MOSFET noise is white noise + flicker noise • Higher ππ 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 (jorgenam@ifi.uio.no) 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, π£ππ . π£ππ π£π π‘ = 4 × π£π π‘ + π£ππ π‘ π£ππ = , π΄0 = 4 π΄0 Amplifier noise ×4 π£π π‘ = sin π0 π‘ 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 (jorgenam@ifi.uio.no) Noise figure (NF) A “figure of merit” for how much noise the amplifier adds, compared to the source. NF π = 10 log10 2 4πππ π + π£ππ π 4πππ π Source noise Spring 2013 Noise and distortion Input referred amplifier noise 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 (jorgenam@ifi.uio.no) Amplifier system example Resistive feedback and noiseless opamp 2 ππ π 2 π 1 2 2 2 = − , πππ = ππ1 + ππ2 ππ π 1 π 2 π 2 π 1 ππ ππ Noiseless Spring 2013 Noise and distortion 25 25 / 45 Amplifier system example 2 πππ1 2 πππ2 2 πΌπ1 π = π = 2 πΌπ+ π π + π 22 + 2 πΌππ 2 ππ2 π + 2 πΌπ− π + ππ2 π π π π 1 + π2πππ π πΆπ 2 π π π 1−1 1+ 1 + π2πππ π πΆπ 2 2 π = π2 πππ ππ1 π 2 + πππ2 (π) Spring 2013 Noise and distortion 26 26 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen (jorgenam@ifi.uio.no) Differential pair example Input stage → most significant noise Several noise sources, we want the total input referred noise, 2 πππ π , assuming device symmetry. Spring 2013 Noise and distortion 27 27 / 45 Differential pair example • Ignore ππ5 , just modulates the bias current • ππ1 and ππ2 are already at the input • Find how ππ3 and ππ4 influence the output (ππ3 π π ) and input refer, ππ = Spring 2013 ππ3 2 ππ1 ππ3 2 2 2 πππ π = 2ππ1 π + 2ππ3 π × ππ1 π½3 2 2 2π½πΌπ· → = 2ππ1 π + 2ππ3 π × π½1 Noise and distortion 2 28 28 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen (jorgenam@ifi.uio.no) Differential pair example Contribution from white noise, 8πππΎ 1 ππ3 + 8πππΎ 2 ππ1 ππ1 • Maximize ππ1 (small overdrive) • Minimize ππ3 (large overdrive) Contribution from flicker noise, 2 πΎ1 ππ πΎ3 πΏ1 + πΆππ₯ π π1 πΏ1 ππ π1 πΏ23 Spring 2013 Noise and distortion 4πππΎ ππ πΎ ππΏπΆππ₯ π • Big devices helps • Especially increased π1 and πΏ3 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 (jorgenam@ifi.uio.no) Distortion Amplification and nonlinearity 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 (jorgenam@ifi.uio.no) Harmonic distortion Using Taylor series allows us to study distortion independent of the specific shape of the nonlinearity (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 (jorgenam@ifi.uio.no) Harmonic distortion Using Taylor expansion we write the output of the amplifier as: π£π π‘ = π0 + πΌ1 π£π π‘ + πΌ2 π£π2 π‘ + πΌ3 π£π3 π‘ + β― Output DC level (Not important) Ideal gain (This is the signal we want) Distortion (harmonics) In fully differential circuits, the even order terms, πΌ2 , πΌ4 , …, cancels out. Spring 2013 Noise and distortion 35 35 / 45 Harmonic distortion The first terms are the most significant π£π π‘ ≈ πΌ1 π£π π‘ + πΌ2 π£π2 π‘ + πΌ3 π£π3 (π‘) In fully differential circuits we approximate the output as π£π π‘ ≈ πΌ1 π£π π‘ + πΌ3 π£π3 (π‘) To analyze the linearity we assume a single tone input: π£π π‘ = π΄ cos ππ‘ Spring 2013 Noise and distortion 36 36 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen (jorgenam@ifi.uio.no) Harmonic distortion From before, π£π π‘ = π΄ cos ππ‘ π£π π‘ ≈ πΌ1 π£π π‘ + πΌ2 π£π2 π‘ + πΌ3 π£π3 π‘ 1 + cos 2π 3 cos π + cos 3π , cos 3 π = 2 4 πΌ2 π΄2 π£π π‘ ≈ πΌ1 π΄ cos ππ‘ + 1 + cos 2ππ‘ 2 πΌ3 π΄3 + 3 cos ππ‘ + cos 3ππ‘ 4 cos2 π = Spring 2013 Noise and distortion 37 37 / 45 Harmonic distortion π£π π‘ ≡ π»π·1 cos ππ‘ + π»π·2 cos 2ππ‘ + π»π·3 cos 3ππ‘ 3 π»π·1 = πΌ1 π΄ + πΌ3 π΄3 ≈ πΌ1 π΄ 4 πΌ2 2 π»π·2 = π΄ 2 πΌ3 3 π»π·3 = π΄ 4 Spring 2013 Noise and distortion 38 38 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen (jorgenam@ifi.uio.no) Harmonic distortion Spring 2013 Noise and distortion 39 39 / 45 Total harmonic distortion As with noise, the ratio between the distortion and the signal is what we are interested in. Total harmonic distortion (sum of all harmonics relative to the fundamental tone): 2 2 2 π»π·2 + π»π·3 + π»π·4 THD = 10 log10 2 π»π·1 Spring 2013 Noise and distortion 40 40 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen (jorgenam@ifi.uio.no) Signal to noise and distortion (SNDR) Spring 2013 Noise and distortion 41 41 / 45 Signal to noise and distortion (SNDR) Spring 2013 Noise and distortion 42 42 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen (jorgenam@ifi.uio.no) Third-order intercept point (IP3) Using two input tones rather than one (same amplitude different frequencies) π£ππ π‘ = π΄ cos π1 π‘ + π΄ cos π2 π‘ Gives rise to two new distortion components close to the input frequencies π1 − Δπ and π2 + Δπ where Δπ ≡ π2 − π1 This distortion increases as π΄3 . We use this to find the intercept point, and infer the third order distortion component. Spring 2013 Noise and distortion 43 43 / 45 Third-order intercept point (IP3) Spring 2013 Noise and distortion 44 44 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen (jorgenam@ifi.uio.no) Spurious free dynamic range (SFDR) Ratio between the input signal power and any “spurs” in the spectrum. Could be from harmonics, or feed through from clocks, etc. Spring 2013 Noise and distortion 45 45 / 45 INF4420 Spring 2013 Noise and distortion Jørgen Andreas Michaelsen (jorgenam@ifi.uio.no)
