The World Leader in High Performance Signal Processing Solutions Amplifier Noise Principles for the Practical Engineer Matt Duff Applications Engineer – Instrumentation Amplifiers Analog Devices, Inc. copyright 2009 Outline Noise z Extrinsic z Intrinsic Three main sources of intrinsic noise z Resistance z Amplifier Voltage Noise Current Noise z ADC Why so many units? z nV/rt(Hz), µVrms, µVp-p z Unit conversion Noise Math & Shortcuts Tips z Applying gain z Source resistance z Feedback resistance 2 Where does noise come from? -Extrinsic - Intrinsic 3 Extrinsic Noise RFI Switching Noise Noise coupling in from external Power sources Supply + Examples z RFI Coupling – z Power Supply Noise z Ground loops Digital circuitry 50/60 Hz Ground Not focus of this talk Loop Noise 4 Intrinsic Noise Intrinsic z Internal noise from components in signal chain Sensor Resistors Amplifier A/D z Specified on the datasheet z Focus of this talk 5 Main Sources of Intrinsic Noise -Resistor - Amplifier -A/D 6 Resistor noise vn 7 Types of Resistor noise Excess Noise z Depends on type: Carbon composition = bad performance vn Thick film = OK performance Thin film, wirewound = good performance z Increases with applied voltage z 1/f characteristic z Can ignore if using good resistors Intrinsic thermal noise z Independent of type z Independent of voltage applied z White noise characteristic z Need to calculate in design 8 Thermal noise of an ideal resistor bandwidth vn = √4k T R Δf resistance rms noise constant Temperature (in Kelvin) Too Complicated! 9 Resistor noise shortcut 1 kΩ→ 4 nV/√(Hz) Noise scales as square root of resistance 4 kΩ→ (2)(4) nV/√(Hz) = 8 nV/√(Hz) 9 kΩ→(3)(4) nV/√(Hz) = 12 nV/√(Hz) 16 kΩ→(4)(4) nV/√(Hz) = 16 nV/√(Hz) 100 kΩ→(10)(4) nV/√(Hz) = 40 nV/√(Hz) 10 Common Resistor Circuits: Resistor Divider VIN R1 R1 R1 || R2 Theory: VOUT VOUT VOUT R2 R2 VIN 200 kΩ 200 kΩ 100 kΩ √(100) * 4 nV /√(Hz) = Example: 40 nV /√(Hz) 200 kΩ 200 kΩ 11 Common Resistor Circuits – Bridge Theory: Example: 12 Amplifier Noise 13 Amplifier Voltage Noise Units: z nV/√(Hz) z µVrms z µV p-p example from AD8295 datasheet: 14 Amplifier Voltage Noise: Referred to What? Options z Referred to Input (RTI) z Referred to Output (RTO) If not stated, referred to Input Multiply by “noise gain” RTI RTO vx + 10 vx – 9 1 15 Instrumentation Amplifiers are Different Op Amps In Amp z All noise dependent on gain eNI In Amps + eNO z Some noise dependent on gain (eNI) z Some noise independent of gain (eNO) – Total In Amp Noise, referred to input 2 2 z √( eNI + (eNO/G) ) example from AD8221 datasheet: 16 Amplifier Current Noise Units: z fA/√(Hz) z pArms z pA p-p example from AD8295 datasheet: 17 Amplifier Current Noise: Effect depends on resistance Source resistance Feedback network + + ix1 ix1 R R ix1 – – ix2 ix2 18 ADC Noise: Sometimes voltage units provided: But most of the time, signal to noise ratio (SNR) z With distortion: SINAD In emergency use ideal equation z SNR = 6.02 * Bits + 1.76 z Gives better performance than reality 19 ADC Noise – Converting SNR to µVrms Full Scale Voltage in µVrms Conversion Equation: = ADC noise in µVrms SNR 20 10 Key Point: Use RMS value for full scale range! Example: z 2 V ADC input range z 69 dB SNR 20 Why so many units? - µVrms, µVp-p, nV/√Hz - RMS, peak to peak, spectral density - converting between units 21 Peak to Peak and RMS noise Peak to peak noise z Distance from min and max points on waveform z Depends on only two points Less accurate z Variable z Measure longer -> bigger result Easy to compute rms z Max - Min RMS noise z One standard deviation (mean is zero) peak to z Depends on all points peak More accurate z Repeatable z Measure longer -> more accurate result Lengthy to compute 2 2 2 x1 + x2 +...+ xn n 22 RMS and Peak to Peak: Dependent on Bandwidth AD8222 Noise (G=100) When measuring: z Circuit bandwidth Bandwidth = 10 Hz z Measurement instrument bandwidth Bandwidth = 100 Hz When specifying z Bandwidth must be noted Bandwidth = 1000 Hz Voltage (0.5 µV/DIV) (0.5 Voltage Time (1 s/DIV) 23 Spectral Noise Density 1k Frequency Domain z Noise density at specific AD8295 frequency Units z nV/√Hz 100 z fA/√Hz NOISE (nV/ Hz) Includes many, many points z Datasheet figure has lots of averaging 10 1 10 100 1k 10k 100k FREQUENCY (Hz) 07343-067 24 Spectral Noise Density – 1/f corner 1k 1/f noise z Noise density increases at AD8295 low frequencies 1/f noise White noise z Noise density flat at high 100 frequencies NOISE (nV/ Hz) white noise 1/f corner z Where 1/f noise and white noise trendlines intersect 10 1 10 100 1k 10k 100k FREQUENCY (Hz) 07343-067 noise corner 25 How to convert Conversion process z nV/√(Hz) → µVrms z µVrms → µVp-p 26 µ nV/√(Hz) -> Vrms: theory 1k Theoretical Equation f HIGH 2 Noise = (SD ) df 100 RMS ∫ f fLOW NOISE (nV/ Hz) Where z SDf: spectral density at frequency f 10 1 10 100 1k 10k 100k z f : low frequency cutoff FREQUENCY (Hz) LOW 07343-067 z fHIGH: high frequency cutoff Too Complicated! 27 µ nV/√(Hz) -> Vrms shortcut1k Assumption z Mostly white noise 1/f corner << bandwidth Equation 100 z RMS Noise = NOISE (nV/ Hz) spectral density * √(bandwidth) spectral density 10 1 10 100 1k 10k 100k FREQUENCY (Hz) 07343-067 bandwidth 28 Equivalent Noise Bandwidth 1k Equivalent Noise bandwidth for Butterworth filters z 1 pole: 1.57 z 2 pole: 1.11 z 3 pole: 1.05 100 NOISE (nV/ Hz) Example: z Given: 40 nV/rt(Hz) 10 10 kHz 1 pole filter 1 10 100 1k 10k 100k FREQUENCY (Hz) z Answer: 07343-067 40 nV/rt(Hz) * sqrt(10 kHz * 1.57) ≈ 5000 nVrms = 5 µVrms 29 nV/√(Hz) -> µVrms Not mostly white noise? z 1/f corner near bandwidth Options 50 Hz z Use theoretical formula? z Use amplifier with low 1/f corner z Compare uVp-p numbers 0.1 to 10 Hz z Autozero/Chopper 200 Hz 30 µVrms -> µVp-p To get peak to peak noise z In theory: peak to peak noise infinite z In practice: multiply rms by 6 Multiplier of ‘6’ is rule of thumb: 99.73% of points Examples z 1 µVrms * 6 ≈ 6 µVp-p z 1 µVrms * 6.6 ≈ 6.6 µVp-p 6 standard deviations covers 99.7% 6.6 standard deviations covers 99.9% graph created by Jeremy Kemp 31 Math and Shortcuts 32 Noise Math Addition Multiplication z Noise adds as sum of z Gain and attenuation work squares just like normal signals Example Example 100k Ω + 40 nV/√Hz ideal √(40^2+40^2) = in amp 57 nV/rt(Hz) 100k Ω G=1 – 40 nV/√Hz 33 Noise shortcuts 1 k Ω resistor -> 4 nV/√Hz When adding noise sources, larger sources dominate z Sum of squares addition z Ignore signals < 1/5th largest signal If first stage gain is large z Later stages typically have little effect 34 Tips 35 Noise Tip #1: Apply Gain Early Noise adds as sum of squares 36 Noise Tip #2: Watch out for source impedance Source Resistance adds noise Current noise calculation Sensor + R SOURCE – 37 Source impedance example Sensor Given the following sensor: 9 kΩ Which op amp is better? Sensor 9 kΩ Noise contributors (RTI): Sensor noise = 4 x √9 = 12 Amp Voltage noise = 1.1 Amp Current noise = 2.3 x 9 = 20.7 Total Noise = √(122+1.12 + 20.72) = 24 nV/rt(Hz) 38 Noise Tip #3: Watch out for feedback resistors Rf acts like voltage source at output Rg acts likes inverting configuration voltage source What noise dominates? z Rf dominates Noninverting config: G<2 Inverting configuration: G > -1 z Rf and Rg noise equal Noninverting config: G=2 Inverting config: G = -1 z Rg dominates Noninverting config: G>2 Inverting config: G<-1 Watch out for current noise 39 Summary Noise z Extrinsic z Intrinsic Three main sources of intrinsic noise z Resistance z Amplifier Voltage Noise Current Noise z ADC Why so many units? z RMS noise, peak to peak noise, spectral density z How to convert between units Noise Math & Shortcuts Tips z Gain Early z Source Impedance z Feedback resistors 40 Where to learn more Application Notes z AN-940: Low Noise Amplifier Selection Guide for Optimal Noise Performance z AN-358: Noise and Operational Amplifier Circuits Analogue Dialogue z Ask The Applications Engineer -7: What should I know about op-amp noise? z Ask The Applications Engineer -8: What is “noise gain”? Webinar z Noise Optimization in Signal Conditioning Circuits (Three part series) Tutorials z MT-047: Op Amp Noise z MT-048:Op Amp Noise Relationships: 1/f Noise, RMS Noise, z and Equivalent Noise Bandwidth z MT-049: Op Amp Total Output Noise Calculations for Single-Pole System z MT-050: Op Amp Total Output Noise Calculations for Second-Order System z MT-065: In-Amp Noise 41 The World Leader in High Performance Signal Processing Solutions Questions? Contact Info: Matt Duff (781) 937-2123.