Input Noise Current Voltage in en 1 of

Input Noise: Current, Voltage (in, en) 1 of 78

Op Amp Noise Model (IN+ and IN- are not correlated) OPA 277 Data VN IN+ IN- Tina Simplified Model VN IN 2 of 78

Understanding The Spectrum: Total Noise Equation (Current or Voltage) en. T = √[(en 1/f)2 + (en. BB)2] where: en. T = Total rms Voltage Noise in volts rms en 1/f = 1/f voltage noise in volts rms en. BB = Broadband voltage noise in volts rms 3 of 78

Real Filter Correction vs Brickwall Filter where: f. P = roll-off frequency of pole or poles f. BF = equivalent brickwall filter frequency 4 of 78

AC Noise Bandwidth Ratios for nth Order Low-Pass Filters BWn = (f. H)(Kn) Effective Noise Bandwidth Real Filter Correction vs Brickwall Filter Number of Poles in Filter Kn AC Noise Bandwidth Ratio 1 1. 57 2 1. 22 3 1. 16 4 1. 13 5 1. 12 5 of 78

Broadband Noise Equation e. BB BWn = (f. H)(Kn) where: BWn = noise bandwidth for a given system f. H = upper frequency of frequency range of operation Kn = “Brickwall” filter multiplier to include the “skirt” effects of a low pass filter en. BB = (e. BB)(√[BWn]) where: en. BB = Broadband voltage noise in volts rms e. BB = Broadband voltage noise density ; usually in n. V/√Hz BWn = Noise bandwidth for a given system 6 of 78

1/f Noise Equation e 1/f@1 Hz = (e 1/f@f)(√[f]) where: e 1/f@1 Hz = normalized noise at 1 Hz (usually in n. V) e 1/f@f = voltage noise density at f ; (usually in n. V/√Hz) f = a frequency in the 1/f region where noise voltage density is known en 1/f = (e 1/f@1 Hz)(√[ln(f. H/f. L)]) where: en 1/f = 1/f voltage noise in volts rms over frequency range of operation e 1/f@1 Hz = voltage noise density at 1 Hz; (usually in n. V) f. H = upper frequency of frequency range of operation (Use BWn as an approximation for f. H) f. L = lower frequency of frequency range of operation 7 of 78

Example Noise Calculation Given: OPA 627 Noise Gain of 101 Find (RTI, RTO): Voltage Noise Current Noise Resistor Noise 8 of 78

Voltage Noise Spectrum and Noise Bandwidth 50 n. V/rt-Hz 5 n. V/rt-Hz Unity Gain Bandwidth = 16 MHz Closed Loop Bandwidth = 16 MHz / 101 = 158 k. Hz 9 of 78

Example Voltage Noise Calculation: Broadband Voltage Noise Component: BWn ≈ (f. H)(Kn) (note Kn = 1. 57 for single pole) BWn ≈ (158 k. Hz)(1. 57) =248 k. Hz en. BB = (e. BB)(√BWn) en. BB = (5 n. V/√Hz)(√ 248 k. Hz) = 2490 n. V rms 1/f Voltage Noise Component: e 1/f@1 Hz = (e 1/f@f)(√f) e 1/f@1 Hz = (50 n. V/√Hz)(√ 1 Hz) = 50 n. V en 1/f = (e 1/f@1 Hz)(√[ln(f. H/f. L)]) Use f. H = BWn en 1/f = (50 n. V)(√[ln(248 k. Hz/1 Hz)]) = 176 n. V rms Total Voltage Noise (referred to the input of the amplifier): en. T = √[(en 1/f)2 + (en. BB)2] en. T = √[(176 n. V rms)2 + (2490 n. V rms)2] = 2496 n. V rms 10 of 78

Example Current Noise Calculation Note: This example amp doesn’t have 1/f component for current noise. en-in= (in)x(Req) en-out= Gain x (in)x(Req) 11 of 78

Example Current Noise Calculation Broadband Current Noise Component: BWn ≈ (f. H)(Kn) BWn ≈ (158 k. Hz)(1. 57) =248 k. Hz in. BB = (i. BB)(√BWn) in. BB = (2. 5 f. A/√Hz)(√ 248 k. Hz) = 1. 244 p. A rms Req = Rf || R 1 = 100 k || 1 k = 0. 99 k eni = (In)( Req) = (1. 244 p. A)(0. 99 k) = 1. 23 n. V rms neglect Since the Total Voltage noise is envt = 2496 n. V rms the current noise can be neglected. 12 of 78

Resistor Noise – Thermal Noise The mean- square open- circuit voltage (e) across a resistor (R) is: en = √ (4 k. TKRΔf) where: TK is Temperature (ºK) R is Resistance (Ω) f is frequency (Hz) k is Boltzmann’s constant (1. 381 E-23 joule/ºK) en is volts (VRMS) To convert Temperature Kelvin to TK = 273. 15 o. C + TC 13 of 78

Resistor Noise – Thermal Noise en density = √ (4 k. TKR) n. V/rt-Hz Noise Spectral Density vs. Resistance (Ohms) 14 of 78

Example Resistor Noise Calculation enr = √(4 k. TKRΔf) where: R = Req = R 1||Rf Δf = BWn enr = √(4 (1. 38 E-23) (273 + 25) (0. 99 k)(248 k. Hz)) = 2010 n. V rms ( (0. 99 k)( en-in= √(4 k. TRΔf) en-out= Gain x (√(4 k. TRΔf)) f) 15 of 78

Total Noise Calculation Voltage Noise From Op-Amp RTI: env = 2510 n. V rms Current Noise From Op-Amp RTI (as a voltage): eni = 1. 24 n. V rms Resistor Noise RTI: enr = 2020 n. V rms Total Noise RTI: en in = √((2510 n. V)2 + ((1. 2 n. V)2 + ((2010 n. V)2) = 3216 n. V rms Total Noise RTO: en out = en in x gain = (3216 n. V)(101) = 325 u. V rms 16 of 78

Calculating Noise Vpp from Noise Vrms Relation of Peak-to-Peak Value of AC Noise Voltage to rms Value Peak-to-Peak Amplitude Probability of Having a Larger Amplitude 2 X rms 32% 3 X rms 13% 4 X rms 4. 6% 5 X rms 1. 2% 6 X rms * 0. 3% 6. 6 X rms 0. 1% *Common Practice is to use: Peak-to-Peak Amplitude = 6 X rms 17 of 78

Voltage Noise (f = 0. 1 Hz to 10 Hz) Low Frequency Low frequency noise spec and curve: Over specific frequency range: 0. 1 Hz < f < 10 Hz Given as Noise Voltage in pp units Measured After Bandpass Filter: 0. 1 Hz Second−Order High−Pass 10 Hz Fourth−Order Low−Pass 18 of 78